TSTP Solution File: ITP302_10 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP302_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 : 300s
% DateTime : Sun May 5 07:14:10 EDT 2024
% Result : Satisfiable 42.07s 6.42s
% Output : FiniteModel 219.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : ITP302_10 : TPTP v8.2.0. Released v8.2.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 19:04:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (13218)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (13222)WARNING: value z3 for option sas not known
% 0.16/0.39 % (13223)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (13221)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (13220)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (13226)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.39 % (13224)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.39 % (13222)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.39 % (13225)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 41.50/6.32 Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 41.50/6.32 Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,2,max,max,max]
% 41.50/6.32 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 41.50/6.37 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1]
% 42.07/6.42 Finite Model Found!
% 42.07/6.42 % SZS status Satisfiable for theBenchmark
% 42.07/6.43 13223 Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.07/6.43 % (13223)------------------------------
% 42.07/6.43 % (13223)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 42.07/6.43 % (13223)Termination reason: Unknown
% 42.07/6.43 % (13223)Termination phase: Finite model building constraint generation
% 42.07/6.43
% 42.07/6.43 % (13223)Memory used [KB]: 95859
% 42.07/6.43 % (13223)Time elapsed: 6.033 s
% 42.07/6.43 % (13223)Instructions burned: 14599 (million)
% 42.07/6.43 % (13223)------------------------------
% 42.07/6.43 % (13223)------------------------------
% 42.07/6.43 Version : Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
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% 42.07/6.46 % (13251)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 73.59/10.92 Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 73.59/10.92 Detected maximum model sizes of [1,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,1,max,max,max,max,max,1,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,1,max,max,max,max,1,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,1,2,max,max,max,max,max,1,max,max,max,max,max,max,max,max,max,max,1,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,1,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,1,max,max,1,1,max,max,max,max,max]
% 73.59/10.92 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 73.87/10.97 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 74.35/11.01 Finite Model Found!
% 74.35/11.01 % SZS status Satisfiable for theBenchmark
% 74.35/11.01 13251 Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 74.35/11.01 % (13251)------------------------------
% 74.35/11.01 % (13251)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 74.35/11.01 % (13251)Termination reason: Unknown
% 74.35/11.01 % (13251)Termination phase: Finite model building constraint generation
% 74.35/11.01
% 74.35/11.01 % (13251)Memory used [KB]: 68980
% 74.35/11.01 % (13251)Time elapsed: 4.570 s
% 74.35/11.01 % (13251)Instructions burned: 10636 (million)
% 74.35/11.01 % (13251)------------------------------
% 74.35/11.01 % (13251)------------------------------
% 74.35/11.01 Version : Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 74.35/11.01 ???
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% 74.35/11.04 % (13264)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 101.32/14.89 TRYING [1]
% 106.16/15.56 TRYING [2]
% 196.61/28.48 Finite Model Found!
% 196.61/28.48 % SZS status Satisfiable for theBenchmark
% 197.23/28.61 13220 Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 197.23/28.61 % (13220)------------------------------
% 197.23/28.61 % (13220)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 197.23/28.61 % (13220)Termination reason: Unknown
% 197.23/28.61 % (13220)Termination phase: Finite model building constraint generation
% 197.23/28.61
% 197.23/28.61 % (13220)Memory used [KB]: 254766
% 197.23/28.61 % (13220)Time elapsed: 28.209 s
% 197.23/28.61 % (13220)Instructions burned: 63765 (million)
% 197.23/28.61 % (13220)------------------------------
% 197.23/28.61 % (13220)------------------------------
% 197.23/28.61 Version : Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
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% 197.82/28.64 % (13520)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 216.77/31.36 Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 216.77/31.36 Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,2,max,max,max,max]
% 216.77/31.38 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 217.72/31.55 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1]
% 218.97/31.67 Finite Model Found!
% 218.97/31.67 % SZS status Satisfiable for theBenchmark
% 218.97/31.71 % (13221)First to succeed.
% 218.97/31.71 % (13221)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13218"
% 219.58/31.77 % SZS output start FiniteModel for theBenchmark
% 219.58/31.77 tff(declare_$i,type,$i:$tType).
% 219.58/31.77 tff(declare_$i1,type,fmb_$i_1:$i).
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:$i] : (
% 219.58/31.77 X = fmb_$i_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff(declare_bool,type,$o:$tType).
% 219.58/31.77 tff(declare_bool1,type,fmb_bool_1:$o).
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:$o] : (
% 219.58/31.77 X = fmb_bool_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_fun$',type,'ZF_ZF_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_fun$1',type,fmb_'ZF_ZF_ZF_prod_fun$'_1:'ZF_ZF_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_ZF_fun_set$',type,'B_ZF_fun_set$':$tType).
% 219.58/31.77 tff('declare_B_ZF_fun_set$1',type,fmb_'B_ZF_fun_set$'_1:'B_ZF_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_ZF_fun_set$'] : (
% 219.58/31.77 X = fmb_'B_ZF_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_fun_set$',type,'Nat_ZF_fun_set$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_fun_set$1',type,'top$g':'Nat_ZF_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_fun_set$'] : (
% 219.58/31.77 X = 'top$g'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_set$',type,'Nat_set_set$':$tType).
% 219.58/31.77 tff('declare_Nat_set_set$1',type,fmb_'Nat_set_set$'_1:'Nat_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_set$'] : (
% 219.58/31.77 X = fmb_'Nat_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',type,'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$1',type,fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1:'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_prod_set$',type,'Nat_ZF_ZF_prod_prod_set$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_prod_set$1',type,fmb_'Nat_ZF_ZF_prod_prod_set$'_1:'Nat_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_prod_prod_set$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_ZF_set_ZF_set_prod_fun_fun$',type,'Nat_nat_ZF_set_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_ZF_set_ZF_set_prod_fun_fun$1',type,fmb_'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'_1:'Nat_nat_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$',type,'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$1',type,fmb_'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'_1:'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set$',type,'ZF_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set$1',type,'top$a':'ZF_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set$'] : (
% 219.58/31.77 X = 'top$a'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_fun_ZF_set_fun$',type,'Nat_nat_fun_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_fun_ZF_set_fun$1',type,fmb_'Nat_nat_fun_ZF_set_fun$'_1:'Nat_nat_fun_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_fun_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_fun_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',type,'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$':$tType).
% 219.58/31.77 tff('declare_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$1',type,fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1:'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] : (
% 219.58/31.77 X = fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_set_fun$',type,'ZF_nat_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_set_fun$1',type,'uxd$':'ZF_nat_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_set_fun$'] : (
% 219.58/31.77 X = 'uxd$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Unit_unit_fun$',type,'Unit_unit_fun$':$tType).
% 219.58/31.77 tff('declare_Unit_unit_fun$1',type,fmb_'Unit_unit_fun$'_1:'Unit_unit_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Unit_unit_fun$'] : (
% 219.58/31.77 X = fmb_'Unit_unit_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_bool_fun_fun$',type,'ZF_nat_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_bool_fun_fun$1',type,fmb_'ZF_nat_bool_fun_fun$'_1:'ZF_nat_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_bool_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_bool_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_b_b_c_LSCategory_ext_Category_ext$',type,'A_b_b_c_LSCategory_ext_Category_ext$':$tType).
% 219.58/31.77 tff('declare_A_b_b_c_LSCategory_ext_Category_ext$1',type,'c$':'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_b_b_c_LSCategory_ext_Category_ext$'] : (
% 219.58/31.77 X = 'c$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_set_ZF_set_set_fun$',type,'Nat_set_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_set_set_ZF_set_set_fun$1',type,fmb_'Nat_set_set_ZF_set_set_fun$'_1:'Nat_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_set_set_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_b_set_fun$',type,'ZF_b_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_b_set_fun$1',type,fmb_'ZF_b_set_fun$'_1:'ZF_b_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_b_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_b_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_prod_set$',type,'Nat_ZF_prod_set$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_prod_set$1',type,'top$d':'Nat_ZF_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_prod_set$'] : (
% 219.58/31.77 X = 'top$d'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set$',type,'ZF_ZF_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set$1',type,'top$b':'ZF_ZF_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set$'] : (
% 219.58/31.77 X = 'top$b'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$',type,'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$1',type,'sup$d':'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = 'sup$d'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_set_set_fun$',type,'ZF_ZF_prod_set_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_set_set_fun$1',type,fmb_'ZF_ZF_prod_set_set_ZF_set_set_fun$'_1:'ZF_ZF_prod_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_set_set_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',type,'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$1',type,fmb_'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1:'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_bool_fun_set$',type,'ZF_set_bool_fun_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set_bool_fun_set$1',type,fmb_'ZF_set_bool_fun_set$'_1:'ZF_set_bool_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_bool_fun_set$'] : (
% 219.58/31.77 X = fmb_'ZF_set_bool_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set$',type,'ZF_set_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set$1',type,fmb_'ZF_set_set$'_1:'ZF_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set$'] : (
% 219.58/31.77 X = fmb_'ZF_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_bool_fun_set$',type,'A_bool_fun_set$':$tType).
% 219.58/31.77 tff('declare_A_bool_fun_set$1',type,fmb_'A_bool_fun_set$'_1:'A_bool_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_bool_fun_set$'] : (
% 219.58/31.77 X = fmb_'A_bool_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_set_fun$',type,'ZF_set_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_set_fun$1',type,'uyn$':'ZF_set_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_set_fun$'] : (
% 219.58/31.77 X = 'uyn$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_fun$',type,'ZF_ZF_prod_ZF_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_fun$1',type,'swap$':'ZF_ZF_prod_ZF_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_prod_fun$'] : (
% 219.58/31.77 X = 'swap$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_set_fun$',type,'ZF_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_set_fun$1',type,'uxc$':'ZF_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_set_fun$'] : (
% 219.58/31.77 X = 'uxc$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_b_fun_set$',type,'A_b_fun_set$':$tType).
% 219.58/31.77 tff('declare_A_b_fun_set$1',type,fmb_'A_b_fun_set$'_1:'A_b_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_b_fun_set$'] : (
% 219.58/31.77 X = fmb_'A_b_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_set_prod_set$',type,'ZF_set_ZF_set_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_set_prod_set$1',type,fmb_'ZF_set_ZF_set_prod_set$'_1:'ZF_set_ZF_set_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_set_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_fun_ZF_set_fun$',type,'ZF_ZF_fun_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_fun_ZF_set_fun$1',type,fmb_'ZF_ZF_fun_ZF_set_fun$'_1:'ZF_ZF_fun_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_fun_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_fun_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_a_fun$',type,'Nat_a_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_a_fun$1',type,fmb_'Nat_a_fun$'_1:'Nat_a_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_a_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_a_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_set_set$',type,'A_set_set$':$tType).
% 219.58/31.77 tff('declare_A_set_set$1',type,fmb_'A_set_set$'_1:'A_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_set_set$'] : (
% 219.58/31.77 X = fmb_'A_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_fun_set$',type,'Nat_nat_fun_set$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_fun_set$1',type,'top$i':'Nat_nat_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_fun_set$'] : (
% 219.58/31.77 X = 'top$i'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_fun$',type,'ZF_ZF_prod_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_fun$1',type,fmb_'ZF_ZF_prod_ZF_fun$'_1:'ZF_ZF_prod_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_ZF_ZF_prod_set_fun_fun$',type,'ZF_nat_ZF_ZF_prod_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_ZF_ZF_prod_set_fun_fun$1',type,fmb_'ZF_nat_ZF_ZF_prod_set_fun_fun$'_1:'ZF_nat_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_ZF_ZF_prod_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_c_LSCategory_ext$',type,'B_c_LSCategory_ext$':$tType).
% 219.58/31.77 tff('declare_B_c_LSCategory_ext$1',type,fmb_'B_c_LSCategory_ext$'_1:'B_c_LSCategory_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_c_LSCategory_ext$'] : (
% 219.58/31.77 X = fmb_'B_c_LSCategory_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_set_nat_set_fun$',type,'Nat_set_set_nat_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_set_set_nat_set_fun$1',type,'sup$f':'Nat_set_set_nat_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_set_nat_set_fun$'] : (
% 219.58/31.77 X = 'sup$f'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$',type,'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$1',type,fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'_1:'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',type,'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$1',type,fmb_'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1:'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_fun$',type,'B_b_fun$':$tType).
% 219.58/31.77 tff('declare_B_b_fun$1',type,fmb_'B_b_fun$'_1:'B_b_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_fun$'] : (
% 219.58/31.77 X = fmb_'B_b_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_ZF_set_ZF_set_prod_fun_fun$',type,'ZF_nat_ZF_set_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_ZF_set_ZF_set_prod_fun_fun$1',type,fmb_'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'_1:'ZF_nat_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_set_prod_set$',type,'ZF_ZF_set_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_set_prod_set$1',type,fmb_'ZF_ZF_set_prod_set$'_1:'ZF_ZF_set_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_set_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_set_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_bool_fun_fun$',type,'Nat_ZF_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_bool_fun_fun$1',type,fmb_'Nat_ZF_bool_fun_fun$'_1:'Nat_ZF_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_bool_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_bool_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_prod_ZF_ZF_prod_set_fun$',type,'ZF_nat_prod_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_prod_ZF_ZF_prod_set_fun$1',type,fmb_'ZF_nat_prod_ZF_ZF_prod_set_fun$'_1:'ZF_nat_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_prod_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_prod_fun$',type,'ZF_ZF_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_prod_fun$1',type,fmb_'ZF_ZF_ZF_set_prod_fun$'_1:'ZF_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_prod_fun_fun$',type,'ZF_ZF_ZF_ZF_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_prod_fun_fun$1',type,'uxj$':'ZF_ZF_ZF_ZF_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_ZF_prod_fun_fun$'] : (
% 219.58/31.77 X = 'uxj$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_set_fun$',type,'ZF_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_set_fun$1',type,fmb_'ZF_ZF_ZF_prod_set_fun$'_1:'ZF_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_fun$',type,'ZF_ZF_prod_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_fun$1',type,fmb_'ZF_ZF_prod_ZF_set_fun$'_1:'ZF_ZF_prod_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',type,'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$':$tType).
% 219.58/31.77 tff('declare_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$1',type,fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1:'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'] : (
% 219.58/31.77 X = fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_set_fun$',type,'ZF_ZF_prod_nat_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_set_fun$1',type,fmb_'ZF_ZF_prod_nat_set_fun$'_1:'ZF_ZF_prod_nat_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_nat_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_nat_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_ZF_set_fun_fun$',type,'ZF_nat_ZF_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_ZF_set_fun_fun$1',type,fmb_'ZF_nat_ZF_set_fun_fun$'_1:'ZF_nat_ZF_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_ZF_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_ZF_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod$',type,'ZF_ZF_prod$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod$1',type,fmb_'ZF_ZF_prod$'_1:'ZF_ZF_prod$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_a_set_fun$',type,'B_a_set_fun$':$tType).
% 219.58/31.77 tff('declare_B_a_set_fun$1',type,fmb_'B_a_set_fun$'_1:'B_a_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_a_set_fun$'] : (
% 219.58/31.77 X = fmb_'B_a_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',type,'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$1',type,fmb_'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1:'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_prod_set$',type,'B_b_prod_set$':$tType).
% 219.58/31.77 tff('declare_B_b_prod_set$1',type,fmb_'B_b_prod_set$'_1:'B_b_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_prod_set$'] : (
% 219.58/31.77 X = fmb_'B_b_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_set_set_fun$',type,'ZF_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_set_set_fun$1',type,fmb_'ZF_ZF_set_set_fun$'_1:'ZF_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_set_prod_set$',type,'Nat_ZF_set_prod_set$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_set_prod_set$1',type,fmb_'Nat_ZF_set_prod_set$'_1:'Nat_ZF_set_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_set_prod_set$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_set_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_set$',type,'ZF_ZF_prod_ZF_ZF_prod_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_set$1',type,fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1:'ZF_ZF_prod_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_prod_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_prod_set$',type,'Nat_nat_prod_set$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_prod_set$1',type,'top$e':'Nat_nat_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_prod_set$'] : (
% 219.58/31.77 X = 'top$e'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B$',type,'B$':$tType).
% 219.58/31.77 tff('declare_B$1',type,'f$':'B$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B$'] : (
% 219.58/31.77 X = 'f$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_bool_fun$',type,'ZF_set_set_bool_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_bool_fun$1',type,fmb_'ZF_set_set_bool_fun$'_1:'ZF_set_set_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_bool_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_set_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_fun_fun$',type,'ZF_ZF_ZF_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_fun_fun$1',type,'vah$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_fun_fun$'] : (
% 219.58/31.77 X = 'vah$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_ZF_set_fun$',type,'A_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_A_ZF_set_fun$1',type,fmb_'A_ZF_set_fun$'_1:'A_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'A_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_bool_fun_set$',type,'B_bool_fun_set$':$tType).
% 219.58/31.77 tff('declare_B_bool_fun_set$1',type,fmb_'B_bool_fun_set$'_1:'B_bool_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_bool_fun_set$'] : (
% 219.58/31.77 X = fmb_'B_bool_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_a_fun$',type,'ZF_set_a_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_a_fun$1',type,fmb_'ZF_set_a_fun$'_1:'ZF_set_a_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_a_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_a_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_fun_set$',type,'ZF_nat_fun_set$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_fun_set$1',type,'top$h':'ZF_nat_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_fun_set$'] : (
% 219.58/31.77 X = 'top$h'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_ZF_set_fun$',type,'B_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_B_ZF_set_fun$1',type,fmb_'B_ZF_set_fun$'_1:'B_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'B_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$',type,'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$1',type,fmb_'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'_1:'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_fun_fun$',type,'ZF_ZF_ZF_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_set_fun_fun$1',type,'uyk$':'ZF_ZF_ZF_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_set_fun_fun$'] : (
% 219.58/31.77 X = 'uyk$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$',type,'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$1',type,fmb_'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'_1:'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_bool_fun_fun$',type,'ZF_set_set_ZF_set_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_bool_fun_fun$1',type,'uub$':'ZF_set_set_ZF_set_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_ZF_set_bool_fun_fun$'] : (
% 219.58/31.77 X = 'uub$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_set_ZF_set_prod_fun$',type,'ZF_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_set_ZF_set_prod_fun$1',type,fmb_'ZF_ZF_set_ZF_set_prod_fun$'_1:'ZF_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$',type,'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$':$tType).
% 219.58/31.77 tff('declare_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$1',type,fmb_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'_1:'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] : (
% 219.58/31.77 X = fmb_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_fun$',type,'Nat_nat_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_fun$1',type,fmb_'Nat_nat_fun$'_1:'Nat_nat_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_C$',type,'C$':$tType).
% 219.58/31.77 tff('declare_C$1',type,fmb_'C$'_1:'C$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'C$'] : (
% 219.58/31.77 X = fmb_'C$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_a_set_fun$',type,'ZF_a_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_a_set_fun$1',type,fmb_'ZF_a_set_fun$'_1:'ZF_a_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_a_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_a_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_b_fun$',type,'ZF_b_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_b_fun$1',type,fmb_'ZF_b_fun$'_1:'ZF_b_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_b_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_b_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_set_ZF_set_set_fun$',type,'ZF_set_set_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_set_ZF_set_set_fun$1',type,'sup$e':'ZF_set_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = 'sup$e'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat$',type,'Nat$':$tType).
% 219.58/31.77 tff('declare_Nat$1',type,fmb_'Nat$'_1:'Nat$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat$'] : (
% 219.58/31.77 X = fmb_'Nat$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_set_set_fun$',type,'Nat_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_set_set_fun$1',type,fmb_'Nat_ZF_set_set_fun$'_1:'Nat_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_ZF_set_set_fun$',type,'Nat_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_set_ZF_set_set_fun$1',type,fmb_'Nat_set_ZF_set_set_fun$'_1:'Nat_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_set_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_prod_ZF_ZF_prod_set_fun$',type,'Nat_nat_prod_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_prod_ZF_ZF_prod_set_fun$1',type,fmb_'Nat_nat_prod_ZF_ZF_prod_set_fun$'_1:'Nat_nat_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_prod_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_prod_bool_fun$',type,'B_b_prod_bool_fun$':$tType).
% 219.58/31.77 tff('declare_B_b_prod_bool_fun$1',type,fmb_'B_b_prod_bool_fun$'_1:'B_b_prod_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_prod_bool_fun$'] : (
% 219.58/31.77 X = fmb_'B_b_prod_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_fun$',type,'Nat_ZF_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_fun$1',type,fmb_'Nat_ZF_ZF_prod_fun$'_1:'Nat_ZF_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_fun_set$',type,'ZF_ZF_prod_ZF_fun_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_fun_set$1',type,fmb_'ZF_ZF_prod_ZF_fun_set$'_1:'ZF_ZF_prod_ZF_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_fun_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_fun$',type,'ZF_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_fun$1',type,'uur$':'ZF_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_fun$'] : (
% 219.58/31.77 X = 'uur$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_bool_fun$',type,'ZF_ZF_prod_bool_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_bool_fun$1',type,fmb_'ZF_ZF_prod_bool_fun$'_1:'ZF_ZF_prod_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_bool_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_set_set_fun$',type,'ZF_set_set_ZF_set_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_set_set_fun$1',type,fmb_'ZF_set_set_ZF_set_set_set_fun$'_1:'ZF_set_set_ZF_set_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_ZF_set_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_set_ZF_set_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_ZF_set_fun$',type,'Nat_set_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_set_ZF_set_fun$1',type,fmb_'Nat_set_ZF_set_fun$'_1:'Nat_set_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_set_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_fun_set$',type,'ZF_ZF_fun_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_fun_set$1',type,'top$f':'ZF_ZF_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_fun_set$'] : (
% 219.58/31.77 X = 'top$f'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_prod_set$',type,'ZF_ZF_prod_nat_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_prod_set$1',type,fmb_'ZF_ZF_prod_nat_prod_set$'_1:'ZF_ZF_prod_nat_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_nat_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_nat_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_prod_b_fun_set$',type,'B_b_prod_b_fun_set$':$tType).
