0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % DateTime : Tue Jul 13 16:50:48 EDT 2021 0.13/0.34 % CPUTime : 2.20/2.64 ============================== Prover9 =============================== 2.20/2.64 Prover9 (32) version 2009-11A, November 2009. 2.20/2.64 Process 25699 was started by sandbox2 on n005.cluster.edu, 2.20/2.64 Tue Jul 13 16:50:50 2021 2.20/2.64 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_25546_n005.cluster.edu". 2.20/2.64 ============================== end of head =========================== 2.20/2.64 2.20/2.64 ============================== INPUT ================================= 2.20/2.64 2.20/2.64 % Reading from file /tmp/Prover9_25546_n005.cluster.edu 2.20/2.64 2.20/2.64 set(prolog_style_variables). 2.20/2.64 set(auto2). 2.20/2.64 % set(auto2) -> set(auto). 2.20/2.64 % set(auto) -> set(auto_inference). 2.20/2.64 % set(auto) -> set(auto_setup). 2.20/2.64 % set(auto_setup) -> set(predicate_elim). 2.20/2.64 % set(auto_setup) -> assign(eq_defs, unfold). 2.20/2.64 % set(auto) -> set(auto_limits). 2.20/2.64 % set(auto_limits) -> assign(max_weight, "100.000"). 2.20/2.64 % set(auto_limits) -> assign(sos_limit, 20000). 2.20/2.64 % set(auto) -> set(auto_denials). 2.20/2.64 % set(auto) -> set(auto_process). 2.20/2.64 % set(auto2) -> assign(new_constants, 1). 2.20/2.64 % set(auto2) -> assign(fold_denial_max, 3). 2.20/2.64 % set(auto2) -> assign(max_weight, "200.000"). 2.20/2.64 % set(auto2) -> assign(max_hours, 1). 2.20/2.64 % assign(max_hours, 1) -> assign(max_seconds, 3600). 2.20/2.64 % set(auto2) -> assign(max_seconds, 0). 2.20/2.64 % set(auto2) -> assign(max_minutes, 5). 2.20/2.64 % assign(max_minutes, 5) -> assign(max_seconds, 300). 2.20/2.64 % set(auto2) -> set(sort_initial_sos). 2.20/2.64 % set(auto2) -> assign(sos_limit, -1). 2.20/2.64 % set(auto2) -> assign(lrs_ticks, 3000). 2.20/2.64 % set(auto2) -> assign(max_megs, 400). 2.20/2.64 % set(auto2) -> assign(stats, some). 2.20/2.64 % set(auto2) -> clear(echo_input). 2.20/2.64 % set(auto2) -> set(quiet). 2.20/2.64 % set(auto2) -> clear(print_initial_clauses). 2.20/2.64 % set(auto2) -> clear(print_given). 2.20/2.64 assign(lrs_ticks,-1). 2.20/2.64 assign(sos_limit,10000). 2.20/2.64 assign(order,kbo). 2.20/2.64 set(lex_order_vars). 2.20/2.64 clear(print_given). 2.20/2.64 2.20/2.64 % formulas(sos). % not echoed (1579 formulas) 2.20/2.64 2.20/2.64 ============================== end of input ========================== 2.20/2.64 2.20/2.64 % From the command line: assign(max_seconds, 1200). 2.20/2.64 2.20/2.64 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 2.20/2.64 2.20/2.64 % Formulas that are not ordinary clauses: 2.20/2.64 1 (all P all Q all R hAPP_A832564074le_alt(hAPP_l618618165le_alt(hAPP_f657005563le_alt(cOMBC_1919297930le_alt,P),Q),R) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_109) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 2 (all A1 all A2 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,A1),A2)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))) <-> (exists X_1 exists Y_9 exists Xs_17 exists Ys (A1 = hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_1),Xs_17) & A2 = hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_9),Ys) & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9)),R_2)) & hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_17),Ys)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))))) | nil_li1922300522le_alt = A2 & nil_li1922300522le_alt = A1)) # label(fact_576_listrel_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 3 (all Y_2 all R_2 ((exists A_7 exists X_1 (is_Arr1861959080le_alt(A_7) & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_7),X_1) = Y_2)) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),Y_2)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))) # label(fact_359_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 4 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_Arr43961803e_indi(hAPP_f836059805e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__032) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 5 (all Xs_34 all Ys_10 (nil_Ar126264853le_alt = Ys_10 -> last_A57386030le_alt(Xs_34) = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_34),Ys_10)))) # label(fact_416_last__appendL) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 6 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> (-hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1)) = hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1)))) # label(fact_717_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 7 (all X_2 all Y_2 all L_2 all Aa all Ba (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Y_2) -> (Aa != Ba -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> (Y_2 != X_2 & (Y_2 = Aa -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Ba)),L_2))) & (Aa != Y_2 -> (Aa = X_2 -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Y_2)),L_2)) | Y_2 = Ba) & (X_2 != Aa -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_2)))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_1539419881_below,L_2),Aa),Ba)))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 8 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),one_one_nat)) = N)) # label(fact_1198_Suc__diff__1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 9 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,B_1)))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),B_1))))) # label(fact_130_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 10 (all X_2 hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool))) # label(fact_376_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 11 (all Pa all Xs_1 (Xs_1 = hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1) <-> (all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) -> hBOOL(hAPP_A862370221t_bool(Pa,X_1))))))) # label(fact_678_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 12 (all X all Y (hAPP_nat_nat(suc,Y) = hAPP_nat_nat(suc,X) -> Y = X)) # label(fact_1010_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 13 (all X_2 all Y_2 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))) -> hAPP_l1872264749lt_nat(size_s1873794948le_alt,Y_2) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,X_2))) # label(fact_627_rtrancl__listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 14 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(hAPP_n1117890248e_indi(drop_A1037593438e_indi,N_2),Xs_1)))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_672_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 15 (all M M = hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat)) # label(fact_1149_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 16 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Ys))) & Xs_1 = hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)))))) # label(fact_873_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 17 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) <-> (exists Ys exists Zs hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)) = Xs_1))) # label(fact_836_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 18 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(butlas995342418e_indi,Ys_1)))) | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(butlas995342418e_indi,Xs_1)))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(butlas995342418e_indi,hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),Ys_1))))))) # label(fact_738_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 19 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A_1),B_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),B_1))))) # label(fact_915_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 20 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> (-hBOOL(hAPP_bool_bool(Pa,X_2)) -> hAPP_l1189022293t_bool(takeWhile_bool(Pa),Xs_1) = hAPP_l1189022293t_bool(takeWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1))))) # label(fact_720_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 21 (all B_1_1 is_Pro1725146340le_alt(last_P736051166le_alt(B_1_1))) # label(gsy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oal) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 22 (all B_1_1 is_Arr43961803e_indi(hd_Arr465110667e_indi(B_1_1))) # label(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 23 (all B_1_1 is_fun158382675l_bool(set_fu335223357t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 24 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_2)),hAPP_P1905961381l_bool(B_1,X_2)))))) # label(fact_170_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 25 (all Pa all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(Pa,Aa)) -> ((all Y_9 all Z_4 (is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(Z_4) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_9)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_9),Z_4)),R_2)) -> (hBOOL(hAPP_A862370221t_bool(Pa,Y_9)) -> hBOOL(hAPP_A862370221t_bool(Pa,Z_4))))))) -> hBOOL(hAPP_A862370221t_bool(Pa,Ba)))))) # label(fact_856_rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 26 (all Xs_1 (nil_fu507235289t_bool != Xs_1 -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hd_fun730195372t_bool(Xs_1)),set_fu1384968698t_bool(Xs_1))))) # label(fact_750_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 27 (all P all Q all R hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) = hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 28 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> (-hBOOL(hAPP_P606313927t_bool(Pa,X_2)) -> hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),Ys_1)) = hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),Xs_1)))) # label(fact_724_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 29 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,hAPP_f1438487600t_bool(cOMBK_488408421t_bool,B_1)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_2)),B_1))))) # label(fact_107_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 30 (all B_1_1 all B_2_1 is_bool(hAPP_f1634113933l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 31 (all X all Y (X != Y | hBOOL(hAPP_f965095724l_bool(hAPP_f1577179519l_bool(fequal785189517t_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 32 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_fun1393352280t_bool(hAPP_f239852716t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_050) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 33 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> (-hBOOL(hAPP_f592646513l_bool(Pa,X_2)) -> hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),Ys_1)) = hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),Xs_1)))) # label(fact_722_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 34 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(hAPP_n1117890248e_indi(take_A1967759030e_indi,N_2),Xs_1)))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_976_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 35 (all N_4 all Xs_3 hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_4),Xs_3)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_4),hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Xs_3))) # label(fact_620_tl__drop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 36 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_960_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 37 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_1)),hAPP_A568203993t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,B_1))))) # label(fact_283_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 