% 219.58/31.77 tff('declare_B_b_prod_b_fun_set$1',type,fmb_'B_b_prod_b_fun_set$'_1:'B_b_prod_b_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_prod_b_fun_set$'] : (
% 219.58/31.77 X = fmb_'B_b_prod_b_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_prod_ZF_set_ZF_set_prod_fun$',type,'Nat_nat_prod_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_prod_ZF_set_ZF_set_prod_fun$1',type,fmb_'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'_1:'Nat_nat_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_prod_set$',type,'ZF_ZF_ZF_prod_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_prod_prod_set$1',type,fmb_'ZF_ZF_ZF_prod_prod_set$'_1:'ZF_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_prod_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_prod$',type,'ZF_set_ZF_prod$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_prod$1',type,fmb_'ZF_set_ZF_prod$'_1:'ZF_set_ZF_prod$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_prod$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_prod$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_set_ZF_set_prod_fun$',type,'Nat_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_set_ZF_set_prod_fun$1',type,fmb_'Nat_ZF_set_ZF_set_prod_fun$'_1:'Nat_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set$',type,'ZF_ZF_prod_set_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set$1',type,fmb_'ZF_ZF_prod_set_set$'_1:'ZF_ZF_prod_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_a_fun$',type,'B_a_fun$':$tType).
% 219.58/31.77 tff('declare_B_a_fun$1',type,fmb_'B_a_fun$'_1:'B_a_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_a_fun$'] : (
% 219.58/31.77 X = fmb_'B_a_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_a_fun$',type,'ZF_a_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_a_fun$1',type,fmb_'ZF_a_fun$'_1:'ZF_a_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_a_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_a_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_set_prod$',type,'ZF_ZF_set_prod$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_set_prod$1',type,fmb_'ZF_ZF_set_prod$'_1:'ZF_ZF_set_prod$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_set_prod$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_set_prod$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_set_fun$',type,'Nat_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_set_fun$1',type,'uxe$':'Nat_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_set_fun$'] : (
% 219.58/31.77 X = 'uxe$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff(declare_tlbool,type,tlbool:$tType).
% 219.58/31.77 tff(declare_tlbool1,type,tltrue:tlbool).
% 219.58/31.77 tff(declare_tlbool2,type,tlfalse:tlbool).
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:tlbool] : (
% 219.58/31.77 X = tltrue | X = tlfalse
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff(distinct_domain,axiom,
% 219.58/31.77 tltrue != tlfalse
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_prod_set$',type,'ZF_nat_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_prod_set$1',type,'top$c':'ZF_nat_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_prod_set$'] : (
% 219.58/31.77 X = 'top$c'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$',type,'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$1',type,fmb_'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'_1:'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_prod$',type,'B_b_prod$':$tType).
% 219.58/31.77 tff('declare_B_b_prod$1',type,fmb_'B_b_prod$'_1:'B_b_prod$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_prod$'] : (
% 219.58/31.77 X = fmb_'B_b_prod$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_fun$',type,'ZF_set_set_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_fun$1',type,'sup$':'ZF_set_set_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_ZF_set_fun$'] : (
% 219.58/31.77 X = 'sup$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_fun_ZF_ZF_fun_fun$',type,'ZF_ZF_fun_ZF_ZF_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_fun_ZF_ZF_fun_fun$1',type,'uym$':'ZF_ZF_fun_ZF_ZF_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_fun_ZF_ZF_fun_fun$'] : (
% 219.58/31.77 X = 'uym$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_set_a_bool_fun_fun$',type,'A_set_a_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_A_set_a_bool_fun_fun$1',type,'uu$':'A_set_a_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_set_a_bool_fun_fun$'] : (
% 219.58/31.77 X = 'uu$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_prod_ZF_ZF_prod_set_fun$',type,'Nat_ZF_prod_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_prod_ZF_ZF_prod_set_fun$1',type,fmb_'Nat_ZF_prod_ZF_ZF_prod_set_fun$'_1:'Nat_ZF_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_prod_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_bool_fun$',type,'A_bool_fun$':$tType).
% 219.58/31.77 tff('declare_A_bool_fun$1',type,fmb_'A_bool_fun$'_1:'A_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_bool_fun$'] : (
% 219.58/31.77 X = fmb_'A_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_fun_ZF_set_fun$',type,'ZF_nat_fun_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_fun_ZF_set_fun$1',type,fmb_'ZF_nat_fun_ZF_set_fun$'_1:'ZF_nat_fun_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_fun_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_fun_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_set$',type,'A_set$':$tType).
% 219.58/31.77 tff('declare_A_set$1',type,fmb_'A_set$'_1:'A_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_set$'] : (
% 219.58/31.77 X = fmb_'A_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$',type,'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$1',type,fmb_'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'_1:'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_a_set_fun$',type,'A_a_set_fun$':$tType).
% 219.58/31.77 tff('declare_A_a_set_fun$1',type,fmb_'A_a_set_fun$'_1:'A_a_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_a_set_fun$'] : (
% 219.58/31.77 X = fmb_'A_a_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',type,'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$':$tType).
% 219.58/31.77 tff('declare_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$1',type,fmb_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'_1:'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] : (
% 219.58/31.77 X = fmb_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_set_set_fun$',type,'ZF_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_set_set_fun$1',type,fmb_'ZF_set_ZF_set_set_fun$'_1:'ZF_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_set_fun$',type,'Nat_nat_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_set_fun$1',type,'uxf$':'Nat_nat_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_set_fun$'] : (
% 219.58/31.77 X = 'uxf$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_b_fun$',type,'A_b_fun$':$tType).
% 219.58/31.77 tff('declare_A_b_fun$1',type,fmb_'A_b_fun$'_1:'A_b_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_b_fun$'] : (
% 219.58/31.77 X = fmb_'A_b_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_prod_ZF_set_ZF_set_prod_fun$',type,'ZF_nat_prod_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_prod_ZF_set_ZF_set_prod_fun$1',type,fmb_'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'_1:'ZF_nat_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_prod_set_fun_fun$',type,'ZF_ZF_ZF_ZF_prod_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_ZF_prod_set_fun_fun$1',type,fmb_'ZF_ZF_ZF_ZF_prod_set_fun_fun$'_1:'ZF_ZF_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_ZF_prod_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_set$',type,'B_set$':$tType).
% 219.58/31.77 tff('declare_B_set$1',type,fmb_'B_set$'_1:'B_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_set$'] : (
% 219.58/31.77 X = fmb_'B_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_ZF_ZF_prod_set_fun_fun$',type,'Nat_nat_ZF_ZF_prod_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_ZF_ZF_prod_set_fun_fun$1',type,fmb_'Nat_nat_ZF_ZF_prod_set_fun_fun$'_1:'Nat_nat_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_ZF_ZF_prod_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_b_fun_bool_fun$',type,'A_b_fun_bool_fun$':$tType).
% 219.58/31.77 tff('declare_A_b_fun_bool_fun$1',type,fmb_'A_b_fun_bool_fun$'_1:'A_b_fun_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_b_fun_bool_fun$'] : (
% 219.58/31.77 X = fmb_'A_b_fun_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_set_fun$',type,'Nat_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_set_fun$1',type,fmb_'Nat_ZF_ZF_prod_set_fun$'_1:'Nat_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A$',type,'A$':$tType).
% 219.58/31.77 tff('declare_A$1',type,fmb_'A$'_1:'A$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A$'] : (
% 219.58/31.77 X = fmb_'A$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_set_b_bool_fun_fun$',type,'B_set_b_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_B_set_b_bool_fun_fun$1',type,'uua$':'B_set_b_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_set_b_bool_fun_fun$'] : (
% 219.58/31.77 X = 'uua$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_unit_Category_ext$',type,'ZF_ZF_unit_Category_ext$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_unit_Category_ext$1',type,'set$':'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_unit_Category_ext$'] : (
% 219.58/31.77 X = 'set$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_bool_fun_fun$',type,'ZF_set_ZF_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_bool_fun_fun$1',type,'uuc$':'ZF_set_ZF_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_bool_fun_fun$'] : (
% 219.58/31.77 X = 'uuc$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_fun_bool_fun$',type,'ZF_ZF_fun_bool_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_fun_bool_fun$1',type,fmb_'ZF_ZF_fun_bool_fun$'_1:'ZF_ZF_fun_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_fun_bool_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_fun_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$',type,'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$1',type,fmb_'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'_1:'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_nat_ZF_set_fun_fun$',type,'Nat_nat_ZF_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_nat_ZF_set_fun_fun$1',type,fmb_'Nat_nat_ZF_set_fun_fun$'_1:'Nat_nat_ZF_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_nat_ZF_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_nat_ZF_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_ZF_set_fun$',type,'ZF_ZF_prod_set_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_ZF_set_fun$1',type,fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1:'ZF_ZF_prod_set_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_set_bool_fun$',type,'B_set_bool_fun$':$tType).
% 219.58/31.77 tff('declare_B_set_bool_fun$1',type,fmb_'B_set_bool_fun$'_1:'B_set_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_set_bool_fun$'] : (
% 219.58/31.77 X = fmb_'B_set_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_b_set_fun$',type,'A_b_set_fun$':$tType).
% 219.58/31.77 tff('declare_A_b_set_fun$1',type,fmb_'A_b_set_fun$'_1:'A_b_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_b_set_fun$'] : (
% 219.58/31.77 X = fmb_'A_b_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_b_fun$',type,'Nat_b_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_b_fun$1',type,fmb_'Nat_b_fun$'_1:'Nat_b_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_b_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_b_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_prod_set$',type,'ZF_set_ZF_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_prod_set$1',type,fmb_'ZF_set_ZF_prod_set$'_1:'ZF_set_ZF_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_set_set$',type,'B_set_set$':$tType).
% 219.58/31.77 tff('declare_B_set_set$1',type,fmb_'B_set_set$'_1:'B_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_set_set$'] : (
% 219.58/31.77 X = fmb_'B_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_set_prod$',type,'ZF_set_ZF_set_prod$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_set_prod$1',type,fmb_'ZF_set_ZF_set_prod$'_1:'ZF_set_ZF_set_prod$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_set_prod$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_set_prod$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_prod_fun$',type,'Nat_ZF_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_prod_fun$1',type,fmb_'Nat_ZF_ZF_set_prod_fun$'_1:'Nat_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_prod_b_fun$',type,'B_b_prod_b_fun$':$tType).
% 219.58/31.77 tff('declare_B_b_prod_b_fun$1',type,fmb_'B_b_prod_b_fun$'_1:'B_b_prod_b_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_prod_b_fun$'] : (
% 219.58/31.77 X = fmb_'B_b_prod_b_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_fun$',type,'ZF_set_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_fun$1',type,fmb_'ZF_set_ZF_fun$'_1:'ZF_set_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_set_b_set_fun$',type,'B_set_b_set_fun$':$tType).
% 219.58/31.77 tff('declare_B_set_b_set_fun$1',type,fmb_'B_set_b_set_fun$'_1:'B_set_b_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_set_b_set_fun$'] : (
% 219.58/31.77 X = fmb_'B_set_b_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_set_fun$',type,'ZF_ZF_prod_set_set_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_set_set_ZF_set_fun$1',type,fmb_'ZF_ZF_prod_set_set_ZF_set_fun$'_1:'ZF_ZF_prod_set_set_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_set_set_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_set_set_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_a_fun_b_a_fun_fun$',type,'B_a_fun_b_a_fun_fun$':$tType).
% 219.58/31.77 tff('declare_B_a_fun_b_a_fun_fun$1',type,fmb_'B_a_fun_b_a_fun_fun$'_1:'B_a_fun_b_a_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_a_fun_b_a_fun_fun$'] : (
% 219.58/31.77 X = fmb_'B_a_fun_b_a_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_a_fun$',type,'A_a_fun$':$tType).
% 219.58/31.77 tff('declare_A_a_fun$1',type,fmb_'A_a_fun$'_1:'A_a_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_a_fun$'] : (
% 219.58/31.77 X = fmb_'A_a_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_bool_fun$',type,'ZF_bool_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_bool_fun$1',type,'uut$':'ZF_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_bool_fun$'] : (
% 219.58/31.77 X = 'uut$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$',type,'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$1',type,fmb_'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'_1:'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_b_fun_fun$',type,'B_b_b_fun_fun$':$tType).
% 219.58/31.77 tff('declare_B_b_b_fun_fun$1',type,fmb_'B_b_b_fun_fun$'_1:'B_b_b_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_b_fun_fun$'] : (
% 219.58/31.77 X = fmb_'B_b_b_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_set_fun$',type,'ZF_set_set_ZF_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_ZF_set_set_fun$1',type,fmb_'ZF_set_set_ZF_set_set_fun$'_1:'ZF_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_ZF_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_set_ZF_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$',type,'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$1',type,fmb_'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'_1:'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set_set_ZF_set_set_set_fun$',type,'Nat_set_set_ZF_set_set_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_set_set_ZF_set_set_set_fun$1',type,fmb_'Nat_set_set_ZF_set_set_set_fun$'_1:'Nat_set_set_ZF_set_set_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set_set_ZF_set_set_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_set_set_ZF_set_set_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$',type,'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$1',type,'uuv$':'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'] : (
% 219.58/31.77 X = 'uuv$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_nat_fun$',type,'ZF_nat_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_nat_fun$1',type,fmb_'ZF_nat_fun$'_1:'ZF_nat_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_nat_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_nat_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_ZF_fun$',type,'A_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_A_ZF_fun$1',type,fmb_'A_ZF_fun$'_1:'A_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_ZF_fun$'] : (
% 219.58/31.77 X = fmb_'A_ZF_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_set_a_set_fun$',type,'A_set_a_set_fun$':$tType).
% 219.58/31.77 tff('declare_A_set_a_set_fun$1',type,fmb_'A_set_a_set_fun$'_1:'A_set_a_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_set_a_set_fun$'] : (
% 219.58/31.77 X = fmb_'A_set_a_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_bool_fun$',type,'ZF_set_bool_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_bool_fun$1',type,fmb_'ZF_set_bool_fun$'_1:'ZF_set_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_bool_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_prod_set$',type,'ZF_ZF_prod_ZF_prod_set$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_prod_set$1',type,fmb_'ZF_ZF_prod_ZF_prod_set$'_1:'ZF_ZF_prod_ZF_prod_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_prod_set$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_prod_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$',type,'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$1',type,fmb_'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'_1:'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Unit$',type,'Unit$':$tType).
% 219.58/31.77 tff('declare_Unit$1',type,'unity$':'Unit$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Unit$'] : (
% 219.58/31.77 X = 'unity$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_bool_fun$',type,'Nat_bool_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_bool_fun$1',type,'uws$':'Nat_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_bool_fun$'] : (
% 219.58/31.77 X = 'uws$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Bool_set$',type,'Bool_set$':$tType).
% 219.58/31.77 tff('declare_Bool_set$1',type,fmb_'Bool_set$'_1:'Bool_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Bool_set$'] : (
% 219.58/31.77 X = fmb_'Bool_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF$',type,'ZF$':$tType).
% 219.58/31.77 tff('declare_ZF$1',type,fmb_'ZF$'_1:'ZF$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF$'] : (
% 219.58/31.77 X = fmb_'ZF$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_ZF_fun$',type,'B_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_B_ZF_fun$1',type,fmb_'B_ZF_fun$'_1:'B_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_ZF_fun$'] : (
% 219.58/31.77 X = fmb_'B_ZF_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_set_set$',type,'ZF_set_set_set$':$tType).
% 219.58/31.77 tff('declare_ZF_set_set_set$1',type,fmb_'ZF_set_set_set$'_1:'ZF_set_set_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_set_set$'] : (
% 219.58/31.77 X = fmb_'ZF_set_set_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_set_ZF_ZF_prod_set_fun$',type,'ZF_set_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_set_ZF_ZF_prod_set_fun$1',type,fmb_'ZF_set_ZF_ZF_prod_set_fun$'_1:'ZF_set_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_set_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_set_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_a_fun_set$',type,'B_a_fun_set$':$tType).
% 219.58/31.77 tff('declare_B_a_fun_set$1',type,fmb_'B_a_fun_set$'_1:'B_a_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_a_fun_set$'] : (
% 219.58/31.77 X = fmb_'B_a_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_fun_ZF_set_fun$',type,'Nat_ZF_fun_ZF_set_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_fun_ZF_set_fun$1',type,fmb_'Nat_ZF_fun_ZF_set_fun$'_1:'Nat_ZF_fun_ZF_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_fun_ZF_set_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_fun_ZF_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_set$',type,'Nat_set$':$tType).
% 219.58/31.77 tff('declare_Nat_set$1',type,'top$':'Nat_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_set$'] : (
% 219.58/31.77 X = 'top$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',type,'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$1',type,fmb_'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1:'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_bool_fun_set$',type,'ZF_bool_fun_set$':$tType).
% 219.58/31.77 tff('declare_ZF_bool_fun_set$1',type,fmb_'ZF_bool_fun_set$'_1:'ZF_bool_fun_set$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_bool_fun_set$'] : (
% 219.58/31.77 X = fmb_'ZF_bool_fun_set$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_fun$',type,'Nat_ZF_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_fun$1',type,fmb_'Nat_ZF_fun$'_1:'Nat_ZF_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_set_fun$',type,'ZF_ZF_prod_ZF_ZF_prod_set_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_ZF_prod_set_fun$1',type,fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1:'ZF_ZF_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_ZF_prod_set_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_a_fun_bool_fun$',type,'B_a_fun_bool_fun$':$tType).
% 219.58/31.77 tff('declare_B_a_fun_bool_fun$1',type,fmb_'B_a_fun_bool_fun$'_1:'B_a_fun_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_a_fun_bool_fun$'] : (
% 219.58/31.77 X = fmb_'B_a_fun_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_bool_fun$',type,'B_bool_fun$':$tType).
% 219.58/31.77 tff('declare_B_bool_fun$1',type,fmb_'B_bool_fun$'_1:'B_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_bool_fun$'] : (
% 219.58/31.77 X = fmb_'B_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_ZF_prod_set_fun_fun$',type,'Nat_ZF_ZF_ZF_prod_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_ZF_prod_set_fun_fun$1',type,fmb_'Nat_ZF_ZF_ZF_prod_set_fun_fun$'_1:'Nat_ZF_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_ZF_prod_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_fun_fun$',type,'Nat_ZF_ZF_set_fun_fun$':$tType).
% 219.58/31.77 tff('declare_Nat_ZF_ZF_set_fun_fun$1',type,fmb_'Nat_ZF_ZF_set_fun_fun$'_1:'Nat_ZF_ZF_set_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'Nat_ZF_ZF_set_fun_fun$'] : (
% 219.58/31.77 X = fmb_'Nat_ZF_ZF_set_fun_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_b_set_fun$',type,'B_b_set_fun$':$tType).
% 219.58/31.77 tff('declare_B_b_set_fun$1',type,fmb_'B_b_set_fun$'_1:'B_b_set_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_b_set_fun$'] : (
% 219.58/31.77 X = fmb_'B_b_set_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_A_set_bool_fun$',type,'A_set_bool_fun$':$tType).
% 219.58/31.77 tff('declare_A_set_bool_fun$1',type,fmb_'A_set_bool_fun$'_1:'A_set_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'A_set_bool_fun$'] : (
% 219.58/31.77 X = fmb_'A_set_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_ZF_prod_fun$',type,'ZF_ZF_prod_ZF_set_ZF_prod_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_prod_ZF_set_ZF_prod_fun$1',type,fmb_'ZF_ZF_prod_ZF_set_ZF_prod_fun$'_1:'ZF_ZF_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_prod_ZF_set_ZF_prod_fun$'] : (
% 219.58/31.77 X = fmb_'ZF_ZF_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_B_ZF_fun_bool_fun$',type,'B_ZF_fun_bool_fun$':$tType).
% 219.58/31.77 tff('declare_B_ZF_fun_bool_fun$1',type,fmb_'B_ZF_fun_bool_fun$'_1:'B_ZF_fun_bool_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'B_ZF_fun_bool_fun$'] : (
% 219.58/31.77 X = fmb_'B_ZF_fun_bool_fun$'_1
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_ZF_ZF_bool_fun_fun$',type,'ZF_ZF_bool_fun_fun$':$tType).
% 219.58/31.77 tff('declare_ZF_ZF_bool_fun_fun$1',type,'uug$':'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff(finite_domain,axiom,
% 219.58/31.77 ! [X:'ZF_ZF_bool_fun_fun$'] : (
% 219.58/31.77 X = 'uug$'
% 219.58/31.77 ) ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuw$',type,'uuw$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('uuw$_definition',axiom,'uuw$' = 'vah$').
% 219.58/31.77 tff('declare_sum$',type,'sum$':'ZF_ZF_fun$').
% 219.58/31.77 tff('sum$_definition',axiom,'sum$' = 'uur$').
% 219.58/31.77 tff('declare_app$',type,'app$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('app$_definition',axiom,'app$' = 'vah$').
% 219.58/31.77 tff('declare_zFfunCod$',type,'zFfunCod$':'ZF_ZF_fun$').
% 219.58/31.77 tff('zFfunCod$_definition',axiom,'zFfunCod$' = 'uur$').
% 219.58/31.77 tff('declare_set$a',type,'set$a':'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('set$a_definition',axiom,'set$a' = 'set$').
% 219.58/31.77 tff('declare_zFfunComp$',type,'zFfunComp$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('zFfunComp$_definition',axiom,'zFfunComp$' = 'vah$').
% 219.58/31.77 tff('declare_opair$',type,'opair$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('opair$_definition',axiom,'opair$' = 'vah$').
% 219.58/31.77 tff('declare_g$',type,'g$':'B$').
% 219.58/31.77 tff('g$_definition',axiom,'g$' = 'f$').
% 219.58/31.77 tff('declare_elem$',type,'elem$':'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('elem$_definition',axiom,'elem$' = 'uug$').
% 219.58/31.77 tff('declare_zFfunDom$',type,'zFfunDom$':'ZF_ZF_fun$').
% 219.58/31.77 tff('zFfunDom$_definition',axiom,'zFfunDom$' = 'uur$').
% 219.58/31.77 tff('declare_zFfunApp$',type,'zFfunApp$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('zFfunApp$_definition',axiom,'zFfunApp$' = 'vah$').
% 219.58/31.77 tff('declare_uwy$',type,'uwy$':'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('uwy$_definition',axiom,'uwy$' = 'uug$').
% 219.58/31.77 tff('declare_uuu$',type,'uuu$':'ZF_ZF_fun$').
% 219.58/31.77 tff('uuu$_definition',axiom,'uuu$' = 'uur$').
% 219.58/31.77 tff('declare_explode$',type,'explode$':'ZF_ZF_set_fun$').
% 219.58/31.77 tff('explode$_definition',axiom,'explode$' = 'uxc$').
% 219.58/31.77 tff('declare_isZFfun$',type,'isZFfun$':'ZF_bool_fun$').
% 219.58/31.77 tff('isZFfun$_definition',axiom,'isZFfun$' = 'uut$').
% 219.58/31.77 tff('declare_cartProd$',type,'cartProd$':'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('cartProd$_definition',axiom,'cartProd$' = 'vah$').
% 219.58/31.77 tff('declare_uuf$',type,'uuf$':'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('uuf$_definition',axiom,'uuf$' = 'uug$').
% 219.58/31.77 tff('declare_image$ai',type,'image$ai': 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_image$ai',axiom,
% 219.58/31.77 'image$ai'(fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'_1,fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1) = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mor_update$a',type,'mor_update$a': 'B_set_b_set_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_mor_update$a',axiom,
% 219.58/31.77 'mor_update$a'(fmb_'B_set_b_set_fun$'_1,'c$') = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_id$',type,'id$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_fun$').
% 219.58/31.77 tff('function_id$',axiom,
% 219.58/31.77 'id$'('c$') = fmb_'A_b_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ah',type,'fun_app$ah': 'ZF_nat_bool_fun_fun$' * 'ZF$' > 'Nat_bool_fun$').
% 219.58/31.77 tff('function_fun_app$ah',axiom,
% 219.58/31.77 'fun_app$ah'(fmb_'ZF_nat_bool_fun_fun$'_1,fmb_'ZF$'_1) = 'uws$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_catDom$a',type,'catDom$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_catDom$a',axiom,
% 219.58/31.77 'catDom$a'(fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1) = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_oppositeCategory$',type,'oppositeCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_oppositeCategory$',axiom,
% 219.58/31.77 'oppositeCategory$'('c$') = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxn$',type,'uxn$': 'ZF_ZF_prod_set$' > 'ZF_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_uxn$',axiom,
% 219.58/31.77 'uxn$'('top$b') = fmb_'ZF_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$b',type,'sigma$b': 'ZF_set$' * 'ZF_nat_set_fun$' > 'ZF_nat_prod_set$').
% 219.58/31.77 tff('function_sigma$b',axiom,
% 219.58/31.77 'sigma$b'('top$a','uxd$') = 'top$c'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bv',type,'fun_app$bv': 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' * 'ZF_ZF_prod$' > 'Nat_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_fun_app$bv',axiom,
% 219.58/31.77 'fun_app$bv'(fmb_'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'_1,fmb_'ZF_ZF_prod$'_1) = fmb_'Nat_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_relInvImage$b',type,'relInvImage$b': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff('function_relInvImage$b',axiom,
% 219.58/31.77 'relInvImage$b'('top$b','top$b',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bg',type,'image$bg': 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.77 tff('function_image$bg',axiom,
% 219.58/31.77 'image$bg'(fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1,'top$b') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_rec_set_unit$',type,'rec_set_unit$': 'ZF$' * 'Unit$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_rec_set_unit$',axiom,
% 219.58/31.77 'rec_set_unit$'(fmb_'ZF$'_1,'unity$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_relcomp$',type,'relcomp$': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_relcomp$',axiom,
% 219.58/31.77 'relcomp$'('top$b','top$b') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwa$',type,'uwa$': 'B_ZF_fun$' * 'B_set$' * 'ZF_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uwa$',axiom,
% 219.58/31.77 'uwa$'(fmb_'B_ZF_fun$'_1,fmb_'B_set$'_1,'uut$') = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapO$a',type,'mapO$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_a_fun$').
% 219.58/31.77 tff('function_mapO$a',axiom,
% 219.58/31.77 'mapO$a'(fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1) = fmb_'A_a_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwl$',type,'uwl$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwl$',axiom,
% 219.58/31.77 'uwl$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'top$b') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vas$',type,'vas$': 'Nat_nat_ZF_set_fun_fun$' * 'Nat_nat_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_vas$',axiom,
% 219.58/31.77 'vas$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1,fmb_'Nat_nat_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$b',type,'fun_app$b': 'ZF_ZF_ZF_fun_fun$' * 'ZF$' > 'ZF_ZF_fun$').
% 219.58/31.77 tff('function_fun_app$b',axiom,
% 219.58/31.77 'fun_app$b'('vah$',fmb_'ZF$'_1) = 'uur$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyt$',type,'uyt$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_fun$').
% 219.58/31.77 tff('function_uyt$',axiom,
% 219.58/31.77 'uyt$'('uxe$') = fmb_'Nat_set_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vbb$',type,'vbb$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_fun_ZF_set_fun$').
% 219.58/31.77 tff('function_vbb$',axiom,
% 219.58/31.77 'vbb$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_nat_fun_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_the$a',type,'the$a': 'B_bool_fun$' > 'B$').
% 219.58/31.77 tff('function_the$a',axiom,
% 219.58/31.77 'the$a'(fmb_'B_bool_fun$'_1) = 'f$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapsTo$',type,'mapsTo$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' * 'A$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_mapsTo$',axiom,
% 219.58/31.77 'mapsTo$'('c$','f$',fmb_'A$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_compDefined$',type,'compDefined$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_compDefined$',axiom,
% 219.58/31.77 'compDefined$'('set$') = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$',type,'case_prod$': 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_prod_ZF_fun$').
% 219.58/31.77 tff('function_case_prod$',axiom,
% 219.58/31.77 'case_prod$'('vah$') = fmb_'ZF_ZF_prod_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyq$',type,'uyq$': 'Nat_ZF_set_fun$' * 'Nat_nat_set_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uyq$',axiom,
% 219.58/31.77 'uyq$'('uxe$','uxf$') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$g',type,'sigma$g': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' > 'ZF_ZF_prod_ZF_prod_set$').
% 219.58/31.77 tff('function_sigma$g',axiom,
% 219.58/31.77 'sigma$g'('top$b',fmb_'ZF_ZF_prod_ZF_set_fun$'_1) = fmb_'ZF_ZF_prod_ZF_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwx$',type,'uwx$': 'Nat_ZF_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwx$',axiom,
% 219.58/31.77 'uwx$'(fmb_'Nat_ZF_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$f',type,'comp$f': 'ZF_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_comp$f',axiom,
% 219.58/31.77 'comp$f'(fmb_'ZF_set_ZF_set_set_fun$'_1,'sup$') = fmb_'ZF_set_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sup$c',type,'sup$c': 'B_set_set$' > 'B_set$').
% 219.58/31.77 tff('function_sup$c',axiom,
% 219.58/31.77 'sup$c'(fmb_'B_set_set$'_1) = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bk',type,'fun_app$bk': 'B_a_fun$' * 'B$' > 'A$').
% 219.58/31.77 tff('function_fun_app$bk',axiom,
% 219.58/31.77 'fun_app$bk'(fmb_'B_a_fun$'_1,'f$') = fmb_'A$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$z',type,'image$z': 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_image$z',axiom,
% 219.58/31.77 'image$z'(fmb_'ZF_ZF_ZF_prod_fun$'_1,'top$a') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_extensional$e',type,'extensional$e': 'B_set$' > 'B_ZF_fun_set$').
% 219.58/31.77 tff('function_extensional$e',axiom,
% 219.58/31.77 'extensional$e'(fmb_'B_set$'_1) = fmb_'B_ZF_fun_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_rec_unit$',type,'rec_unit$': 'ZF$' * 'Unit$' > 'ZF$').
% 219.58/31.77 tff('function_rec_unit$',axiom,
% 219.58/31.77 'rec_unit$'(fmb_'ZF$'_1,'unity$') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzv$',type,'uzv$': 'ZF_ZF_bool_fun_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uzv$',axiom,
% 219.58/31.77 'uzv$'('uug$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_member$c',type,'member$c': 'A$' > 'A_set_bool_fun$').
% 219.58/31.77 tff('function_member$c',axiom,
% 219.58/31.77 'member$c'(fmb_'A$'_1) = fmb_'A_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inf$',type,'inf$': 'ZF_set_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_inf$',axiom,
% 219.58/31.77 'inf$'(fmb_'ZF_set_set$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sup$h',type,'sup$h': 'B_bool_fun_set$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_sup$h',axiom,
% 219.58/31.77 'sup$h'(fmb_'B_bool_fun_set$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_cod_update$',type,'cod_update$': 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_cod_update$',axiom,
% 219.58/31.77 'cod_update$'('uym$','set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_rec_bool$',type,'rec_bool$': 'ZF$' * 'ZF$' * tlbool > 'ZF$').
% 219.58/31.77 tff('function_rec_bool$',axiom,
% 219.58/31.77 'rec_bool$'(fmb_'ZF$'_1,fmb_'ZF$'_1,tltrue) = fmb_'ZF$'_1
% 219.58/31.77 % 'rec_bool$'(fmb_'ZF$'_1,fmb_'ZF$'_1,tlfalse) undefined in model
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_member$a',type,'member$a': 'ZF_set$' > 'ZF_set_set_bool_fun$').
% 219.58/31.77 tff('function_member$a',axiom,
% 219.58/31.77 'member$a'('top$a') = fmb_'ZF_set_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyh$',type,'uyh$': 'ZF_ZF_fun$' * 'ZF_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyh$',axiom,
% 219.58/31.77 'uyh$'('uur$','top$a') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_extensional$d',type,'extensional$d': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_fun_set$').
% 219.58/31.77 tff('function_extensional$d',axiom,
% 219.58/31.77 'extensional$d'('top$b') = fmb_'ZF_ZF_prod_ZF_fun_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$av',type,'fun_app$av': 'ZF_ZF_ZF_prod_set_fun$' * 'ZF$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_fun_app$av',axiom,
% 219.58/31.77 'fun_app$av'(fmb_'ZF_ZF_ZF_prod_set_fun$'_1,fmb_'ZF$'_1) = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$dd',type,'fun_app$dd': 'ZF_set_set_ZF_set_set_set_fun$' * 'ZF_set_set$' > 'ZF_set_set_set$').
% 219.58/31.77 tff('function_fun_app$dd',axiom,
% 219.58/31.77 'fun_app$dd'(fmb_'ZF_set_set_ZF_set_set_set_fun$'_1,fmb_'ZF_set_set$'_1) = fmb_'ZF_set_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$k',type,'sigma$k': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff('function_sigma$k',axiom,
% 219.58/31.77 'sigma$k'('top$b',fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1) = fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_restrict$a',type,'restrict$a': 'B_b_prod_b_fun$' * 'B_b_prod_set$' * 'B_b_prod$' > 'B$').
% 219.58/31.77 tff('function_restrict$a',axiom,
% 219.58/31.77 'restrict$a'(fmb_'B_b_prod_b_fun$'_1,fmb_'B_b_prod_set$'_1,fmb_'B_b_prod$'_1) = 'f$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ai',type,'fun_app$ai': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' > 'ZF$').
% 219.58/31.77 tff('function_fun_app$ai',axiom,
% 219.58/31.77 'fun_app$ai'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_prod$'_1) = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwk$',type,'uwk$': 'ZF_ZF_set_fun$' * 'ZF_set$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uwk$',axiom,
% 219.58/31.77 'uwk$'('uxc$','top$a') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cr',type,'fun_app$cr': 'A_a_set_fun$' * 'A$' > 'A_set$').
% 219.58/31.77 tff('function_fun_app$cr',axiom,
% 219.58/31.77 'fun_app$cr'(fmb_'A_a_set_fun$'_1,fmb_'A$'_1) = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_obj_update$',type,'obj_update$': 'A_set_a_set_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_obj_update$',axiom,
% 219.58/31.77 'obj_update$'(fmb_'A_set_a_set_fun$'_1,'c$') = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uux$',type,'uux$': 'A_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_uux$',axiom,
% 219.58/31.77 'uux$'(fmb_'A_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bq',type,'image$bq': 'Nat_nat_fun_ZF_set_fun$' * 'Nat_nat_fun_set$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_image$bq',axiom,
% 219.58/31.77 'image$bq'(fmb_'Nat_nat_fun_ZF_set_fun$'_1,'top$i') = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwd$',type,'uwd$': 'ZF_set_a_fun$' * 'ZF_set_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_uwd$',axiom,
% 219.58/31.77 'uwd$'(fmb_'ZF_set_a_fun$'_1,fmb_'ZF_set_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyb$',type,'uyb$': 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff('function_uyb$',axiom,
% 219.58/31.77 'uyb$'('uxe$','uxe$') = fmb_'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_id_update$',type,'id_update$': 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_id_update$',axiom,
% 219.58/31.77 'id_update$'('uym$','set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$e',type,'image$e': 'A_set_bool_fun$' * 'A_set_set$' > 'Bool_set$').
% 219.58/31.77 tff('function_image$e',axiom,
% 219.58/31.77 'image$e'(fmb_'A_set_bool_fun$'_1,fmb_'A_set_set$'_1) = fmb_'Bool_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$o',type,'fun_app$o': 'A_set_a_bool_fun_fun$' * 'A_set$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_fun_app$o',axiom,
% 219.58/31.77 'fun_app$o'('uu$',fmb_'A_set$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inverse_rel$',type,'inverse_rel$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_inverse_rel$',axiom,
% 219.58/31.77 'inverse_rel$'('c$','f$') = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapO$b',type,'mapO$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$').
% 219.58/31.77 tff('function_mapO$b',axiom,
% 219.58/31.77 'mapO$b'(fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1) = 'uur$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$co',type,'fun_app$co': 'A_ZF_set_fun$' * 'A$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$co',axiom,
% 219.58/31.77 'fun_app$co'(fmb_'A_ZF_set_fun$'_1,fmb_'A$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwp$',type,'uwp$': 'ZF_set_ZF_fun$' * 'ZF_set_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwp$',axiom,
% 219.58/31.77 'uwp$'(fmb_'ZF_set_ZF_fun$'_1,fmb_'ZF_set_set$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bn',type,'fun_app$bn': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' * 'ZF$' > 'ZF_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_fun_app$bn',axiom,
% 219.58/31.77 'fun_app$bn'(fmb_'ZF_ZF_ZF_ZF_prod_set_fun_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uye$',type,'uye$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_uye$',axiom,
% 219.58/31.77 'uye$'('top$b') = fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$g',type,'comp$g': 'ZF_set_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_set_set_fun$' > 'ZF_ZF_prod_set_set_ZF_set_fun$').
% 219.58/31.77 tff('function_comp$g',axiom,
% 219.58/31.77 'comp$g'('sup$',fmb_'ZF_ZF_prod_set_set_ZF_set_set_fun$'_1) = fmb_'ZF_ZF_prod_set_set_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sup$j',type,'sup$j': 'ZF_bool_fun_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_sup$j',axiom,
% 219.58/31.77 'sup$j'(fmb_'ZF_bool_fun_set$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$f',type,'image$f': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set_ZF_set_fun$').
% 219.58/31.77 tff('function_image$f',axiom,
% 219.58/31.77 'image$f'(fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uww$',type,'uww$': 'Nat_ZF_set_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uww$',axiom,
% 219.58/31.77 'uww$'('uxe$') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$',type,'image$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_image$',axiom,
% 219.58/31.77 'image$'('uxe$') = fmb_'Nat_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$aa',type,'fun_app$aa': 'Nat_nat_ZF_set_fun_fun$' * 'Nat$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_fun_app$aa',axiom,
% 219.58/31.77 'fun_app$aa'(fmb_'Nat_nat_ZF_set_fun_fun$'_1,fmb_'Nat$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cg',type,'fun_app$cg': 'ZF_ZF_prod_nat_set_fun$' * 'ZF_ZF_prod$' > 'Nat_set$').
% 219.58/31.77 tff('function_fun_app$cg',axiom,
% 219.58/31.77 'fun_app$cg'(fmb_'ZF_ZF_prod_nat_set_fun$'_1,fmb_'ZF_ZF_prod$'_1) = 'top$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ac',type,'image$ac': 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$' * 'ZF_nat_prod_set$' > 'ZF_set_ZF_set_prod_set$').
% 219.58/31.77 tff('function_image$ac',axiom,
% 219.58/31.77 'image$ac'(fmb_'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'_1,'top$c') = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_converse$',type,'converse$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_converse$',axiom,
% 219.58/31.77 'converse$'('top$b') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwv$',type,'uwv$': 'ZF_ZF_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwv$',axiom,
% 219.58/31.77 'uwv$'('uur$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzb$',type,'uzb$': 'Nat_ZF_ZF_set_fun_fun$' * 'ZF_set$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uzb$',axiom,
% 219.58/31.77 'uzb$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1,'top$a') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxi$',type,'uxi$': 'ZF_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uxi$',axiom,
% 219.58/31.77 'uxi$'('top$a') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxl$',type,'uxl$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uxl$',axiom,
% 219.58/31.77 'uxl$'('uug$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bf',type,'fun_app$bf': 'A_ZF_fun$' * 'A$' > 'ZF$').
% 219.58/31.77 tff('function_fun_app$bf',axiom,
% 219.58/31.77 'fun_app$bf'(fmb_'A_ZF_fun$'_1,fmb_'A$'_1) = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxh$',type,'uxh$': 'ZF_bool_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uxh$',axiom,
% 219.58/31.77 'uxh$'('uut$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$j',type,'comp$j': 'ZF_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_fun$').
% 219.58/31.77 tff('function_comp$j',axiom,
% 219.58/31.77 'comp$j'('uyn$','sup$') = 'sup$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_gr$',type,'gr$': 'ZF_set$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_set_prod_set$').
% 219.58/31.77 tff('function_gr$',axiom,
% 219.58/31.77 'gr$'('top$a','uxc$') = fmb_'ZF_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$e',type,'comp$e': 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_set_set_fun$' > 'ZF_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_comp$e',axiom,
% 219.58/31.77 'comp$e'('sup$e',fmb_'ZF_set_set_ZF_set_set_set_fun$'_1) = fmb_'ZF_set_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuh$',type,'uuh$': tlbool * 'ZF$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_uuh$',axiom,
% 219.58/31.77 'uuh$'(tltrue,fmb_'ZF$'_1) = 'uug$'
% 219.58/31.77 & 'uuh$'(tlfalse,fmb_'ZF$'_1) = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$f',type,'sigma$f': 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' > 'ZF_set_ZF_prod_set$').
% 219.58/31.77 tff('function_sigma$f',axiom,
% 219.58/31.77 'sigma$f'(fmb_'ZF_set_set$'_1,'uyn$') = fmb_'ZF_set_ZF_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$',type,'sigma$': 'ZF_set$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_sigma$',axiom,
% 219.58/31.77 'sigma$'('top$a','uxc$') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sup$i',type,'sup$i': 'ZF_set_bool_fun_set$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_sup$i',axiom,
% 219.58/31.77 'sup$i'(fmb_'ZF_set_bool_fun_set$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_pair$a',type,'pair$a': 'B$' * 'B$' > 'B_b_prod$').
% 219.58/31.77 tff('function_pair$a',axiom,
% 219.58/31.77 'pair$a'('f$','f$') = fmb_'B_b_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyp$',type,'uyp$': 'Nat_ZF_set_fun$' * 'ZF_nat_set_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyp$',axiom,
% 219.58/31.77 'uyp$'('uxe$','uxd$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vao$',type,'vao$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_vao$',axiom,
% 219.58/31.77 'vao$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1) = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzn$',type,'uzn$': 'Nat_ZF_set_fun$' > 'Nat_ZF_ZF_set_fun_fun$').