38 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_1)),hAPP_A187815023l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,B_1))))) # label(fact_293_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 39 (all B_1_1 all B_2_1 is_bool(hAPP_f1757554033l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 40 (all Y_13 (is_Pro1725146340le_alt(Y_13) -> -(all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) != Y_13)))) # label(fact_309_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 41 (all B_1_1 all B_2_1 is_fun288122577l_bool(hAPP_n2095207769l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 42 (all P (hBOOL(hAPP_bool_bool(fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 43 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> (exists Ys exists Zs (Xs_1 = hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs)) & -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Ys))))))) # label(fact_872_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 44 (all A_1 (is_fun279392540l_bool(A_1) -> ((all X_1 (is_fun961089132t_bool(X_1) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)))) -> top_to1853035173l_bool = A_1))) # label(fact_459_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 45 (all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) <-> X_2 = Y_2)) # label(fact_970_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 46 (all I_2 all J all K_2 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),J)),K_2) = hAPP_nat_nat(minus_minus_nat(I_2),hAPP_nat_nat(plus_plus_nat(J),K_2))) # label(fact_1107_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 47 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> (exists Ys exists Zs hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs)) = Xs_1))) # label(fact_890_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 48 (all P all Q (is_fun288122577l_bool(P) -> P = hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_119) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 49 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,B_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B_1,X_2)))))) # label(fact_143_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 50 (all P all Q all R hAPP_P1056860425le_alt(P,hAPP_l391088160le_alt(Q,R)) = hAPP_l391088160le_alt(hAPP_f1514103381le_alt(hAPP_f500394983le_alt(cOMBB_500037706le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 51 (all B_1_1 all B_2_1 (is_fun1393352280t_bool(B_2_1) -> is_fun1393352280t_bool(hAPP_f2014742713t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___025) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 52 (all X_2 all Y_2 all L_2 all Aa all Ba (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(Y_2) -> (Aa != Ba -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> (Y_2 != X_2 & (Ba != X_2 -> (Ba = Y_2 -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Aa)),L_2)) | Aa = X_2) & (Y_2 != Ba -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_2)))) & (Ba = X_2 -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_2)),L_2))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(arrow_230821333_above(L_2,Aa),Ba)))))))) # label(fact_35_in__above) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 53 (all X_2 all Xs_1 (hBOOL(hAPP_l982832318l_bool(distin1691228364t_bool,Xs_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(takeWh1512678354t_bool(hAPP_f111185985l_bool(hAPP_f1982584345l_bool(cOMBB_310009925t_bool,fNot),hAPP_f863359027l_bool(hAPP_f495827653l_bool(cOMBC_1136104858l_bool,fequal1258273448t_bool),X_2))),hAPP_l1075146559t_bool(rev_fu1041356345t_bool,Xs_1)) = hAPP_l1075146559t_bool(rev_fu1041356345t_bool,hAPP_l1075146559t_bool(tl_fun2071351216t_bool,hAPP_l1075146559t_bool(dropWh1133555834t_bool(hAPP_f111185985l_bool(hAPP_f1982584345l_bool(cOMBB_310009925t_bool,fNot),hAPP_f863359027l_bool(hAPP_f495827653l_bool(cOMBC_1136104858l_bool,fequal1258273448t_bool),X_2))),Xs_1)))))) # label(fact_647_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 54 (all As (nil_Pr1357826771le_alt != As -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,last_P723779706le_alt(As)),set_Pr1404309362le_alt(As))))) # label(fact_727_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 55 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),zero_zero_nat)) <-> N_2 = zero_zero_nat)) # label(fact_1128_le__0__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 56 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_1)),hAPP_n588788980t_bool(B_1,X_1))))) -> hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,B_1))))) # label(fact_281_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 57 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,B_1))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B_1,X_2)))))) # label(fact_152_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 58 (all P all Q (is_fun1393352280t_bool(P) -> P = hAPP_f228695594t_bool(hAPP_f898562478t_bool(cOMBK_607931107t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___125) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 59 (exists X_1 (is_fun961089132t_bool(X_1) & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),top_to1853035173l_bool)))) # label(fact_450_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.64 60 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_Arr43961803e_indi(hAPP_P710098616e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__088) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 61 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun1236654035i_bool(hAPP_f244157820i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___081) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 62 (all B_1_1 all B_2_1 (is_fun1236654035i_bool(B_2_1) -> is_bool(hAPP_f1599966040l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 63 (all Pa all Xs_1 (nil_Ar126264853le_alt != Xs_1 -> ((all X_1 (is_Arr1861959080le_alt(X_1) -> hBOOL(hAPP_l1386638586t_bool(Pa,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt))))) -> ((all X_1 all Xs_17 (is_Arr1861959080le_alt(X_1) -> (Xs_17 != nil_Ar126264853le_alt -> (hBOOL(hAPP_l1386638586t_bool(Pa,Xs_17)) -> hBOOL(hAPP_l1386638586t_bool(Pa,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs_17))))))) -> hBOOL(hAPP_l1386638586t_bool(Pa,Xs_1)))))) # label(fact_313_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 64 (all B_1_1 all B_2_1 (is_fun2093718614t_bool(B_2_1) -> is_fun961089132t_bool(hAPP_f791205069t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___027) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 65 (all N_11 all X_20 all K_3 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_11),X_20)),hAPP_A832564074le_alt(replic351609551le_alt(K_3),X_20)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(K_3),X_20)),hAPP_A832564074le_alt(replic351609551le_alt(N_11),X_20))) # label(fact_582_append__replicate__commute) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 66 (all I_2 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> hAPP_nat_nat(suc,J_1) != K_2)))) # label(fact_1058_Suc__lessE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 67 (all A_1 top_to1853035173l_bool = pi_Pro666468413t_bool(A_1,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool))) # label(fact_351_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 68 (all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))) -> -(all X_1 all Xs_17 (hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_1),Xs_17) = Xs_1 -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_2)),R_2)) -> -hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_17),Ys_1)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2)))))))) # label(fact_545_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 69 (all Aa ((hBOOL(top_top_bool) <-> hBOOL(Aa)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa)))) # label(fact_990_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 70 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (exists M_1 hAPP_nat_nat(suc,M_1) = N))) # label(fact_1181_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 71 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) -> M = N))) # label(fact_1029_less__antisym) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 72 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n1674354836l_bool(B_1,X_1))))) -> hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,B_1))))) # label(fact_291_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 73 (all F all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(produc212588606t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P606313927t_bool(F,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_331_curryE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 74 (all Pa collect_nat(Pa) = Pa) # label(fact_323_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 75 (all P all Q all R hAPP_n1875670159le_alt(hAPP_A1043896845le_alt(hAPP_f1956511609le_alt(cOMBC_1697899890le_alt,P),Q),R) = hAPP_A832564074le_alt(hAPP_n49391885le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 76 (all X_2 all Xs_1 (hBOOL(hAPP_l54057324t_bool(distin1553582624le_alt,Xs_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> hAPP_l1493873365le_alt(rev_Pr464210035le_alt,hAPP_l1493873365le_alt(tl_Pro292865596le_alt,hAPP_l1493873365le_alt(dropWh1604595954le_alt(hAPP_f1642286869t_bool(hAPP_f62793075t_bool(cOMBB_1604919143le_alt,fNot),hAPP_P163071551t_bool(hAPP_f2139078121t_bool(cOMBC_1470522126t_bool,fequal673514820le_alt),X_2))),Xs_1))) = hAPP_l1493873365le_alt(takeWh416411546le_alt(hAPP_f1642286869t_bool(hAPP_f62793075t_bool(cOMBB_1604919143le_alt,fNot),hAPP_P163071551t_bool(hAPP_f2139078121t_bool(cOMBC_1470522126t_bool,fequal673514820le_alt),X_2))),hAPP_l1493873365le_alt(rev_Pr464210035le_alt,Xs_1))))) # label(fact_643_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 77 (all B_1_1 all B_2_1 is_fun158382675l_bool(hAPP_P1606644490l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_098) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 78 (all B_1_1 all B_2_1 is_bool(hAPP_f10461143l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_061) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 79 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B_1,X_2)))))) # label(fact_178_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 80 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) & hBOOL(hAPP_f965095724l_bool(Pa,X_2)))) # label(fact_686_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 81 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B_1,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))))) # label(fact_61_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 82 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,hAPP_f584002568l_bool(cOMBK_532713098ol_nat,B_1)))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_2)),B_1))))) # label(fact_115_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 83 (all P_a all Pa all A_8 all B_7 all Aa all Ba (is_Arr1861959080le_alt(A_8) & is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(B_7) -> (Ba != Aa -> (A_8 != B_7 -> (B_7 != Aa -> (Ba != A_8 -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_a),arrow_1721807329e_Prof)) -> ((all I (is_Arr43961803e_indi(I) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_8),B_7)),hAPP_A1677245848t_bool(P_a,I))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I)))))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_8),B_7)),hAPP_f412050202t_bool(f,P_a))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))))))))))))) # label(fact_24__C2_C) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 