% 219.58/31.77 tff('function_uzn$',axiom,
% 219.58/31.77 'uzn$'('uxe$') = fmb_'Nat_ZF_ZF_set_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$m',type,'image$m': 'B_a_fun$' * 'B_set$' > 'A_set$').
% 219.58/31.77 tff('function_image$m',axiom,
% 219.58/31.77 'image$m'(fmb_'B_a_fun$'_1,fmb_'B_set$'_1) = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzs$',type,'uzs$': 'ZF_ZF_set_fun$' * 'ZF_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uzs$',axiom,
% 219.58/31.77 'uzs$'('uxc$','top$a') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$a',type,'case_prod$a': 'B_b_b_fun_fun$' > 'B_b_prod_b_fun$').
% 219.58/31.77 tff('function_case_prod$a',axiom,
% 219.58/31.77 'case_prod$a'(fmb_'B_b_b_fun_fun$'_1) = fmb_'B_b_prod_b_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzp$',type,'uzp$': 'Nat_ZF_set_fun$' * 'Nat_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uzp$',axiom,
% 219.58/31.77 'uzp$'('uxe$','top$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_collect$i',type,'collect$i': 'B_bool_fun$' > 'B_set$').
% 219.58/31.77 tff('function_collect$i',axiom,
% 219.58/31.77 'collect$i'(fmb_'B_bool_fun$'_1) = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uve$',type,'uve$': 'ZF_set_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uve$',axiom,
% 219.58/31.77 'uve$'('uyn$','uxe$') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyc$',type,'uyc$': 'Nat_set$' > 'Nat_nat_set_fun$').
% 219.58/31.77 tff('function_uyc$',axiom,
% 219.58/31.77 'uyc$'('top$') = 'uxf$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$a',type,'image$a': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_image$a',axiom,
% 219.58/31.77 'image$a'('uxc$') = fmb_'ZF_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bc',type,'image$bc': 'Nat_ZF_set_set_fun$' * 'Nat_set$' > 'ZF_set_set_set$').
% 219.58/31.77 tff('function_image$bc',axiom,
% 219.58/31.77 'image$bc'(fmb_'Nat_ZF_set_set_fun$'_1,'top$') = fmb_'ZF_set_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_makeCat$',type,'makeCat$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_makeCat$',axiom,
% 219.58/31.77 'makeCat$'('c$') = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$p',type,'image$p': 'A_a_fun$' > 'A_set_a_set_fun$').
% 219.58/31.77 tff('function_image$p',axiom,
% 219.58/31.77 'image$p'(fmb_'A_a_fun$'_1) = fmb_'A_set_a_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bh',type,'image$bh': 'A_set_a_bool_fun_fun$' * 'A_set_set$' > 'A_bool_fun_set$').
% 219.58/31.77 tff('function_image$bh',axiom,
% 219.58/31.77 'image$bh'('uu$',fmb_'A_set_set$'_1) = fmb_'A_bool_fun_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$aq',type,'fun_app$aq': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' * 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('function_fun_app$aq',axiom,
% 219.58/31.77 'fun_app$aq'('uuv$','vah$') = 'vah$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mor$a',type,'mor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$').
% 219.58/31.77 tff('function_mor$a',axiom,
% 219.58/31.77 'mor$a'('set$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxa$',type,'uxa$': 'Nat_ZF_set_fun$' * 'Nat_set$' > 'ZF_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_uxa$',axiom,
% 219.58/31.77 'uxa$'('uxe$','top$') = fmb_'ZF_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$c',type,'sigma$c': 'Nat_set$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_prod_set$').
% 219.58/31.77 tff('function_sigma$c',axiom,
% 219.58/31.77 'sigma$c'('top$','uxe$') = 'top$d'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_catDom$',type,'catDom$': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_catDom$',axiom,
% 219.58/31.77 'catDom$'(fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1) = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uui$',type,'uui$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_prod_bool_fun$').
% 219.58/31.77 tff('function_uui$',axiom,
% 219.58/31.77 'uui$'('c$') = fmb_'B_b_prod_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuz$',type,'uuz$': 'ZF_set_set$' * 'ZF_set_bool_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uuz$',axiom,
% 219.58/31.77 'uuz$'(fmb_'ZF_set_set$'_1,fmb_'ZF_set_bool_fun$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuj$',type,'uuj$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_prod_bool_fun$').
% 219.58/31.77 tff('function_uuj$',axiom,
% 219.58/31.77 'uuj$'('set$') = fmb_'ZF_ZF_prod_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_extensional$a',type,'extensional$a': 'ZF_set$' > 'ZF_ZF_fun_set$').
% 219.58/31.77 tff('function_extensional$a',axiom,
% 219.58/31.77 'extensional$a'('top$a') = 'top$f'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ay',type,'fun_app$ay': 'Nat_ZF_set_set_fun$' * 'Nat$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_fun_app$ay',axiom,
% 219.58/31.77 'fun_app$ay'(fmb_'Nat_ZF_set_set_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzg$',type,'uzg$': 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uzg$',axiom,
% 219.58/31.77 'uzg$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1,'top$') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$e',type,'sigma$e': 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' > 'ZF_ZF_ZF_prod_prod_set$').
% 219.58/31.77 tff('function_sigma$e',axiom,
% 219.58/31.77 'sigma$e'('top$a',fmb_'ZF_ZF_ZF_prod_set_fun$'_1) = fmb_'ZF_ZF_ZF_prod_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$az',type,'fun_app$az': 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' > 'ZF_ZF_prod$').
% 219.58/31.77 tff('function_fun_app$az',axiom,
% 219.58/31.77 'fun_app$az'('swap$',fmb_'ZF_ZF_prod$'_1) = fmb_'ZF_ZF_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwr$',type,'uwr$': 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_ZF_prod_fun$' > 'Nat_ZF_fun$').
% 219.58/31.77 tff('function_uwr$',axiom,
% 219.58/31.77 'uwr$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'Nat_ZF_ZF_prod_fun$'_1) = fmb_'Nat_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ah',type,'image$ah': 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$' * 'Nat_nat_prod_set$' > 'ZF_set_ZF_set_prod_set$').
% 219.58/31.77 tff('function_image$ah',axiom,
% 219.58/31.77 'image$ah'(fmb_'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'_1,'top$e') = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$h',type,'image$h': 'ZF_b_fun$' * 'ZF_set$' > 'B_set$').
% 219.58/31.77 tff('function_image$h',axiom,
% 219.58/31.77 'image$h'(fmb_'ZF_b_fun$'_1,'top$a') = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwt$',type,'uwt$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwt$',axiom,
% 219.58/31.77 'uwt$'(fmb_'ZF_ZF_prod_ZF_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyv$',type,'uyv$': 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyv$',axiom,
% 219.58/31.77 'uyv$'('uyk$','top$a') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_repl$',type,'repl$': 'ZF$' * 'ZF_ZF_fun$' > 'ZF$').
% 219.58/31.77 tff('function_repl$',axiom,
% 219.58/31.77 'repl$'(fmb_'ZF$'_1,'uur$') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inf$b',type,'inf$b': 'B_set_set$' > 'B_set$').
% 219.58/31.77 tff('function_inf$b',axiom,
% 219.58/31.77 'inf$b'(fmb_'B_set_set$'_1) = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$x',type,'fun_app$x': 'ZF_set_ZF_set_set_fun$' * 'ZF_set$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_fun_app$x',axiom,
% 219.58/31.77 'fun_app$x'(fmb_'ZF_set_ZF_set_set_fun$'_1,'top$a') = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$d',type,'comp$d': 'Nat_set_ZF_set_set_fun$' * 'Nat_set_set_nat_set_fun$' > 'Nat_set_set_ZF_set_set_fun$').
% 219.58/31.77 tff('function_comp$d',axiom,
% 219.58/31.77 'comp$d'(fmb_'Nat_set_ZF_set_set_fun$'_1,'sup$f') = fmb_'Nat_set_set_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_val$',type,'val$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_val$',axiom,
% 219.58/31.77 'val$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_obj_update$a',type,'obj_update$a': 'ZF_set_ZF_set_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_obj_update$a',axiom,
% 219.58/31.77 'obj_update$a'('uyn$','set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mor2ZF$',type,'mor2ZF$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_ZF_fun$').
% 219.58/31.77 tff('function_mor2ZF$',axiom,
% 219.58/31.77 'mor2ZF$'('c$') = fmb_'B_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uva$',type,'uva$': 'ZF_set$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uva$',axiom,
% 219.58/31.77 'uva$'('top$a','uut$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp_update$',type,'comp_update$': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_comp_update$',axiom,
% 219.58/31.77 'comp_update$'('uuv$','set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxy$',type,'uxy$': 'ZF_set$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uxy$',axiom,
% 219.58/31.77 'uxy$'('top$a') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvg$',type,'uvg$': 'ZF_ZF_set_fun$' * 'Nat_ZF_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uvg$',axiom,
% 219.58/31.77 'uvg$'('uxc$',fmb_'Nat_ZF_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvi$',type,'uvi$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' > 'ZF_ZF_prod_ZF_fun$').
% 219.58/31.77 tff('function_uvi$',axiom,
% 219.58/31.77 'uvi$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'swap$') = fmb_'ZF_ZF_prod_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ca',type,'fun_app$ca': 'Nat_ZF_set_ZF_set_prod_fun$' * 'Nat$' > 'ZF_set_ZF_set_prod$').
% 219.58/31.77 tff('function_fun_app$ca',axiom,
% 219.58/31.77 'fun_app$ca'(fmb_'Nat_ZF_set_ZF_set_prod_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_set_ZF_set_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvb$',type,'uvb$': 'ZF_bool_fun$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uvb$',axiom,
% 219.58/31.77 'uvb$'('uut$','uut$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bj',type,'image$bj': 'ZF_set_set_ZF_set_bool_fun_fun$' * 'ZF_set_set_set$' > 'ZF_set_bool_fun_set$').
% 219.58/31.77 tff('function_image$bj',axiom,
% 219.58/31.77 'image$bj'('uub$',fmb_'ZF_set_set_set$'_1) = fmb_'ZF_set_bool_fun_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bw',type,'fun_app$bw': 'ZF_ZF_prod_ZF_set_ZF_prod_fun$' * 'ZF_ZF_prod$' > 'ZF_set_ZF_prod$').
% 219.58/31.77 tff('function_fun_app$bw',axiom,
% 219.58/31.77 'fun_app$bw'(fmb_'ZF_ZF_prod_ZF_set_ZF_prod_fun$'_1,fmb_'ZF_ZF_prod$'_1) = fmb_'ZF_set_ZF_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuk$',type,'uuk$': 'ZF_ZF_fun$' > 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$').
% 219.58/31.77 tff('function_uuk$',axiom,
% 219.58/31.77 'uuk$'('uur$') = 'uuv$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_gr$a',type,'gr$a': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_prod_set$').
% 219.58/31.77 tff('function_gr$a',axiom,
% 219.58/31.77 'gr$a'('top$b',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_ZF_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxb$',type,'uxb$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uxb$',axiom,
% 219.58/31.77 'uxb$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'top$b') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_dom_update$',type,'dom_update$': 'B_a_fun_b_a_fun_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_dom_update$',axiom,
% 219.58/31.77 'dom_update$'(fmb_'B_a_fun_b_a_fun_fun$'_1,'c$') = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vaw$',type,'vaw$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_vaw$',axiom,
% 219.58/31.77 'vaw$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_zFfun$',type,'zFfun$': 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' > 'ZF$').
% 219.58/31.77 tff('function_zFfun$',axiom,
% 219.58/31.77 'zFfun$'(fmb_'ZF$'_1,fmb_'ZF$'_1,'uur$') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cx',type,'fun_app$cx': 'B_ZF_set_fun$' * 'B$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$cx',axiom,
% 219.58/31.77 'fun_app$cx'(fmb_'B_ZF_set_fun$'_1,'f$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$az',type,'image$az': 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.77 tff('function_image$az',axiom,
% 219.58/31.77 'image$az'(fmb_'ZF_ZF_ZF_prod_set_fun$'_1,'top$a') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vba$',type,'vba$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_vba$',axiom,
% 219.58/31.77 'vba$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvo$',type,'uvo$': 'B_a_fun$' * 'B_set$' * 'A_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uvo$',axiom,
% 219.58/31.77 'uvo$'(fmb_'B_a_fun$'_1,fmb_'B_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$as',type,'image$as': 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.77 tff('function_image$as',axiom,
% 219.58/31.77 'image$as'(fmb_'ZF_set_ZF_ZF_prod_set_fun$'_1,fmb_'ZF_set_set$'_1) = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$h',type,'comp$h': 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set_set_ZF_set_fun$').
% 219.58/31.77 tff('function_comp$h',axiom,
% 219.58/31.77 'comp$h'(fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1,'sup$d') = fmb_'ZF_ZF_prod_set_set_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_pair$',type,'pair$': 'ZF$' > 'ZF_ZF_ZF_prod_fun$').
% 219.58/31.77 tff('function_pair$',axiom,
% 219.58/31.77 'pair$'(fmb_'ZF$'_1) = fmb_'ZF_ZF_ZF_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$n',type,'case_prod$n': 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' > 'Nat_ZF_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_case_prod$n',axiom,
% 219.58/31.77 'case_prod$n'(fmb_'Nat_ZF_ZF_ZF_prod_set_fun_fun$'_1) = fmb_'Nat_ZF_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvh$',type,'uvh$': 'ZF_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_set_fun$').
% 219.58/31.77 tff('function_uvh$',axiom,
% 219.58/31.77 'uvh$'('uxc$',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vac$',type,'vac$': 'Nat_ZF_set_fun$' > 'Nat_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_vac$',axiom,
% 219.58/31.77 'vac$'('uxe$') = fmb_'Nat_ZF_bool_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$w',type,'fun_app$w': 'ZF_nat_fun_ZF_set_fun$' * 'ZF_nat_fun$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$w',axiom,
% 219.58/31.77 'fun_app$w'(fmb_'ZF_nat_fun_ZF_set_fun$'_1,fmb_'ZF_nat_fun$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vax$',type,'vax$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_fun_ZF_set_fun$').
% 219.58/31.77 tff('function_vax$',axiom,
% 219.58/31.77 'vax$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_ZF_fun_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$an',type,'image$an': 'B_b_set_fun$' * 'B_set$' > 'B_set_set$').
% 219.58/31.77 tff('function_image$an',axiom,
% 219.58/31.77 'image$an'(fmb_'B_b_set_fun$'_1,fmb_'B_set$'_1) = fmb_'B_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_obj$a',type,'obj$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$').
% 219.58/31.77 tff('function_obj$a',axiom,
% 219.58/31.77 'obj$a'('set$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwf$',type,'uwf$': 'Nat_ZF_set_fun$' * 'Nat_bool_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uwf$',axiom,
% 219.58/31.77 'uwf$'('uxe$','uws$') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvr$',type,'uvr$': 'B_b_fun$' * 'B_set$' * 'B_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uvr$',axiom,
% 219.58/31.77 'uvr$'(fmb_'B_b_fun$'_1,fmb_'B_set$'_1,fmb_'B_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwu$',type,'uwu$': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uwu$',axiom,
% 219.58/31.77 'uwu$'('uxc$') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$aj',type,'fun_app$aj': 'Nat_ZF_fun$' * 'Nat$' > 'ZF$').
% 219.58/31.77 tff('function_fun_app$aj',axiom,
% 219.58/31.77 'fun_app$aj'(fmb_'Nat_ZF_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzm$',type,'uzm$': 'ZF_ZF_fun$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uzm$',axiom,
% 219.58/31.77 'uzm$'('uur$','uxe$') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ct',type,'fun_app$ct': 'B_a_set_fun$' * 'B$' > 'A_set$').
% 219.58/31.77 tff('function_fun_app$ct',axiom,
% 219.58/31.77 'fun_app$ct'(fmb_'B_a_set_fun$'_1,'f$') = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvu$',type,'uvu$': 'ZF_a_fun$' * 'ZF_set$' * 'A_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uvu$',axiom,
% 219.58/31.77 'uvu$'(fmb_'ZF_a_fun$'_1,'top$a',fmb_'A_bool_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uze$',type,'uze$': 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uze$',axiom,
% 219.58/31.77 'uze$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1,'top$') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ax',type,'image$ax': 'Nat_nat_set_fun$' * 'Nat_set$' > 'Nat_set_set$').
% 219.58/31.77 tff('function_image$ax',axiom,
% 219.58/31.77 'image$ax'('uxf$','top$') = fmb_'Nat_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyl$',type,'uyl$': 'ZF$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_uyl$',axiom,
% 219.58/31.77 'uyl$'(fmb_'ZF$'_1) = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$l',type,'case_prod$l': 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_case_prod$l',axiom,
% 219.58/31.77 'case_prod$l'(fmb_'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'_1) = fmb_'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uun$',type,'uun$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('function_uun$',axiom,
% 219.58/31.77 'uun$'('set$') = 'vah$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cn',type,'fun_app$cn': 'ZF_set_set_ZF_set_set_fun$' * 'ZF_set_set$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_fun_app$cn',axiom,
% 219.58/31.77 'fun_app$cn'(fmb_'ZF_set_set_ZF_set_set_fun$'_1,fmb_'ZF_set_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bb',type,'image$bb': 'ZF_ZF_set_set_fun$' * 'ZF_set$' > 'ZF_set_set_set$').
% 219.58/31.77 tff('function_image$bb',axiom,
% 219.58/31.77 'image$bb'(fmb_'ZF_ZF_set_set_fun$'_1,'top$a') = fmb_'ZF_set_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyg$',type,'uyg$': 'ZF_ZF_fun$' * 'ZF_ZF_fun$' > 'ZF_ZF_ZF_ZF_prod_fun_fun$').
% 219.58/31.77 tff('function_uyg$',axiom,
% 219.58/31.77 'uyg$'('uur$','uur$') = 'uxj$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzd$',type,'uzd$': 'Nat_ZF_ZF_set_fun_fun$' * 'Nat_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uzd$',axiom,
% 219.58/31.77 'uzd$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1,'top$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_var$',type,'var$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_var$',axiom,
% 219.58/31.77 'var$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_homFtor$',type,'homFtor$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$').
% 219.58/31.77 tff('function_homFtor$',axiom,
% 219.58/31.77 'homFtor$'('c$',fmb_'A$'_1) = fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_category_ext$',type,'category_ext$': 'A_set$' * 'B_set$' * 'B_a_fun$' * 'B_a_fun$' * 'A_b_fun$' * 'B_b_b_fun_fun$' * 'B_c_LSCategory_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$').
% 219.58/31.77 tff('function_category_ext$',axiom,
% 219.58/31.77 'category_ext$'(fmb_'A_set$'_1,fmb_'B_set$'_1,fmb_'B_a_fun$'_1,fmb_'B_a_fun$'_1,fmb_'A_b_fun$'_1,fmb_'B_b_b_fun_fun$'_1,fmb_'B_c_LSCategory_ext$'_1) = 'c$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxk$',type,'uxk$': 'ZF_bool_fun$' * 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_uxk$',axiom,
% 219.58/31.77 'uxk$'('uut$','uug$') = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vau$',type,'vau$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_vau$',axiom,
% 219.58/31.77 'vau$'('uyk$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bm',type,'fun_app$bm': 'A_a_fun$' * 'A$' > 'A$').
% 219.58/31.77 tff('function_fun_app$bm',axiom,
% 219.58/31.77 'fun_app$bm'(fmb_'A_a_fun$'_1,fmb_'A$'_1) = fmb_'A$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxm$',type,'uxm$': 'ZF_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$').
% 219.58/31.77 tff('function_uxm$',axiom,
% 219.58/31.77 'uxm$'('uxc$',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vaf$',type,'vaf$': 'ZF_set_set_set$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_vaf$',axiom,
% 219.58/31.77 'vaf$'(fmb_'ZF_set_set_set$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_collect$b',type,'collect$b': 'B_b_prod_bool_fun$' > 'B_b_prod_set$').
% 219.58/31.77 tff('function_collect$b',axiom,
% 219.58/31.77 'collect$b'(fmb_'B_b_prod_bool_fun$'_1) = fmb_'B_b_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvz$',type,'uvz$': 'B_ZF_fun$' * 'B_set$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uvz$',axiom,
% 219.58/31.77 'uvz$'(fmb_'B_ZF_fun$'_1,fmb_'B_set$'_1,'uut$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_cod$',type,'cod$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$').
% 219.58/31.77 tff('function_cod$',axiom,
% 219.58/31.77 'cod$'('c$') = fmb_'B_a_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cy',type,'fun_app$cy': 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_fun_app$cy',axiom,
% 219.58/31.77 'fun_app$cy'('sup$d',fmb_'ZF_ZF_prod_set_set$'_1) = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$e',type,'case_prod$e': 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' > 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_case_prod$e',axiom,
% 219.58/31.77 'case_prod$e'(fmb_'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'_1) = fmb_'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$a',type,'sigma$a': 'ZF_set_set$' * 'ZF_set_ZF_set_set_fun$' > 'ZF_set_ZF_set_prod_set$').
% 219.58/31.77 tff('function_sigma$a',axiom,
% 219.58/31.77 'sigma$a'(fmb_'ZF_set_set$'_1,fmb_'ZF_set_ZF_set_set_fun$'_1) = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxg$',type,'uxg$': 'ZF_bool_fun$' * 'ZF_bool_fun$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_uxg$',axiom,
% 219.58/31.77 'uxg$'('uut$','uut$') = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxp$',type,'uxp$': 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff('function_uxp$',axiom,
% 219.58/31.77 'uxp$'('uxc$','uxe$') = fmb_'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sigma$h',type,'sigma$h': 'ZF_set$' * 'ZF_ZF_set_set_fun$' > 'ZF_ZF_set_prod_set$').
% 219.58/31.77 tff('function_sigma$h',axiom,
% 219.58/31.77 'sigma$h'('top$a',fmb_'ZF_ZF_set_set_fun$'_1) = fmb_'ZF_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapM$',type,'mapM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'B_ZF_fun$').
% 219.58/31.77 tff('function_mapM$',axiom,
% 219.58/31.77 'mapM$'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1) = fmb_'B_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_obj$',type,'obj$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_set$').
% 219.58/31.77 tff('function_obj$',axiom,
% 219.58/31.77 'obj$'('c$') = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inverse$',type,'inverse$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_fun$').
% 219.58/31.77 tff('function_inverse$',axiom,
% 219.58/31.77 'inverse$'('c$') = fmb_'B_b_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxq$',type,'uxq$': 'Nat_set$' > 'ZF_nat_set_fun$').
% 219.58/31.77 tff('function_uxq$',axiom,
% 219.58/31.77 'uxq$'('top$') = 'uxd$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxo$',type,'uxo$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' > 'ZF_set_ZF_set_fun$').
% 219.58/31.77 tff('function_uxo$',axiom,
% 219.58/31.77 'uxo$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'top$b') = 'uyn$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvv$',type,'uvv$': 'ZF_b_fun$' * 'ZF_set$' * 'B_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uvv$',axiom,
% 219.58/31.77 'uvv$'(fmb_'ZF_b_fun$'_1,'top$a',fmb_'B_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bc',type,'fun_app$bc': 'ZF_nat_set_fun$' * 'ZF$' > 'Nat_set$').
% 219.58/31.77 tff('function_fun_app$bc',axiom,
% 219.58/31.77 'fun_app$bc'('uxd$',fmb_'ZF$'_1) = 'top$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_collect$j',type,'collect$j': 'ZF_set_bool_fun$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_collect$j',axiom,
% 219.58/31.77 'collect$j'(fmb_'ZF_set_bool_fun$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uud$',type,'uud$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$').
% 219.58/31.77 tff('function_uud$',axiom,
% 219.58/31.77 'uud$'('c$') = fmb_'B_b_b_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cd',type,'fun_app$cd': 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' * 'Nat$' > 'ZF_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_fun_app$cd',axiom,
% 219.58/31.77 'fun_app$cd'(fmb_'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cc',type,'fun_app$cc': 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' * 'Nat$' > 'ZF_ZF_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff('function_fun_app$cc',axiom,
% 219.58/31.77 'fun_app$cc'(fmb_'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_ZF_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzu$',type,'uzu$': 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff('function_uzu$',axiom,
% 219.58/31.77 'uzu$'('uxc$','uxc$') = fmb_'ZF_ZF_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vam$',type,'vam$': 'ZF_nat_ZF_set_fun_fun$' * 'Nat_ZF_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_vam$',axiom,
% 219.58/31.77 'vam$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1,fmb_'Nat_ZF_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvc$',type,'uvc$': 'ZF_set_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uvc$',axiom,
% 219.58/31.77 'uvc$'('uyn$','uxc$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ad',type,'fun_app$ad': 'ZF_ZF_ZF_set_fun_fun$' * 'ZF$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_fun_app$ad',axiom,
% 219.58/31.77 'fun_app$ad'('uyk$',fmb_'ZF$'_1) = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$be',type,'fun_app$be': 'ZF_set_ZF_fun$' * 'ZF_set$' > 'ZF$').
% 219.58/31.77 tff('function_fun_app$be',axiom,
% 219.58/31.77 'fun_app$be'(fmb_'ZF_set_ZF_fun$'_1,'top$a') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uza$',type,'uza$': 'ZF_nat_ZF_set_fun_fun$' * 'ZF_set$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_uza$',axiom,
% 219.58/31.77 'uza$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1,'top$a') = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapsTo$a',type,'mapsTo$a': 'ZF_ZF_unit_Category_ext$' * 'ZF$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_mapsTo$a',axiom,
% 219.58/31.77 'mapsTo$a'('set$',fmb_'ZF$'_1) = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$aq',type,'image$aq': 'A_ZF_set_fun$' * 'A_set$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_image$aq',axiom,
% 219.58/31.77 'image$aq'(fmb_'A_ZF_set_fun$'_1,fmb_'A_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bd',type,'fun_app$bd': 'Nat_nat_set_fun$' * 'Nat$' > 'Nat_set$').
% 219.58/31.77 tff('function_fun_app$bd',axiom,
% 219.58/31.77 'fun_app$bd'('uxf$',fmb_'Nat$'_1) = 'top$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bp',type,'fun_app$bp': 'ZF_nat_ZF_ZF_prod_set_fun_fun$' * 'ZF$' > 'Nat_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_fun_app$bp',axiom,
% 219.58/31.77 'fun_app$bp'(fmb_'ZF_nat_ZF_ZF_prod_set_fun_fun$'_1,fmb_'ZF$'_1) = fmb_'Nat_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvp$',type,'uvp$': 'A_b_fun$' * 'A_set$' * 'B_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uvp$',axiom,
% 219.58/31.77 'uvp$'(fmb_'A_b_fun$'_1,fmb_'A_set$'_1,fmb_'B_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bi',type,'fun_app$bi': 'ZF_a_fun$' * 'ZF$' > 'A$').
% 219.58/31.77 tff('function_fun_app$bi',axiom,
% 219.58/31.77 'fun_app$bi'(fmb_'ZF_a_fun$'_1,fmb_'ZF$'_1) = fmb_'A$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$al',type,'image$al': 'A_b_set_fun$' * 'A_set$' > 'B_set_set$').
% 219.58/31.77 tff('function_image$al',axiom,
% 219.58/31.77 'image$al'(fmb_'A_b_set_fun$'_1,fmb_'A_set$'_1) = fmb_'B_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$f',type,'case_prod$f': 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_case_prod$f',axiom,
% 219.58/31.77 'case_prod$f'(fmb_'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'_1) = fmb_'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_sup$g',type,'sup$g': 'A_bool_fun_set$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_sup$g',axiom,
% 219.58/31.77 'sup$g'(fmb_'A_bool_fun_set$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_homFtorContra$a',type,'homFtorContra$a': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$').
% 219.58/31.77 tff('function_homFtorContra$a',axiom,
% 219.58/31.77 'homFtorContra$a'('c$',fmb_'A$'_1) = fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_homFtorContra$',type,'homFtorContra$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$').
% 219.58/31.77 tff('function_homFtorContra$',axiom,
% 219.58/31.77 'homFtorContra$'('c$',fmb_'A$'_1) = fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyz$',type,'uyz$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_ZF_set_fun_fun$').
% 219.58/31.77 tff('function_uyz$',axiom,
% 219.58/31.77 'uyz$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_ZF_ZF_set_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$w',type,'image$w': 'ZF_set_ZF_fun$' * 'ZF_set_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_image$w',axiom,
% 219.58/31.77 'image$w'(fmb_'ZF_set_ZF_fun$'_1,fmb_'ZF_set_set$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$u',type,'fun_app$u': 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$u',axiom,
% 219.58/31.77 'fun_app$u'('sup$',fmb_'ZF_set_set$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inf$a',type,'inf$a': 'A_set_set$' > 'A_set$').
% 219.58/31.77 tff('function_inf$a',axiom,
% 219.58/31.77 'inf$a'(fmb_'A_set_set$'_1) = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$db',type,'fun_app$db': 'Nat_set_set_ZF_set_set_set_fun$' * 'Nat_set_set$' > 'ZF_set_set_set$').
% 219.58/31.77 tff('function_fun_app$db',axiom,
% 219.58/31.77 'fun_app$db'(fmb_'Nat_set_set_ZF_set_set_set_fun$'_1,fmb_'Nat_set_set$'_1) = fmb_'ZF_set_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzw$',type,'uzw$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_uzw$',axiom,
% 219.58/31.77 'uzw$'('uug$') = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$n',type,'image$n': 'A_ZF_fun$' * 'A_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_image$n',axiom,
% 219.58/31.77 'image$n'(fmb_'A_ZF_fun$'_1,fmb_'A_set$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$r',type,'image$r': 'Nat_ZF_fun$' * 'Nat_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_image$r',axiom,
% 219.58/31.77 'image$r'(fmb_'Nat_ZF_fun$'_1,'top$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ak',type,'image$ak': 'A_a_set_fun$' * 'A_set$' > 'A_set_set$').
% 219.58/31.77 tff('function_image$ak',axiom,
% 219.58/31.77 'image$ak'(fmb_'A_a_set_fun$'_1,fmb_'A_set$'_1) = fmb_'A_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_compDefined$a',type,'compDefined$a': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_compDefined$a',axiom,
% 219.58/31.77 'compDefined$a'('c$','f$') = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_oppositeCategory$a',type,'oppositeCategory$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_oppositeCategory$a',axiom,
% 219.58/31.77 'oppositeCategory$a'('set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_the$',type,'the$': 'ZF_bool_fun$' > 'ZF$').
% 219.58/31.77 tff('function_the$',axiom,
% 219.58/31.77 'the$'('uut$') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ag',type,'image$ag': 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' * 'Nat_ZF_ZF_prod_prod_set$' > 'ZF_set_ZF_prod_set$').
% 219.58/31.77 tff('function_image$ag',axiom,
% 219.58/31.77 'image$ag'(fmb_'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1,fmb_'Nat_ZF_ZF_prod_prod_set$'_1) = fmb_'ZF_set_ZF_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwb$',type,'uwb$': 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwb$',axiom,
% 219.58/31.77 'uwb$'('uur$','top$a','uut$') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$a',type,'fun_app$a': 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_fun$' > 'ZF_ZF_fun$').
% 219.58/31.77 tff('function_fun_app$a',axiom,
% 219.58/31.77 'fun_app$a'('uym$','uur$') = 'uur$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvw$',type,'uvw$': 'ZF_b_fun$' * 'ZF_set$' * 'B_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uvw$',axiom,
% 219.58/31.77 'uvw$'(fmb_'ZF_b_fun$'_1,'top$a',fmb_'B_bool_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vap$',type,'vap$': 'Nat_ZF_ZF_set_fun_fun$' * 'ZF_nat_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_vap$',axiom,
% 219.58/31.77 'vap$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1,fmb_'ZF_nat_fun$'_1) = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$as',type,'fun_app$as': 'ZF_b_fun$' * 'ZF$' > 'B$').
% 219.58/31.77 tff('function_fun_app$as',axiom,
% 219.58/31.77 'fun_app$as'(fmb_'ZF_b_fun$'_1,fmb_'ZF$'_1) = 'f$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzf$',type,'uzf$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_ZF_set_fun_fun$').
% 219.58/31.77 tff('function_uzf$',axiom,
% 219.58/31.77 'uzf$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_nat_ZF_set_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ad',type,'image$ad': 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$' * 'ZF_ZF_prod_ZF_prod_set$' > 'ZF_ZF_set_prod_set$').
% 219.58/31.77 tff('function_image$ad',axiom,
% 219.58/31.77 'image$ad'(fmb_'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'_1,fmb_'ZF_ZF_prod_ZF_prod_set$'_1) = fmb_'ZF_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxv$',type,'uxv$': 'Nat_set$' > 'ZF_ZF_prod_nat_set_fun$').
% 219.58/31.77 tff('function_uxv$',axiom,
% 219.58/31.77 'uxv$'('top$') = fmb_'ZF_ZF_prod_nat_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$af',type,'fun_app$af': 'Nat_set_ZF_set_fun$' * 'Nat_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$af',axiom,
% 219.58/31.77 'fun_app$af'(fmb_'Nat_set_ZF_set_fun$'_1,'top$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$g',type,'image$g': 'ZF_ZF_fun$' > 'ZF_set_ZF_set_fun$').
% 219.58/31.77 tff('function_image$g',axiom,
% 219.58/31.77 'image$g'('uur$') = 'uyn$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_rec_set_bool$',type,'rec_set_bool$': 'ZF$' * 'ZF$' * tlbool > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_rec_set_bool$',axiom,
% 219.58/31.77 'rec_set_bool$'(fmb_'ZF$'_1,fmb_'ZF$'_1,tltrue) = 'uut$'
% 219.58/31.77 % 'rec_set_bool$'(fmb_'ZF$'_1,fmb_'ZF$'_1,tlfalse) undefined in model
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bh',type,'fun_app$bh': 'A_set_a_set_fun$' * 'A_set$' > 'A_set$').
% 219.58/31.77 tff('function_fun_app$bh',axiom,
% 219.58/31.77 'fun_app$bh'(fmb_'A_set_a_set_fun$'_1,fmb_'A_set$'_1) = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vag$',type,'vag$': 'ZF_set_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_vag$',axiom,
% 219.58/31.77 'vag$'(fmb_'ZF_set_set$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxr$',type,'uxr$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff('function_uxr$',axiom,
% 219.58/31.77 'uxr$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'uxc$') = fmb_'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$br',type,'fun_app$br': 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' * 'ZF_ZF_prod$' > 'ZF_ZF_prod_ZF_ZF_prod_fun$').
% 219.58/31.77 tff('function_fun_app$br',axiom,
% 219.58/31.77 'fun_app$br'(fmb_'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'_1,fmb_'ZF_ZF_prod$'_1) = 'swap$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bx',type,'fun_app$bx': 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' * 'ZF$' > 'ZF_ZF_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff('function_fun_app$bx',axiom,
% 219.58/31.77 'fun_app$bx'(fmb_'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_ZF_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$m',type,'case_prod$m': 'ZF_nat_ZF_ZF_prod_set_fun_fun$' > 'ZF_nat_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_case_prod$m',axiom,
% 219.58/31.77 'case_prod$m'(fmb_'ZF_nat_ZF_ZF_prod_set_fun_fun$'_1) = fmb_'ZF_nat_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$c',type,'case_prod$c': 'ZF_ZF_ZF_ZF_prod_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_fun$').
% 219.58/31.77 tff('function_case_prod$c',axiom,
% 219.58/31.77 'case_prod$c'('uxj$') = 'swap$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_gr$c',type,'gr$c': 'ZF_set$' * 'ZF_ZF_fun$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_gr$c',axiom,
% 219.58/31.77 'gr$c'('top$a','uur$') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvm$',type,'uvm$': 'A_a_fun$' * 'A_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_uvm$',axiom,
% 219.58/31.77 'uvm$'(fmb_'A_a_fun$'_1,fmb_'A_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvf$',type,'uvf$': 'ZF_ZF_set_fun$' * 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uvf$',axiom,
% 219.58/31.77 'uvf$'('uxc$','uur$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vaq$',type,'vaq$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$').
% 219.58/31.77 tff('function_vaq$',axiom,
% 219.58/31.77 'vaq$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1) = fmb_'ZF_nat_fun_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwn$',type,'uwn$': 'B_ZF_fun$' * 'B_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwn$',axiom,
% 219.58/31.77 'uwn$'(fmb_'B_ZF_fun$'_1,fmb_'B_set$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_identityFunctor$',type,'identityFunctor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$').
% 219.58/31.77 tff('function_identityFunctor$',axiom,
% 219.58/31.77 'identityFunctor$'('c$') = fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$i',type,'image$i': 'ZF_a_fun$' * 'ZF_set$' > 'A_set$').
% 219.58/31.77 tff('function_image$i',axiom,
% 219.58/31.77 'image$i'(fmb_'ZF_a_fun$'_1,'top$a') = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_lSCategory_ext$',type,'lSCategory_ext$': 'B_ZF_fun$' * 'C$' > 'B_c_LSCategory_ext$').
% 219.58/31.77 tff('function_lSCategory_ext$',axiom,
% 219.58/31.77 'lSCategory_ext$'(fmb_'B_ZF_fun$'_1,fmb_'C$'_1) = fmb_'B_c_LSCategory_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_identityFunctor$a',type,'identityFunctor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$').
% 219.58/31.77 tff('function_identityFunctor$a',axiom,
% 219.58/31.77 'identityFunctor$a'('set$') = fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ar',type,'fun_app$ar': 'B_ZF_fun$' * 'B$' > 'ZF$').
% 219.58/31.77 tff('function_fun_app$ar',axiom,
% 219.58/31.77 'fun_app$ar'(fmb_'B_ZF_fun$'_1,'f$') = fmb_'ZF$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_restrict$b',type,'restrict$b': 'B_a_fun$' * 'B_set$' > 'B_a_fun$').
% 219.58/31.77 tff('function_restrict$b',axiom,
% 219.58/31.77 'restrict$b'(fmb_'B_a_fun$'_1,fmb_'B_set$'_1) = fmb_'B_a_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$d',type,'fun_app$d': 'ZF_ZF_ZF_prod_fun$' * 'ZF$' > 'ZF_ZF_prod$').
% 219.58/31.77 tff('function_fun_app$d',axiom,
% 219.58/31.77 'fun_app$d'(fmb_'ZF_ZF_ZF_prod_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_ZF_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cp',type,'fun_app$cp': 'Nat_a_fun$' * 'Nat$' > 'A$').
% 219.58/31.77 tff('function_fun_app$cp',axiom,
% 219.58/31.77 'fun_app$cp'(fmb_'Nat_a_fun$'_1,fmb_'Nat$'_1) = fmb_'A$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyw$',type,'uyw$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_ZF_set_fun_fun$').
% 219.58/31.77 tff('function_uyw$',axiom,
% 219.58/31.77 'uyw$'('uyk$') = 'uyk$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$c',type,'image$c': 'ZF_set_set_bool_fun$' * 'ZF_set_set_set$' > 'Bool_set$').
% 219.58/31.77 tff('function_image$c',axiom,
% 219.58/31.77 'image$c'(fmb_'ZF_set_set_bool_fun$'_1,fmb_'ZF_set_set_set$'_1) = fmb_'Bool_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inverse_rel$a',type,'inverse_rel$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.77 tff('function_inverse_rel$a',axiom,
% 219.58/31.77 'inverse_rel$a'('set$') = 'uug$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$x',type,'image$x': 'Nat_a_fun$' * 'Nat_set$' > 'A_set$').
% 219.58/31.77 tff('function_image$x',axiom,
% 219.58/31.77 'image$x'(fmb_'Nat_a_fun$'_1,'top$') = fmb_'A_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$d',type,'case_prod$d': 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' > 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.77 tff('function_case_prod$d',axiom,
% 219.58/31.77 'case_prod$d'(fmb_'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1) = fmb_'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$g',type,'case_prod$g': 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_case_prod$g',axiom,
% 219.58/31.77 'case_prod$g'(fmb_'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'_1) = fmb_'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvy$',type,'uvy$': 'A_ZF_fun$' * 'A_set$' * 'ZF_bool_fun$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_uvy$',axiom,
% 219.58/31.77 'uvy$'(fmb_'A_ZF_fun$'_1,fmb_'A_set$'_1,'uut$') = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ab',type,'fun_app$ab': 'ZF_nat_ZF_set_fun_fun$' * 'ZF$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_fun_app$ab',axiom,
% 219.58/31.77 'fun_app$ab'(fmb_'ZF_nat_ZF_set_fun_fun$'_1,fmb_'ZF$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vai$',type,'vai$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_vai$',axiom,
% 219.58/31.77 'vai$'('uyk$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_van$',type,'van$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_fun_ZF_set_fun$').
% 219.58/31.77 tff('function_van$',axiom,
% 219.58/31.77 'van$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_ZF_fun_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvq$',type,'uvq$': 'A_b_fun$' * 'A_set$' * 'B_bool_fun$' > 'A_bool_fun$').
% 219.58/31.77 tff('function_uvq$',axiom,
% 219.58/31.77 'uvq$'(fmb_'A_b_fun$'_1,fmb_'A_set$'_1,fmb_'B_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxu$',type,'uxu$': 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_set_fun$' > 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$').
% 219.58/31.77 tff('function_uxu$',axiom,
% 219.58/31.77 'uxu$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'uxe$') = fmb_'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_member$',type,'member$': 'ZF$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_member$',axiom,
% 219.58/31.77 'member$'(fmb_'ZF$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vat$',type,'vat$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_fun_ZF_set_fun$').
% 219.58/31.77 tff('function_vat$',axiom,
% 219.58/31.77 'vat$'(fmb_'Nat_nat_ZF_set_fun_fun$'_1) = fmb_'Nat_nat_fun_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cu',type,'fun_app$cu': 'B_b_set_fun$' * 'B$' > 'B_set$').
% 219.58/31.77 tff('function_fun_app$cu',axiom,
% 219.58/31.77 'fun_app$cu'(fmb_'B_b_set_fun$'_1,'f$') = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwe$',type,'uwe$': 'ZF_set_a_fun$' * 'ZF_set_set$' * 'A_bool_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.77 tff('function_uwe$',axiom,
% 219.58/31.77 'uwe$'(fmb_'ZF_set_a_fun$'_1,fmb_'ZF_set_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uum$',type,'uum$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$').
% 219.58/31.77 tff('function_uum$',axiom,
% 219.58/31.77 'uum$'('c$') = fmb_'B_b_b_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyx$',type,'uyx$': 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyx$',axiom,
% 219.58/31.77 'uyx$'('uyk$','top$a') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$b',type,'image$b': 'ZF_set_bool_fun$' * 'ZF_set_set$' > 'Bool_set$').
% 219.58/31.77 tff('function_image$b',axiom,
% 219.58/31.77 'image$b'(fmb_'ZF_set_bool_fun$'_1,fmb_'ZF_set_set$'_1) = fmb_'Bool_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwo$',type,'uwo$': 'ZF_ZF_fun$' * 'ZF_set$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwo$',axiom,
% 219.58/31.77 'uwo$'('uur$','top$a') = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uya$',type,'uya$': 'ZF_ZF_prod_set$' > 'Nat_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_uya$',axiom,
% 219.58/31.77 'uya$'('top$b') = fmb_'Nat_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxs$',type,'uxs$': 'ZF_set$' > 'ZF_ZF_prod_ZF_set_fun$').
% 219.58/31.77 tff('function_uxs$',axiom,
% 219.58/31.77 'uxs$'('top$a') = fmb_'ZF_ZF_prod_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_hOMCollection$',type,'hOMCollection$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_set_fun$').
% 219.58/31.77 tff('function_hOMCollection$',axiom,
% 219.58/31.77 'hOMCollection$'('c$',fmb_'A$'_1) = fmb_'A_ZF_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$y',type,'image$y': 'Nat_b_fun$' * 'Nat_set$' > 'B_set$').
% 219.58/31.77 tff('function_image$y',axiom,
% 219.58/31.77 'image$y'(fmb_'Nat_b_fun$'_1,'top$') = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_case_prod$h',type,'case_prod$h': 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' > 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_case_prod$h',axiom,
% 219.58/31.77 'case_prod$h'(fmb_'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'_1) = fmb_'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ab',type,'image$ab': 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' * 'ZF_ZF_ZF_prod_prod_set$' > 'ZF_set_ZF_prod_set$').
% 219.58/31.77 tff('function_image$ab',axiom,
% 219.58/31.77 'image$ab'(fmb_'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1,fmb_'ZF_ZF_ZF_prod_prod_set$'_1) = fmb_'ZF_set_ZF_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$s',type,'fun_app$s': 'ZF_ZF_set_fun$' * 'ZF$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$s',axiom,
% 219.58/31.77 'fun_app$s'('uxc$',fmb_'ZF$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vaa$',type,'vaa$': 'ZF_nat_bool_fun_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.77 tff('function_vaa$',axiom,
% 219.58/31.77 'vaa$'(fmb_'ZF_nat_bool_fun_fun$'_1) = 'uxe$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyi$',type,'uyi$': 'ZF_set_set$' > 'ZF_ZF_set_set_fun$').
% 219.58/31.77 tff('function_uyi$',axiom,
% 219.58/31.77 'uyi$'(fmb_'ZF_set_set$'_1) = fmb_'ZF_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cq',type,'fun_app$cq': 'Nat_b_fun$' * 'Nat$' > 'B$').
% 219.58/31.77 tff('function_fun_app$cq',axiom,
% 219.58/31.77 'fun_app$cq'(fmb_'Nat_b_fun$'_1,fmb_'Nat$'_1) = 'f$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ae',type,'fun_app$ae': 'ZF_set_ZF_set_fun$' * 'ZF_set$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$ae',axiom,
% 219.58/31.77 'fun_app$ae'('uyn$','top$a') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_inverse$a',type,'inverse$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$').
% 219.58/31.77 tff('function_inverse$a',axiom,
% 219.58/31.77 'inverse$a'('set$') = 'uur$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_mapO$',type,'mapO$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$').
% 219.58/31.77 tff('function_mapO$',axiom,
% 219.58/31.77 'mapO$'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1) = fmb_'A_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$y',type,'fun_app$y': 'Nat_ZF_fun_ZF_set_fun$' * 'Nat_ZF_fun$' > 'ZF_set$').
% 219.58/31.77 tff('function_fun_app$y',axiom,
% 219.58/31.77 'fun_app$y'(fmb_'Nat_ZF_fun_ZF_set_fun$'_1,fmb_'Nat_ZF_fun$'_1) = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$ap',type,'image$ap': 'ZF_b_set_fun$' * 'ZF_set$' > 'B_set_set$').
% 219.58/31.77 tff('function_image$ap',axiom,
% 219.58/31.77 'image$ap'(fmb_'ZF_b_set_fun$'_1,'top$a') = fmb_'B_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bu',type,'fun_app$bu': 'Nat_ZF_ZF_set_prod_fun$' * 'Nat$' > 'ZF_ZF_set_prod$').
% 219.58/31.77 tff('function_fun_app$bu',axiom,
% 219.58/31.77 'fun_app$bu'(fmb_'Nat_ZF_ZF_set_prod_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_ZF_set_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bg',type,'fun_app$bg': 'B_set_b_set_fun$' * 'B_set$' > 'B_set$').
% 219.58/31.77 tff('function_fun_app$bg',axiom,
% 219.58/31.77 'fun_app$bg'(fmb_'B_set_b_set_fun$'_1,fmb_'B_set$'_1) = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bo',type,'fun_app$bo': 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' * 'Nat$' > 'ZF_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_fun_app$bo',axiom,
% 219.58/31.77 'fun_app$bo'(fmb_'Nat_ZF_ZF_ZF_prod_set_fun_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_category_ext$a',type,'category_ext$a': 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_ZF_fun_fun$' * 'Unit$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_category_ext$a',axiom,
% 219.58/31.77 'category_ext$a'('top$a','top$a','uur$','uur$','uur$','vah$','unity$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyo$',type,'uyo$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_ZF_prod_set_fun$').
% 219.58/31.77 tff('function_uyo$',axiom,
% 219.58/31.77 'uyo$'('uxc$') = fmb_'ZF_set_ZF_ZF_prod_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_homFtorMap$',type,'homFtorMap$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'B_ZF_fun$').
% 219.58/31.77 tff('function_homFtorMap$',axiom,
% 219.58/31.77 'homFtorMap$'('c$',fmb_'A$'_1) = fmb_'B_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzt$',type,'uzt$': 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'Nat_nat_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.77 tff('function_uzt$',axiom,
% 219.58/31.77 'uzt$'('uxe$','uxe$') = fmb_'Nat_nat_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuq$',type,'uuq$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' > 'ZF_ZF_fun$').
% 219.58/31.77 tff('function_uuq$',axiom,
% 219.58/31.77 'uuq$'('c$','f$') = 'uur$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bt',type,'fun_app$bt': 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' * 'ZF_ZF_prod$' > 'ZF_ZF_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_fun_app$bt',axiom,
% 219.58/31.77 'fun_app$bt'(fmb_'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'_1,fmb_'ZF_ZF_prod$'_1) = fmb_'ZF_ZF_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$aj',type,'image$aj': 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$' * 'ZF_ZF_prod_set$' > 'ZF_set_ZF_set_prod_set$').
% 219.58/31.77 tff('function_image$aj',axiom,
% 219.58/31.77 'image$aj'(fmb_'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'_1,'top$b') = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$d',type,'image$d': 'B_set_bool_fun$' * 'B_set_set$' > 'Bool_set$').
% 219.58/31.77 tff('function_image$d',axiom,
% 219.58/31.77 'image$d'(fmb_'B_set_bool_fun$'_1,fmb_'B_set_set$'_1) = fmb_'Bool_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cw',type,'fun_app$cw': 'ZF_b_set_fun$' * 'ZF$' > 'B_set$').
% 219.58/31.77 tff('function_fun_app$cw',axiom,
% 219.58/31.77 'fun_app$cw'(fmb_'ZF_b_set_fun$'_1,fmb_'ZF$'_1) = fmb_'B_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuo$',type,'uuo$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'ZF$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uuo$',axiom,
% 219.58/31.77 'uuo$'('c$',fmb_'ZF$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uuy$',type,'uuy$': 'B_set$' * 'B_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uuy$',axiom,
% 219.58/31.77 'uuy$'(fmb_'B_set$'_1,fmb_'B_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyy$',type,'uyy$': 'ZF_nat_ZF_set_fun_fun$' * 'Nat_set$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyy$',axiom,
% 219.58/31.77 'uyy$'(fmb_'ZF_nat_ZF_set_fun_fun$'_1,'top$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_collect$',type,'collect$': 'ZF_bool_fun$' > 'ZF_set$').
% 219.58/31.77 tff('function_collect$',axiom,
% 219.58/31.77 'collect$'('uut$') = 'top$a'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ao',type,'fun_app$ao': 'ZF_nat_fun$' * 'ZF$' > 'Nat$').
% 219.58/31.77 tff('function_fun_app$ao',axiom,
% 219.58/31.77 'fun_app$ao'(fmb_'ZF_nat_fun$'_1,fmb_'ZF$'_1) = fmb_'Nat$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vae$',type,'vae$': 'B_set_set$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_vae$',axiom,
% 219.58/31.77 'vae$'(fmb_'B_set_set$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_member$b',type,'member$b': 'B$' > 'B_set_bool_fun$').
% 219.58/31.77 tff('function_member$b',axiom,
% 219.58/31.77 'member$b'('f$') = fmb_'B_set_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$ac',type,'fun_app$ac': 'Nat_ZF_ZF_set_fun_fun$' * 'Nat$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_fun_app$ac',axiom,
% 219.58/31.77 'fun_app$ac'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1,fmb_'Nat$'_1) = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_more_update$',type,'more_update$': 'Unit_unit_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.77 tff('function_more_update$',axiom,
% 219.58/31.77 'more_update$'(fmb_'Unit_unit_fun$'_1,'set$') = 'set$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$aa',type,'image$aa': 'Nat_ZF_ZF_prod_fun$' * 'Nat_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.77 tff('function_image$aa',axiom,
% 219.58/31.77 'image$aa'(fmb_'Nat_ZF_ZF_prod_fun$'_1,'top$') = 'top$b'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzy$',type,'uzy$': 'ZF_nat_bool_fun_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uzy$',axiom,
% 219.58/31.77 'uzy$'(fmb_'ZF_nat_bool_fun_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uxw$',type,'uxw$': 'Nat_ZF_set_fun$' * 'Nat_set$' > 'ZF_ZF_set_set_fun$').
% 219.58/31.77 tff('function_uxw$',axiom,
% 219.58/31.77 'uxw$'('uxe$','top$') = fmb_'ZF_ZF_set_set_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$b',type,'comp$b': 'ZF_ZF_fun$' > 'ZF_ZF_fun_ZF_ZF_fun_fun$').
% 219.58/31.77 tff('function_comp$b',axiom,
% 219.58/31.77 'comp$b'('uur$') = 'uym$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_more$',type,'more$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_c_LSCategory_ext$').
% 219.58/31.77 tff('function_more$',axiom,
% 219.58/31.77 'more$'('c$') = fmb_'B_c_LSCategory_ext$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uwh$',type,'uwh$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.77 tff('function_uwh$',axiom,
% 219.58/31.77 'uwh$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_prod_bool_fun$'_1) = 'uut$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uyr$',type,'uyr$': 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_uyr$',axiom,
% 219.58/31.77 'uyr$'('uxc$','uxc$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_restrict$',type,'restrict$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_fun$').
% 219.58/31.77 tff('function_restrict$',axiom,
% 219.58/31.77 'restrict$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,'top$b') = fmb_'ZF_ZF_prod_ZF_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bi',type,'image$bi': 'B_set_b_bool_fun_fun$' * 'B_set_set$' > 'B_bool_fun_set$').
% 219.58/31.77 tff('function_image$bi',axiom,
% 219.58/31.77 'image$bi'('uua$',fmb_'B_set_set$'_1) = fmb_'B_bool_fun_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_more$a',type,'more$a': 'ZF_ZF_unit_Category_ext$' > 'Unit$').
% 219.58/31.77 tff('function_more$a',axiom,
% 219.58/31.77 'more$a'('set$') = 'unity$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uvs$',type,'uvs$': 'B_b_fun$' * 'B_set$' * 'B_bool_fun$' > 'B_bool_fun$').
% 219.58/31.77 tff('function_uvs$',axiom,
% 219.58/31.77 'uvs$'(fmb_'B_b_fun$'_1,fmb_'B_set$'_1,fmb_'B_bool_fun$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_comp$i',type,'comp$i': 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_fun$').
% 219.58/31.77 tff('function_comp$i',axiom,
% 219.58/31.77 'comp$i'('sup$',fmb_'ZF_set_set_ZF_set_set_fun$'_1) = 'sup$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_image$bn',type,'image$bn': 'ZF_ZF_fun_ZF_set_fun$' * 'ZF_ZF_fun_set$' > 'ZF_set_set$').
% 219.58/31.77 tff('function_image$bn',axiom,
% 219.58/31.77 'image$bn'(fmb_'ZF_ZF_fun_ZF_set_fun$'_1,'top$f') = fmb_'ZF_set_set$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$cb',type,'fun_app$cb': 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' * 'ZF$' > 'Nat_ZF_set_ZF_set_prod_fun$').
% 219.58/31.77 tff('function_fun_app$cb',axiom,
% 219.58/31.77 'fun_app$cb'(fmb_'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'_1,fmb_'ZF$'_1) = fmb_'Nat_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_fun_app$bs',type,'fun_app$bs': 'ZF_ZF_ZF_set_prod_fun$' * 'ZF$' > 'ZF_ZF_set_prod$').
% 219.58/31.77 tff('function_fun_app$bs',axiom,
% 219.58/31.77 'fun_app$bs'(fmb_'ZF_ZF_ZF_set_prod_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_ZF_set_prod$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_vaj$',type,'vaj$': 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.77 tff('function_vaj$',axiom,
% 219.58/31.77 'vaj$'('uyk$','uur$') = 'uxc$'
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_restrict$c',type,'restrict$c': 'A_b_fun$' * 'A_set$' > 'A_b_fun$').
% 219.58/31.77 tff('function_restrict$c',axiom,
% 219.58/31.77 'restrict$c'(fmb_'A_b_fun$'_1,fmb_'A_set$'_1) = fmb_'A_b_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_dom$',type,'dom$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$').
% 219.58/31.77 tff('function_dom$',axiom,
% 219.58/31.77 'dom$'('c$') = fmb_'B_a_fun$'_1
% 219.58/31.77
% 219.58/31.77 ).
% 219.58/31.77
% 219.58/31.77 tff('declare_uzk$',type,'uzk$': 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_set_set_fun$').
% 219.58/31.78 tff('function_uzk$',axiom,
% 219.58/31.78 'uzk$'('uxc$','uxe$') = fmb_'Nat_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vak$',type,'vak$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$').
% 219.58/31.78 tff('function_vak$',axiom,
% 219.58/31.78 'vak$'('uyk$') = fmb_'ZF_ZF_fun_ZF_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$o',type,'image$o': 'A_b_fun$' * 'A_set$' > 'B_set$').
% 219.58/31.78 tff('function_image$o',axiom,
% 219.58/31.78 'image$o'(fmb_'A_b_fun$'_1,fmb_'A_set$'_1) = fmb_'B_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$bb',type,'fun_app$bb': 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod$' > 'ZF_set$').
% 219.58/31.78 tff('function_fun_app$bb',axiom,
% 219.58/31.78 'fun_app$bb'(fmb_'ZF_ZF_prod_ZF_set_fun$'_1,fmb_'ZF_ZF_prod$'_1) = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzr$',type,'uzr$': 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'Nat_ZF_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.78 tff('function_uzr$',axiom,
% 219.58/31.78 'uzr$'('uxe$','uxc$') = fmb_'Nat_ZF_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$p',type,'case_prod$p': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.78 tff('function_case_prod$p',axiom,
% 219.58/31.78 'case_prod$p'(fmb_'ZF_ZF_ZF_ZF_prod_set_fun_fun$'_1) = fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwg$',type,'uwg$': 'ZF_ZF_set_fun$' * 'ZF_bool_fun$' > 'ZF_set_bool_fun$').
% 219.58/31.78 tff('function_uwg$',axiom,
% 219.58/31.78 'uwg$'('uxc$','uut$') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$b',type,'case_prod$b': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_prod_bool_fun$').
% 219.58/31.78 tff('function_case_prod$b',axiom,
% 219.58/31.78 'case_prod$b'('uug$') = fmb_'ZF_ZF_prod_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_lambda$',type,'lambda$': 'ZF$' * 'ZF_ZF_fun$' > 'ZF$').
% 219.58/31.78 tff('function_lambda$',axiom,
% 219.58/31.78 'lambda$'(fmb_'ZF$'_1,'uur$') = fmb_'ZF$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzo$',type,'uzo$': 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'ZF_nat_ZF_ZF_prod_set_fun_fun$').
% 219.58/31.78 tff('function_uzo$',axiom,
% 219.58/31.78 'uzo$'('uxc$','uxe$') = fmb_'ZF_nat_ZF_ZF_prod_set_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_cod$a',type,'cod$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_cod$a',axiom,
% 219.58/31.78 'cod$a'('set$') = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvn$',type,'uvn$': 'B_a_fun$' * 'B_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.78 tff('function_uvn$',axiom,
% 219.58/31.78 'uvn$'(fmb_'B_a_fun$'_1,fmb_'B_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_more$b',type,'more$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'C$').
% 219.58/31.78 tff('function_more$b',axiom,
% 219.58/31.78 'more$b'('c$') = fmb_'C$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$v',type,'fun_app$v': 'Nat_set_ZF_set_set_fun$' * 'Nat_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_fun_app$v',axiom,
% 219.58/31.78 'fun_app$v'(fmb_'Nat_set_ZF_set_set_fun$'_1,'top$') = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vad$',type,'vad$': 'A_set_set$' > 'A_bool_fun$').
% 219.58/31.78 tff('function_vad$',axiom,
% 219.58/31.78 'vad$'(fmb_'A_set_set$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cf',type,'fun_app$cf': 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_fun_app$cf',axiom,
% 219.58/31.78 'fun_app$cf'(fmb_'ZF_ZF_prod_ZF_ZF_prod_set_fun$'_1,fmb_'ZF_ZF_prod$'_1) = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_comp$',type,'comp$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.78 tff('function_comp$',axiom,
% 219.58/31.78 'comp$'('set$') = 'vah$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$ar',type,'image$ar': 'B_ZF_set_fun$' * 'B_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_image$ar',axiom,
% 219.58/31.78 'image$ar'(fmb_'B_ZF_set_fun$'_1,fmb_'B_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_zF2mor$',type,'zF2mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_b_fun$').
% 219.58/31.78 tff('function_zF2mor$',axiom,
% 219.58/31.78 'zF2mor$'('c$') = fmb_'ZF_b_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uus$',type,'uus$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.78 tff('function_uus$',axiom,
% 219.58/31.78 'uus$'(fmb_'ZF$'_1) = 'vah$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$t',type,'image$t': 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_image$t',axiom,
% 219.58/31.78 'image$t'('swap$','top$b') = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uxz$',type,'uxz$': 'Nat_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' > 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$').
% 219.58/31.78 tff('function_uxz$',axiom,
% 219.58/31.78 'uxz$'('uxe$',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_dom_update$a',type,'dom_update$a': 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.78 tff('function_dom_update$a',axiom,
% 219.58/31.78 'dom_update$a'('uym$','set$') = 'set$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwm$',type,'uwm$': 'A_ZF_fun$' * 'A_set$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_uwm$',axiom,
% 219.58/31.78 'uwm$'(fmb_'A_ZF_fun$'_1,fmb_'A_set$'_1) = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ce',type,'fun_app$ce': 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' * 'Nat$' > 'Nat_ZF_set_ZF_set_prod_fun$').
% 219.58/31.78 tff('function_fun_app$ce',axiom,
% 219.58/31.78 'fun_app$ce'(fmb_'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'_1,fmb_'Nat$'_1) = fmb_'Nat_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cm',type,'fun_app$cm': 'Unit_unit_fun$' * 'Unit$' > 'Unit$').
% 219.58/31.78 tff('function_fun_app$cm',axiom,
% 219.58/31.78 'fun_app$cm'(fmb_'Unit_unit_fun$'_1,'unity$') = 'unity$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$at',type,'fun_app$at': 'Nat_ZF_bool_fun_fun$' * 'Nat$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_fun_app$at',axiom,
% 219.58/31.78 'fun_app$at'(fmb_'Nat_ZF_bool_fun_fun$'_1,fmb_'Nat$'_1) = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_homFtorMapContra$',type,'homFtorMapContra$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' > 'A_ZF_fun$').
% 219.58/31.78 tff('function_homFtorMapContra$',axiom,
% 219.58/31.78 'homFtorMapContra$'('c$','f$') = fmb_'A_ZF_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uue$',type,'uue$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.78 tff('function_uue$',axiom,
% 219.58/31.78 'uue$'('set$') = 'vah$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzj$',type,'uzj$': 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_set_set_fun$').
% 219.58/31.78 tff('function_uzj$',axiom,
% 219.58/31.78 'uzj$'('uxc$','uxc$') = fmb_'ZF_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzq$',type,'uzq$': 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_set_fun_fun$').
% 219.58/31.78 tff('function_uzq$',axiom,
% 219.58/31.78 'uzq$'('uxc$') = 'uyk$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_collect$g',type,'collect$g': 'Nat_bool_fun$' > 'Nat_set$').
% 219.58/31.78 tff('function_collect$g',axiom,
% 219.58/31.78 'collect$g'('uws$') = 'top$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$by',type,'fun_app$by': 'ZF_ZF_set_ZF_set_prod_fun$' * 'ZF$' > 'ZF_set_ZF_set_prod$').
% 219.58/31.78 tff('function_fun_app$by',axiom,
% 219.58/31.78 'fun_app$by'(fmb_'ZF_ZF_set_ZF_set_prod_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_set_ZF_set_prod$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$am',type,'fun_app$am': 'B_b_fun$' * 'B$' > 'B$').
% 219.58/31.78 tff('function_fun_app$am',axiom,
% 219.58/31.78 'fun_app$am'(fmb_'B_b_fun$'_1,'f$') = 'f$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_collect$h',type,'collect$h': 'A_bool_fun$' > 'A_set$').
% 219.58/31.78 tff('function_collect$h',axiom,
% 219.58/31.78 'collect$h'(fmb_'A_bool_fun$'_1) = fmb_'A_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzh$',type,'uzh$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_set_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.78 tff('function_uzh$',axiom,
% 219.58/31.78 'uzh$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_ZF_prod_set_fun$'_1) = 'uxc$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_comp$a',type,'comp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$').
% 219.58/31.78 tff('function_comp$a',axiom,
% 219.58/31.78 'comp$a'('c$') = fmb_'B_b_b_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$au',type,'fun_app$au': 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set$' > 'ZF_set$').
% 219.58/31.78 tff('function_fun_app$au',axiom,
% 219.58/31.78 'fun_app$au'(fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1,'top$b') = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uyu$',type,'uyu$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_fun$').
% 219.58/31.78 tff('function_uyu$',axiom,
% 219.58/31.78 'uyu$'('uxc$') = 'uyn$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_relImage$b',type,'relImage$b': 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_relImage$b',axiom,
% 219.58/31.78 'relImage$b'(fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_set$'_1,fmb_'ZF_ZF_prod_ZF_fun$'_1) = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uxx$',type,'uxx$': 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.78 tff('function_uxx$',axiom,
% 219.58/31.78 'uxx$'('uxe$','uxc$') = fmb_'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$bq',type,'fun_app$bq': 'Nat_nat_ZF_ZF_prod_set_fun_fun$' * 'Nat$' > 'Nat_ZF_ZF_prod_set_fun$').
% 219.58/31.78 tff('function_fun_app$bq',axiom,
% 219.58/31.78 'fun_app$bq'(fmb_'Nat_nat_ZF_ZF_prod_set_fun_fun$'_1,fmb_'Nat$'_1) = fmb_'Nat_ZF_ZF_prod_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_product$',type,'product$': 'ZF_set$' * 'ZF_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_product$',axiom,
% 219.58/31.78 'product$'('top$a','top$a') = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uyd$',type,'uyd$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$').
% 219.58/31.78 tff('function_uyd$',axiom,
% 219.58/31.78 'uyd$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvj$',type,'uvj$': 'Nat_ZF_set_fun$' * 'ZF_nat_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.78 tff('function_uvj$',axiom,
% 219.58/31.78 'uvj$'('uxe$',fmb_'ZF_nat_fun$'_1) = 'uxc$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwq$',type,'uwq$': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_fun$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_uwq$',axiom,
% 219.58/31.78 'uwq$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_ZF_prod_fun$'_1) = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_pair$d',type,'pair$d': 'ZF_set$' * 'ZF_set$' > 'ZF_set_ZF_set_prod$').
% 219.58/31.78 tff('function_pair$d',axiom,
% 219.58/31.78 'pair$d'('top$a','top$a') = fmb_'ZF_set_ZF_set_prod$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$j',type,'image$j': 'ZF_set_a_fun$' * 'ZF_set_set$' > 'A_set$').
% 219.58/31.78 tff('function_image$j',axiom,
% 219.58/31.78 'image$j'(fmb_'ZF_set_a_fun$'_1,fmb_'ZF_set_set$'_1) = fmb_'A_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$',type,'fun_app$': 'ZF_ZF_fun$' * 'ZF$' > 'ZF$').
% 219.58/31.78 tff('function_fun_app$',axiom,
% 219.58/31.78 'fun_app$'('uur$',fmb_'ZF$'_1) = fmb_'ZF$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$l',type,'fun_app$l': 'B_set_b_bool_fun_fun$' * 'B_set$' > 'B_bool_fun$').
% 219.58/31.78 tff('function_fun_app$l',axiom,
% 219.58/31.78 'fun_app$l'('uua$',fmb_'B_set$'_1) = fmb_'B_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_objIso$',type,'objIso$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.78 tff('function_objIso$',axiom,
% 219.58/31.78 'objIso$'('set$') = 'uug$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ax',type,'fun_app$ax': 'ZF_ZF_set_set_fun$' * 'ZF$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_fun_app$ax',axiom,
% 219.58/31.78 'fun_app$ax'(fmb_'ZF_ZF_set_set_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cs',type,'fun_app$cs': 'A_b_set_fun$' * 'A$' > 'B_set$').
% 219.58/31.78 tff('function_fun_app$cs',axiom,
% 219.58/31.78 'fun_app$cs'(fmb_'A_b_set_fun$'_1,fmb_'A$'_1) = fmb_'B_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzz$',type,'uzz$': 'ZF_nat_bool_fun_fun$' * 'Nat$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_uzz$',axiom,
% 219.58/31.78 'uzz$'(fmb_'ZF_nat_bool_fun_fun$'_1,fmb_'Nat$'_1) = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$aw',type,'fun_app$aw': 'Nat_ZF_ZF_prod_set_fun$' * 'Nat$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_fun_app$aw',axiom,
% 219.58/31.78 'fun_app$aw'(fmb_'Nat_ZF_ZF_prod_set_fun$'_1,fmb_'Nat$'_1) = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$g',type,'fun_app$g': 'ZF_set_ZF_bool_fun_fun$' * 'ZF_set$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_fun_app$g',axiom,
% 219.58/31.78 'fun_app$g'('uuc$','top$a') = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_restrict$d',type,'restrict$d': 'ZF_ZF_fun$' * 'ZF_set$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_restrict$d',axiom,
% 219.58/31.78 'restrict$d'('uur$','top$a') = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$af',type,'image$af': 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$' * 'Nat_ZF_prod_set$' > 'ZF_set_ZF_set_prod_set$').
% 219.58/31.78 tff('function_image$af',axiom,
% 219.58/31.78 'image$af'(fmb_'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'_1,'top$d') = fmb_'ZF_set_ZF_set_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvl$',type,'uvl$': 'A_a_fun$' * 'A_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.78 tff('function_uvl$',axiom,
% 219.58/31.78 'uvl$'(fmb_'A_a_fun$'_1,fmb_'A_set$'_1,fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_isomorphism$a',type,'isomorphism$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_bool_fun$').
% 219.58/31.78 tff('function_isomorphism$a',axiom,
% 219.58/31.78 'isomorphism$a'('c$') = fmb_'B_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bd',type,'image$bd': 'ZF_nat_prod_ZF_ZF_prod_set_fun$' * 'ZF_nat_prod_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.78 tff('function_image$bd',axiom,
% 219.58/31.78 'image$bd'(fmb_'ZF_nat_prod_ZF_ZF_prod_set_fun$'_1,'top$c') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$q',type,'image$q': 'ZF_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$').
% 219.58/31.78 tff('function_image$q',axiom,
% 219.58/31.78 'image$q'('uyn$') = fmb_'ZF_set_set_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$an',type,'fun_app$an': 'B_b_b_fun_fun$' * 'B$' > 'B_b_fun$').
% 219.58/31.78 tff('function_fun_app$an',axiom,
% 219.58/31.78 'fun_app$an'(fmb_'B_b_b_fun_fun$'_1,'f$') = fmb_'B_b_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwz$',type,'uwz$': 'ZF_ZF_set_fun$' * 'ZF_set$' > 'ZF_set_ZF_set_set_fun$').
% 219.58/31.78 tff('function_uwz$',axiom,
% 219.58/31.78 'uwz$'('uxc$','top$a') = fmb_'ZF_set_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$av',type,'image$av': 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set_set_ZF_set_set_fun$').
% 219.58/31.78 tff('function_image$av',axiom,
% 219.58/31.78 'image$av'(fmb_'ZF_ZF_prod_set_ZF_set_fun$'_1) = fmb_'ZF_ZF_prod_set_set_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$aw',type,'image$aw': 'ZF_nat_set_fun$' * 'ZF_set$' > 'Nat_set_set$').
% 219.58/31.78 tff('function_image$aw',axiom,
% 219.58/31.78 'image$aw'('uxd$','top$a') = fmb_'Nat_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bp',type,'image$bp': 'ZF_nat_fun_ZF_set_fun$' * 'ZF_nat_fun_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_image$bp',axiom,
% 219.58/31.78 'image$bp'(fmb_'ZF_nat_fun_ZF_set_fun$'_1,'top$h') = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ap',type,'fun_app$ap': 'Nat_nat_fun$' * 'Nat$' > 'Nat$').
% 219.58/31.78 tff('function_fun_app$ap',axiom,
% 219.58/31.78 'fun_app$ap'(fmb_'Nat_nat_fun$'_1,fmb_'Nat$'_1) = fmb_'Nat$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$am',type,'image$am': 'B_a_set_fun$' * 'B_set$' > 'A_set_set$').
% 219.58/31.78 tff('function_image$am',axiom,
% 219.58/31.78 'image$am'(fmb_'B_a_set_fun$'_1,fmb_'B_set$'_1) = fmb_'A_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vab$',type,'vab$': 'ZF_ZF_set_fun$' > 'ZF_ZF_bool_fun_fun$').
% 219.58/31.78 tff('function_vab$',axiom,
% 219.58/31.78 'vab$'('uxc$') = 'uug$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sup$b',type,'sup$b': 'A_set_set$' > 'A_set$').
% 219.58/31.78 tff('function_sup$b',axiom,
% 219.58/31.78 'sup$b'(fmb_'A_set_set$'_1) = fmb_'A_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$z',type,'fun_app$z': 'ZF_ZF_fun_ZF_set_fun$' * 'ZF_ZF_fun$' > 'ZF_set$').
% 219.58/31.78 tff('function_fun_app$z',axiom,
% 219.58/31.78 'fun_app$z'(fmb_'ZF_ZF_fun_ZF_set_fun$'_1,'uur$') = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_isomorphism$',type,'isomorphism$': 'ZF_ZF_unit_Category_ext$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_isomorphism$',axiom,
% 219.58/31.78 'isomorphism$'('set$') = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$ae',type,'image$ae': 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$' * 'ZF_ZF_prod_nat_prod_set$' > 'ZF_ZF_set_prod_set$').
% 219.58/31.78 tff('function_image$ae',axiom,
% 219.58/31.78 'image$ae'(fmb_'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'_1,fmb_'ZF_ZF_prod_nat_prod_set$'_1) = fmb_'ZF_ZF_set_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzi$',type,'uzi$': 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_ZF_prod_set_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.78 tff('function_uzi$',axiom,
% 219.58/31.78 'uzi$'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'Nat_ZF_ZF_prod_set_fun$'_1) = 'uxe$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_id$a',type,'id$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_id$a',axiom,
% 219.58/31.78 'id$a'('set$') = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$k',type,'case_prod$k': 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$').
% 219.58/31.78 tff('function_case_prod$k',axiom,
% 219.58/31.78 'case_prod$k'(fmb_'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'_1) = fmb_'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sigma$j',type,'sigma$j': 'Nat_set$' * 'Nat_ZF_ZF_prod_set_fun$' > 'Nat_ZF_ZF_prod_prod_set$').
% 219.58/31.78 tff('function_sigma$j',axiom,
% 219.58/31.78 'sigma$j'('top$',fmb_'Nat_ZF_ZF_prod_set_fun$'_1) = fmb_'Nat_ZF_ZF_prod_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzc$',type,'uzc$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_ZF_set_fun_fun$').
% 219.58/31.78 tff('function_uzc$',axiom,
% 219.58/31.78 'uzc$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1) = fmb_'ZF_nat_ZF_set_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_comp$c',type,'comp$c': 'ZF_set_set_set_ZF_set_set_fun$' * 'Nat_set_set_ZF_set_set_set_fun$' > 'Nat_set_set_ZF_set_set_fun$').
% 219.58/31.78 tff('function_comp$c',axiom,
% 219.58/31.78 'comp$c'('sup$e',fmb_'Nat_set_set_ZF_set_set_set_fun$'_1) = fmb_'Nat_set_set_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvd$',type,'uvd$': 'ZF_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_fun$').
% 219.58/31.78 tff('function_uvd$',axiom,
% 219.58/31.78 'uvd$'('uur$',fmb_'ZF_ZF_prod_ZF_fun$'_1) = fmb_'ZF_ZF_prod_ZF_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvt$',type,'uvt$': 'ZF_a_fun$' * 'ZF_set$' * 'A_bool_fun$' > 'A_bool_fun$').
% 219.58/31.78 tff('function_uvt$',axiom,
% 219.58/31.78 'uvt$'(fmb_'ZF_a_fun$'_1,'top$a',fmb_'A_bool_fun$'_1) = fmb_'A_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$dc',type,'fun_app$dc': 'ZF_ZF_prod_set_set_ZF_set_set_fun$' * 'ZF_ZF_prod_set_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_fun_app$dc',axiom,
% 219.58/31.78 'fun_app$dc'(fmb_'ZF_ZF_prod_set_set_ZF_set_set_fun$'_1,fmb_'ZF_ZF_prod_set_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cz',type,'fun_app$cz': 'Nat_set_set_nat_set_fun$' * 'Nat_set_set$' > 'Nat_set$').
% 219.58/31.78 tff('function_fun_app$cz',axiom,
% 219.58/31.78 'fun_app$cz'('sup$f',fmb_'Nat_set_set$'_1) = 'top$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwi$',type,'uwi$': 'ZF_ZF_fun$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_uwi$',axiom,
% 219.58/31.78 'uwi$'('uur$','uut$') = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uyf$',type,'uyf$': 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$').
% 219.58/31.78 tff('function_uyf$',axiom,
% 219.58/31.78 'uyf$'('uxc$','uxc$') = fmb_'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$k',type,'image$k': 'B_ZF_fun$' * 'B_set$' > 'ZF_set$').
% 219.58/31.78 tff('function_image$k',axiom,
% 219.58/31.78 'image$k'(fmb_'B_ZF_fun$'_1,fmb_'B_set$'_1) = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$j',type,'case_prod$j': 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' > 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$').
% 219.58/31.78 tff('function_case_prod$j',axiom,
% 219.58/31.78 'case_prod$j'(fmb_'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'_1) = fmb_'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ba',type,'fun_app$ba': 'Nat_ZF_ZF_prod_fun$' * 'Nat$' > 'ZF_ZF_prod$').
% 219.58/31.78 tff('function_fun_app$ba',axiom,
% 219.58/31.78 'fun_app$ba'(fmb_'Nat_ZF_ZF_prod_fun$'_1,fmb_'Nat$'_1) = fmb_'ZF_ZF_prod$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$be',type,'image$be': 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' * 'Nat_ZF_prod_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.78 tff('function_image$be',axiom,
% 219.58/31.78 'image$be'(fmb_'Nat_ZF_prod_ZF_ZF_prod_set_fun$'_1,'top$d') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_homFtor$a',type,'homFtor$a': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$').
% 219.58/31.78 tff('function_homFtor$a',axiom,
% 219.58/31.78 'homFtor$a'('c$',fmb_'A$'_1) = fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sigma$l',type,'sigma$l': 'Nat_set$' * 'Nat_ZF_set_set_fun$' > 'Nat_ZF_set_prod_set$').
% 219.58/31.78 tff('function_sigma$l',axiom,
% 219.58/31.78 'sigma$l'('top$',fmb_'Nat_ZF_set_set_fun$'_1) = fmb_'Nat_ZF_set_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$bj',type,'fun_app$bj': 'ZF_set_a_fun$' * 'ZF_set$' > 'A$').
% 219.58/31.78 tff('function_fun_app$bj',axiom,
% 219.58/31.78 'fun_app$bj'(fmb_'ZF_set_a_fun$'_1,'top$a') = fmb_'A$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzx$',type,'uzx$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.78 tff('function_uzx$',axiom,
% 219.58/31.78 'uzx$'('uug$') = 'uxc$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$i',type,'case_prod$i': 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' > 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$').
% 219.58/31.78 tff('function_case_prod$i',axiom,
% 219.58/31.78 'case_prod$i'(fmb_'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'_1) = fmb_'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vav$',type,'vav$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$').
% 219.58/31.78 tff('function_vav$',axiom,
% 219.58/31.78 'vav$'('uyk$') = fmb_'ZF_ZF_fun_ZF_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ch',type,'fun_app$ch': 'B_a_fun_b_a_fun_fun$' * 'B_a_fun$' > 'B_a_fun$').
% 219.58/31.78 tff('function_fun_app$ch',axiom,
% 219.58/31.78 'fun_app$ch'(fmb_'B_a_fun_b_a_fun_fun$'_1,fmb_'B_a_fun$'_1) = fmb_'B_a_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bl',type,'image$bl': 'ZF_ZF_bool_fun_fun$' * 'ZF_set$' > 'ZF_bool_fun_set$').
% 219.58/31.78 tff('function_image$bl',axiom,
% 219.58/31.78 'image$bl'('uug$','top$a') = fmb_'ZF_bool_fun_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_case_prod$o',type,'case_prod$o': 'Nat_nat_ZF_ZF_prod_set_fun_fun$' > 'Nat_nat_prod_ZF_ZF_prod_set_fun$').
% 219.58/31.78 tff('function_case_prod$o',axiom,
% 219.58/31.78 'case_prod$o'(fmb_'Nat_nat_ZF_ZF_prod_set_fun_fun$'_1) = fmb_'Nat_nat_prod_ZF_ZF_prod_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$da',type,'fun_app$da': 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_fun_app$da',axiom,
% 219.58/31.78 'fun_app$da'('sup$e',fmb_'ZF_set_set_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uul$',type,'uul$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_ZF_fun_fun$').
% 219.58/31.78 tff('function_uul$',axiom,
% 219.58/31.78 'uul$'(fmb_'ZF_ZF_prod_ZF_fun$'_1) = 'vah$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sigma$d',type,'sigma$d': 'Nat_set$' * 'Nat_nat_set_fun$' > 'Nat_nat_prod_set$').
% 219.58/31.78 tff('function_sigma$d',axiom,
% 219.58/31.78 'sigma$d'('top$','uxf$') = 'top$e'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$s',type,'image$s': 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_image$s',axiom,
% 219.58/31.78 'image$s'(fmb_'ZF_ZF_prod_ZF_set_fun$'_1,'top$b') = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$v',type,'image$v': 'Nat_nat_fun$' * 'Nat_set$' > 'Nat_set$').
% 219.58/31.78 tff('function_image$v',axiom,
% 219.58/31.78 'image$v'(fmb_'Nat_nat_fun$'_1,'top$') = 'top$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvx$',type,'uvx$': 'A_ZF_fun$' * 'A_set$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_uvx$',axiom,
% 219.58/31.78 'uvx$'(fmb_'A_ZF_fun$'_1,fmb_'A_set$'_1,'uut$') = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_homSet$',type,'homSet$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' > 'A_ZF_fun$').
% 219.58/31.78 tff('function_homSet$',axiom,
% 219.58/31.78 'homSet$'('c$',fmb_'A$'_1) = fmb_'A_ZF_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bm',type,'image$bm': 'Nat_ZF_bool_fun_fun$' * 'Nat_set$' > 'ZF_bool_fun_set$').
% 219.58/31.78 tff('function_image$bm',axiom,
% 219.58/31.78 'image$bm'(fmb_'Nat_ZF_bool_fun_fun$'_1,'top$') = fmb_'ZF_bool_fun_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cv',type,'fun_app$cv': 'ZF_a_set_fun$' * 'ZF$' > 'A_set$').
% 219.58/31.78 tff('function_fun_app$cv',axiom,
% 219.58/31.78 'fun_app$cv'(fmb_'ZF_a_set_fun$'_1,fmb_'ZF$'_1) = fmb_'A_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uzl$',type,'uzl$': 'ZF_ZF_fun$' * 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.78 tff('function_uzl$',axiom,
% 219.58/31.78 'uzl$'('uur$','uxc$') = 'uxc$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_pair$b',type,'pair$b': 'ZF$' * 'ZF_set$' > 'ZF_ZF_set_prod$').
% 219.58/31.78 tff('function_pair$b',axiom,
% 219.58/31.78 'pair$b'(fmb_'ZF$'_1,'top$a') = fmb_'ZF_ZF_set_prod$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_mor_update$',type,'mor_update$': 'ZF_set_ZF_set_fun$' * 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.78 tff('function_mor_update$',axiom,
% 219.58/31.78 'mor_update$'('uyn$','set$') = 'set$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bo',type,'image$bo': 'Nat_ZF_fun_ZF_set_fun$' * 'Nat_ZF_fun_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_image$bo',axiom,
% 219.58/31.78 'image$bo'(fmb_'Nat_ZF_fun_ZF_set_fun$'_1,'top$g') = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$ay',type,'image$ay': 'Nat_set_ZF_set_fun$' * 'Nat_set_set$' > 'ZF_set_set$').
% 219.58/31.78 tff('function_image$ay',axiom,
% 219.58/31.78 'image$ay'(fmb_'Nat_set_ZF_set_fun$'_1,fmb_'Nat_set_set$'_1) = fmb_'ZF_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bf',type,'image$bf': 'Nat_nat_prod_ZF_ZF_prod_set_fun$' * 'Nat_nat_prod_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.78 tff('function_image$bf',axiom,
% 219.58/31.78 'image$bf'(fmb_'Nat_nat_prod_ZF_ZF_prod_set_fun$'_1,'top$e') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sigma$i',type,'sigma$i': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_nat_set_fun$' > 'ZF_ZF_prod_nat_prod_set$').
% 219.58/31.78 tff('function_sigma$i',axiom,
% 219.58/31.78 'sigma$i'('top$b',fmb_'ZF_ZF_prod_nat_set_fun$'_1) = fmb_'ZF_ZF_prod_nat_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$l',type,'image$l': 'B_b_fun$' > 'B_set_b_set_fun$').
% 219.58/31.78 tff('function_image$l',axiom,
% 219.58/31.78 'image$l'(fmb_'B_b_fun$'_1) = fmb_'B_set_b_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uxt$',type,'uxt$': 'ZF_ZF_set_fun$' * 'ZF_set$' > 'ZF_ZF_set_set_fun$').
% 219.58/31.78 tff('function_uxt$',axiom,
% 219.58/31.78 'uxt$'('uxc$','top$a') = fmb_'ZF_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$at',type,'image$at': 'Nat_set_ZF_set_set_fun$' > 'Nat_set_set_ZF_set_set_set_fun$').
% 219.58/31.78 tff('function_image$at',axiom,
% 219.58/31.78 'image$at'(fmb_'Nat_set_ZF_set_set_fun$'_1) = fmb_'Nat_set_set_ZF_set_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vaz$',type,'vaz$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$').
% 219.58/31.78 tff('function_vaz$',axiom,
% 219.58/31.78 'vaz$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1) = fmb_'ZF_nat_fun_ZF_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uvk$',type,'uvk$': 'Nat_ZF_set_fun$' * 'Nat_nat_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.78 tff('function_uvk$',axiom,
% 219.58/31.78 'uvk$'('uxe$',fmb_'Nat_nat_fun$'_1) = 'uxe$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$q',type,'fun_app$q': 'ZF_ZF_bool_fun_fun$' * 'ZF$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_fun_app$q',axiom,
% 219.58/31.78 'fun_app$q'('uug$',fmb_'ZF$'_1) = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwc$',type,'uwc$': 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' > 'ZF_bool_fun$').
% 219.58/31.78 tff('function_uwc$',axiom,
% 219.58/31.78 'uwc$'('uur$','top$a','uut$') = 'uut$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$bl',type,'fun_app$bl': 'A_b_fun$' * 'A$' > 'B$').
% 219.58/31.78 tff('function_fun_app$bl',axiom,
% 219.58/31.78 'fun_app$bl'(fmb_'A_b_fun$'_1,fmb_'A$'_1) = 'f$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uys$',type,'uys$': 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$').
% 219.58/31.78 tff('function_uys$',axiom,
% 219.58/31.78 'uys$'('uxc$','uxe$') = 'uxe$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_gr$b',type,'gr$b': 'Nat_set$' * 'Nat_ZF_set_fun$' > 'Nat_ZF_set_prod_set$').
% 219.58/31.78 tff('function_gr$b',axiom,
% 219.58/31.78 'gr$b'('top$','uxe$') = fmb_'Nat_ZF_set_prod_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$c',type,'less_eq$c': 'ZF_set$' > 'ZF_set_bool_fun$').
% 219.58/31.78 tff('function_less_eq$c',axiom,
% 219.58/31.78 'less_eq$c'('top$a') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$c',type,'fun_app$c': 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_fun_app$c',axiom,
% 219.58/31.78 'fun_app$c'(fmb_'ZF_set_ZF_ZF_prod_set_fun$'_1,'top$a') = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uyj$',type,'uyj$': 'ZF_set_set$' > 'Nat_ZF_set_set_fun$').
% 219.58/31.78 tff('function_uyj$',axiom,
% 219.58/31.78 'uyj$'(fmb_'ZF_set_set$'_1) = fmb_'Nat_ZF_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_vay$',type,'vay$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$').
% 219.58/31.78 tff('function_vay$',axiom,
% 219.58/31.78 'vay$'(fmb_'Nat_ZF_ZF_set_fun_fun$'_1) = 'uxc$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$au',type,'image$au': 'ZF_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_set_set_fun$').
% 219.58/31.78 tff('function_image$au',axiom,
% 219.58/31.78 'image$au'(fmb_'ZF_set_ZF_set_set_fun$'_1) = fmb_'ZF_set_set_ZF_set_set_set_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_pair$c',type,'pair$c': 'ZF_set$' * 'ZF$' > 'ZF_set_ZF_prod$').
% 219.58/31.78 tff('function_pair$c',axiom,
% 219.58/31.78 'pair$c'('top$a',fmb_'ZF$'_1) = fmb_'ZF_set_ZF_prod$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$e',type,'fun_app$e': 'ZF_ZF_ZF_ZF_prod_fun_fun$' * 'ZF$' > 'ZF_ZF_ZF_prod_fun$').
% 219.58/31.78 tff('function_fun_app$e',axiom,
% 219.58/31.78 'fun_app$e'('uxj$',fmb_'ZF$'_1) = fmb_'ZF_ZF_ZF_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_makeCat$a',type,'makeCat$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$').
% 219.58/31.78 tff('function_makeCat$a',axiom,
% 219.58/31.78 'makeCat$a'('set$') = 'set$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$u',type,'image$u': 'ZF_nat_fun$' * 'ZF_set$' > 'Nat_set$').
% 219.58/31.78 tff('function_image$u',axiom,
% 219.58/31.78 'image$u'(fmb_'ZF_nat_fun$'_1,'top$a') = 'top$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$bz',type,'fun_app$bz': 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' * 'ZF$' > 'ZF_ZF_set_ZF_set_prod_fun$').
% 219.58/31.78 tff('function_fun_app$bz',axiom,
% 219.58/31.78 'fun_app$bz'(fmb_'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'_1,fmb_'ZF$'_1) = fmb_'ZF_ZF_set_ZF_set_prod_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_dom$a',type,'dom$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_dom$a',axiom,
% 219.58/31.78 'dom$a'('set$') = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$r',type,'fun_app$r': 'Nat_ZF_set_fun$' * 'Nat$' > 'ZF_set$').
% 219.58/31.78 tff('function_fun_app$r',axiom,
% 219.58/31.78 'fun_app$r'('uxe$',fmb_'Nat$'_1) = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$t',type,'fun_app$t': 'Nat_nat_fun_ZF_set_fun$' * 'Nat_nat_fun$' > 'ZF_set$').
% 219.58/31.78 tff('function_fun_app$t',axiom,
% 219.58/31.78 'fun_app$t'(fmb_'Nat_nat_fun_ZF_set_fun$'_1,fmb_'Nat_nat_fun$'_1) = 'top$a'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$i',type,'fun_app$i': 'ZF_set_set_ZF_set_bool_fun_fun$' * 'ZF_set_set$' > 'ZF_set_bool_fun$').
% 219.58/31.78 tff('function_fun_app$i',axiom,
% 219.58/31.78 'fun_app$i'('uub$',fmb_'ZF_set_set$'_1) = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uup$',type,'uup$': 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' > 'ZF_ZF_fun$').
% 219.58/31.78 tff('function_uup$',axiom,
% 219.58/31.78 'uup$'('c$','f$') = 'uur$'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_uwj$',type,'uwj$': 'Nat_ZF_set_fun$' * 'Nat_set$' > 'ZF_set_bool_fun$').
% 219.58/31.78 tff('function_uwj$',axiom,
% 219.58/31.78 'uwj$'('uxe$','top$') = fmb_'ZF_set_bool_fun$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$ba',type,'image$ba': 'Nat_ZF_ZF_prod_set_fun$' * 'Nat_set$' > 'ZF_ZF_prod_set_set$').
% 219.58/31.78 tff('function_image$ba',axiom,
% 219.58/31.78 'image$ba'(fmb_'Nat_ZF_ZF_prod_set_fun$'_1,'top$') = fmb_'ZF_ZF_prod_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$bk',type,'image$bk': 'ZF_set_ZF_bool_fun_fun$' * 'ZF_set_set$' > 'ZF_bool_fun_set$').
% 219.58/31.78 tff('function_image$bk',axiom,
% 219.58/31.78 'image$bk'('uuc$',fmb_'ZF_set_set$'_1) = fmb_'ZF_bool_fun_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_image$ao',type,'image$ao': 'ZF_a_set_fun$' * 'ZF_set$' > 'A_set_set$').
% 219.58/31.78 tff('function_image$ao',axiom,
% 219.58/31.78 'image$ao'(fmb_'ZF_a_set_fun$'_1,'top$a') = fmb_'A_set_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_collect$a',type,'collect$a': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_set$').
% 219.58/31.78 tff('function_collect$a',axiom,
% 219.58/31.78 'collect$a'(fmb_'ZF_ZF_prod_bool_fun$'_1) = 'top$b'
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_mor$',type,'mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_set$').
% 219.58/31.78 tff('function_mor$',axiom,
% 219.58/31.78 'mor$'('c$') = fmb_'B_set$'_1
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$e',type,'less_eq$e': 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$e',axiom,
% 219.58/31.78 'less_eq$e'('top$b','top$b')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functorM$',type,'functorM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functorM$',axiom,
% 219.58/31.78 'functorM$'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ak',type,'fun_app$ak': 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$ak',axiom,
% 219.58/31.78 'fun_app$ak'(fmb_'ZF_ZF_prod_bool_fun$'_1,fmb_'ZF_ZF_prod$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$f',type,'less_eq$f': 'ZF_ZF_set_prod_set$' * 'ZF_ZF_set_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$f',axiom,
% 219.58/31.78 'less_eq$f'(fmb_'ZF_ZF_set_prod_set$'_1,fmb_'ZF_ZF_set_prod_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_lSCategory$',type,'lSCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_lSCategory$',axiom,
% 219.58/31.78 'lSCategory$'('c$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$k',type,'less_eq$k': 'B_bool_fun$' * 'B_bool_fun$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$k',axiom,
% 219.58/31.78 'less_eq$k'(fmb_'B_bool_fun$'_1,fmb_'B_bool_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$l',type,'member$l': 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$l',axiom,
% 219.58/31.78 'member$l'(fmb_'ZF_ZF_prod_ZF_fun$'_1,fmb_'ZF_ZF_prod_ZF_fun_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_category$a',type,'category$a': 'ZF_ZF_unit_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_category$a',axiom,
% 219.58/31.78 'category$a'('set$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functorM$b',type,'functorM$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functorM$b',axiom,
% 219.58/31.78 % 'functorM$b'(fmb_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_category$',type,'category$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_category$',axiom,
% 219.58/31.78 'category$'('c$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functorM$a',type,'functorM$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functorM$a',axiom,
% 219.58/31.78 % 'functorM$a'(fmb_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ck',type,'fun_app$ck': 'B_a_fun_bool_fun$' * 'B_a_fun$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$ck',axiom,
% 219.58/31.78 ~'fun_app$ck'(fmb_'B_a_fun_bool_fun$'_1,fmb_'B_a_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$m',type,'less_eq$m': 'ZF_set_bool_fun$' * 'ZF_set_bool_fun$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$m',axiom,
% 219.58/31.78 'less_eq$m'(fmb_'ZF_set_bool_fun$'_1,fmb_'ZF_set_bool_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$h',type,'fun_app$h': 'ZF_set_bool_fun$' * 'ZF_set$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$h',axiom,
% 219.58/31.78 'fun_app$h'(fmb_'ZF_set_bool_fun$'_1,'top$a')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functor$b',type,'functor$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functor$b',axiom,
% 219.58/31.78 % 'functor$b'(fmb_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functor$a',type,'functor$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functor$a',axiom,
% 219.58/31.78 % 'functor$a'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$f',type,'fun_app$f': 'ZF_bool_fun$' * 'ZF$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$f',axiom,
% 219.58/31.78 'fun_app$f'('uut$',fmb_'ZF$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$j',type,'member$j': 'B_b_prod$' * 'B_b_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_member$j',axiom,
% 219.58/31.78 'member$j'(fmb_'B_b_prod$'_1,fmb_'B_b_prod_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_preFunctor$b',type,'preFunctor$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_preFunctor$b',axiom,
% 219.58/31.78 % 'preFunctor$b'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$k',type,'member$k': 'B_b_prod_b_fun$' * 'B_b_prod_b_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$k',axiom,
% 219.58/31.78 ~'member$k'(fmb_'B_b_prod_b_fun$'_1,fmb_'B_b_prod_b_fun_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_lSCategory_axioms$',type,'lSCategory_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_lSCategory_axioms$',axiom,
% 219.58/31.78 'lSCategory_axioms$'('c$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_extCategory$a',type,'extCategory$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_extCategory$a',axiom,
% 219.58/31.78 ~'extCategory$a'('c$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ag',type,'fun_app$ag': 'Nat_bool_fun$' * 'Nat$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$ag',axiom,
% 219.58/31.78 'fun_app$ag'('uws$',fmb_'Nat$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$g',type,'member$g': 'B_ZF_fun$' * 'B_ZF_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$g',axiom,
% 219.58/31.78 'member$g'(fmb_'B_ZF_fun$'_1,fmb_'B_ZF_fun_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_extCategory$',type,'extCategory$': 'ZF_ZF_unit_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_extCategory$',axiom,
% 219.58/31.78 'extCategory$'('set$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$i',type,'less_eq$i': 'Nat_set$' * 'Nat_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$i',axiom,
% 219.58/31.78 % 'less_eq$i'('top$','top$') undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_category_axioms$',type,'category_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_category_axioms$',axiom,
% 219.58/31.78 'category_axioms$'('c$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functor_abbrev$',type,'functor_abbrev$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' * 'A_b_b_c_LSCategory_ext_Category_ext$' * 'ZF_ZF_unit_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_functor_abbrev$',axiom,
% 219.58/31.78 % 'functor_abbrev$'(fmb_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'_1,'c$','set$') undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functorM$c',type,'functorM$c': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functorM$c',axiom,
% 219.58/31.78 % 'functorM$c'(fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$f',type,'member$f': 'ZF_ZF_fun$' * 'ZF_ZF_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$f',axiom,
% 219.58/31.78 'member$f'('uur$','top$f')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$',type,'less_eq$': 'A_set$' * 'A_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$',axiom,
% 219.58/31.78 'less_eq$'(fmb_'A_set$'_1,fmb_'A_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$j',type,'less_eq$j': 'A_bool_fun$' * 'A_bool_fun$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$j',axiom,
% 219.58/31.78 'less_eq$j'(fmb_'A_bool_fun$'_1,fmb_'A_bool_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$a',type,'less_eq$a': 'B_set$' * 'B_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$a',axiom,
% 219.58/31.78 'less_eq$a'(fmb_'B_set$'_1,fmb_'B_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cl',type,'fun_app$cl': 'A_b_fun_bool_fun$' * 'A_b_fun$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$cl',axiom,
% 219.58/31.78 ~'fun_app$cl'(fmb_'A_b_fun_bool_fun$'_1,fmb_'A_b_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_sup$a',type,'sup$a': 'Bool_set$' > $o ).
% 219.58/31.78 tff('predicate_sup$a',axiom,
% 219.58/31.78 'sup$a'(fmb_'Bool_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$l',type,'less_eq$l': 'ZF_bool_fun$' * 'ZF_bool_fun$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$l',axiom,
% 219.58/31.78 'less_eq$l'('uut$','uut$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$k',type,'fun_app$k': 'B_bool_fun$' * 'B$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$k',axiom,
% 219.58/31.78 'fun_app$k'(fmb_'B_bool_fun$'_1,'f$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$i',type,'member$i': 'A_b_fun$' * 'A_b_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$i',axiom,
% 219.58/31.78 ~'member$i'(fmb_'A_b_fun$'_1,fmb_'A_b_fun_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$h',type,'less_eq$h': 'Nat_ZF_set_prod_set$' * 'Nat_ZF_set_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$h',axiom,
% 219.58/31.78 'less_eq$h'(fmb_'Nat_ZF_set_prod_set$'_1,fmb_'Nat_ZF_set_prod_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$al',type,'fun_app$al': 'B_b_prod_bool_fun$' * 'B_b_prod$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$al',axiom,
% 219.58/31.78 'fun_app$al'(fmb_'B_b_prod_bool_fun$'_1,fmb_'B_b_prod$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$d',type,'member$d': 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_member$d',axiom,
% 219.58/31.78 'member$d'(fmb_'ZF_ZF_prod$'_1,'top$b')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$d',type,'less_eq$d': 'ZF_set_ZF_set_prod_set$' * 'ZF_set_ZF_set_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$d',axiom,
% 219.58/31.78 % 'less_eq$d'(fmb_'ZF_set_ZF_set_prod_set$'_1,fmb_'ZF_set_ZF_set_prod_set$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$g',type,'less_eq$g': 'ZF_ZF_prod_ZF_prod_set$' * 'ZF_ZF_prod_ZF_prod_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$g',axiom,
% 219.58/31.78 'less_eq$g'(fmb_'ZF_ZF_prod_ZF_prod_set$'_1,fmb_'ZF_ZF_prod_ZF_prod_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_category_axioms$a',type,'category_axioms$a': 'ZF_ZF_unit_Category_ext$' > $o ).
% 219.58/31.78 tff('predicate_category_axioms$a',axiom,
% 219.58/31.78 'category_axioms$a'('set$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_preFunctor$a',type,'preFunctor$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_preFunctor$a',axiom,
% 219.58/31.78 % 'preFunctor$a'(fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functor$',type,'functor$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functor$',axiom,
% 219.58/31.78 % 'functor$'(fmb_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_less_eq$b',type,'less_eq$b': 'ZF_set_set$' * 'ZF_set_set$' > $o ).
% 219.58/31.78 tff('predicate_less_eq$b',axiom,
% 219.58/31.78 'less_eq$b'(fmb_'ZF_set_set$'_1,fmb_'ZF_set_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$n',type,'fun_app$n': 'A_bool_fun$' * 'A$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$n',axiom,
% 219.58/31.78 'fun_app$n'(fmb_'A_bool_fun$'_1,fmb_'A$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_functor$c',type,'functor$c': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_functor$c',axiom,
% 219.58/31.78 % 'functor$c'(fmb_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$e',type,'member$e': 'Nat$' * 'Nat_set$' > $o ).
% 219.58/31.78 tff('predicate_member$e',axiom,
% 219.58/31.78 'member$e'(fmb_'Nat$'_1,'top$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$j',type,'fun_app$j': 'ZF_set_set_bool_fun$' * 'ZF_set_set$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$j',axiom,
% 219.58/31.78 'fun_app$j'(fmb_'ZF_set_set_bool_fun$'_1,fmb_'ZF_set_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$m',type,'fun_app$m': 'B_set_bool_fun$' * 'B_set$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$m',axiom,
% 219.58/31.78 'fun_app$m'(fmb_'B_set_bool_fun$'_1,fmb_'B_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_preFunctor$',type,'preFunctor$': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
% 219.58/31.78 tff('predicate_preFunctor$',axiom,
% 219.58/31.78 % 'preFunctor$'(fmb_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'_1) undefined in model
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_member$h',type,'member$h': 'B_a_fun$' * 'B_a_fun_set$' > $o ).
% 219.58/31.78 tff('predicate_member$h',axiom,
% 219.58/31.78 ~'member$h'(fmb_'B_a_fun$'_1,fmb_'B_a_fun_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$cj',type,'fun_app$cj': 'B_ZF_fun_bool_fun$' * 'B_ZF_fun$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$cj',axiom,
% 219.58/31.78 'fun_app$cj'(fmb_'B_ZF_fun_bool_fun$'_1,fmb_'B_ZF_fun$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$p',type,'fun_app$p': 'A_set_bool_fun$' * 'A_set$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$p',axiom,
% 219.58/31.78 'fun_app$p'(fmb_'A_set_bool_fun$'_1,fmb_'A_set$'_1)
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 tff('declare_fun_app$ci',type,'fun_app$ci': 'ZF_ZF_fun_bool_fun$' * 'ZF_ZF_fun$' > $o ).
% 219.58/31.78 tff('predicate_fun_app$ci',axiom,
% 219.58/31.78 'fun_app$ci'(fmb_'ZF_ZF_fun_bool_fun$'_1,'uur$')
% 219.58/31.78
% 219.58/31.78 ).
% 219.58/31.78
% 219.58/31.78 % SZS output end FiniteModel for theBenchmark
% 219.58/31.78 % (13221)------------------------------
% 219.58/31.78 % (13221)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 219.58/31.78 % (13221)Termination reason: Satisfiable
% 219.58/31.78
% 219.58/31.78 % (13221)Memory used [KB]: 558194
% 219.58/31.78 % (13221)Time elapsed: 31.312 s
% 219.58/31.78 % (13221)Instructions burned: 78907 (million)
% 219.58/31.78 % (13218)Success in time 31.426 s
%------------------------------------------------------------------------------