84 (all X_2 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),top_to772840767t_bool))) # label(fact_365_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 85 (all Ca all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_1),B_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),B_1))))) # label(fact_916_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 86 (all Y_2 all X_2 all Xs_1 (is_Pro1725146340le_alt(Y_2) & is_Pro1725146340le_alt(X_2) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Y_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Xs_1)))) -> X_2 = Y_2 | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Y_2),set_Pr604701398le_alt(Xs_1)))))) # label(fact_667_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 87 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_l1284365004t_bool(hAPP_l1538437917t_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_P1861769507t_bool(hAPP_f906821569t_bool(produc2091914181t_bool,Ca),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)))))) # label(fact_524_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 88 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> M_2 != N_2)) # label(fact_1012_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 89 (all F all Aa all Ba (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P1327827171t_bool(hAPP_f1331183759t_bool(produc1102988737t_bool,F),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))))) # label(fact_515_splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 90 (all X_2 all Xs_1 (hBOOL(hAPP_l89806901l_bool(distin22312297t_bool,Xs_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> hAPP_l1660244757t_bool(dropWh1552197947t_bool(hAPP_f146009813l_bool(hAPP_f356431923l_bool(cOMBB_871930928t_bool,fNot),hAPP_f1577179519l_bool(hAPP_f1688301673l_bool(cOMBC_2105056416l_bool,fequal785189517t_bool),X_2))),hAPP_l1660244757t_bool(rev_fu1957290812t_bool,Xs_1)) = hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),hAPP_l1660244757t_bool(rev_fu1957290812t_bool,hAPP_l1660244757t_bool(takeWh1309019107t_bool(hAPP_f146009813l_bool(hAPP_f356431923l_bool(cOMBB_871930928t_bool,fNot),hAPP_f1577179519l_bool(hAPP_f1688301673l_bool(cOMBC_2105056416l_bool,fequal785189517t_bool),X_2))),Xs_1)))))) # label(fact_657_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 91 (all B_1_1 all B_2_1 (is_fun288122577l_bool(B_1_1) -> is_fun158382675l_bool(pi_fun150026276t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 92 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,hAPP_f1609079369t_bool(cOMBK_1369841150le_alt,B_1)))))) # label(fact_223_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 93 (all B_1_1 all B_2_1 (is_fun158382675l_bool(B_2_1) -> is_fun158382675l_bool(hAPP_f1765205l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_059) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 94 (all F F = hAPP_f1078809103le_alt(produc748227559le_alt,produc335266950le_alt(F))) # label(fact_496_split__curry) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 95 (all X_2 all A_1 (hBOOL(hAPP_A862370221t_bool(A_1,X_2)) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)))) # label(fact_316_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 96 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(L_1))) -> (hBOOL(hAPP_nat_bool(Q_1,X_1)) <-> hBOOL(hAPP_nat_bool(Pa,X_1))))) -> hAPP_l248265089st_nat(takeWhile_nat(Q_1),K) = hAPP_l248265089st_nat(takeWhile_nat(Pa),L_1)))) # label(fact_846_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 97 (all I_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(suc,I_2))),N)))) # label(fact_1117_diff__Suc__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 98 (all A_1 (is_fun1393352280t_bool(A_1) -> ((all X_1 (is_Arr1861959080le_alt(X_1) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)))) -> top_to2076077793t_bool = A_1))) # label(fact_456_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 99 (all B_1_1 all B_2_1 is_fun158382675l_bool(hAPP_n295497947l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 100 (all Xs_1 (hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs_1)) <-> Xs_1 = nil_Ar126264853le_alt)) # label(fact_338_eq__Nil__null) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 101 (all Y_2 all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),set_nat(Xs_1))) | X_2 = Y_2)) # label(fact_659_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 102 (all X_32 all Xs_45 ((nil_Ar126264853le_alt != Xs_45 -> hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_32),Xs_45)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_32),hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_45))) & (Xs_45 = nil_Ar126264853le_alt -> nil_Ar126264853le_alt = hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_32),Xs_45))))) # label(fact_356_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 103 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(hAPP_n19406600le_alt(drop_P283022739le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))))) # label(fact_671_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 104 (all M all K_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))))) # label(fact_1082_add__leE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 105 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),one_one_nat)) = N)) # label(fact_1197_Suc__pred_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 106 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_1)),hAPP_A366518464l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,B_1))))) # label(fact_215_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 107 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> (-hBOOL(hAPP_nat_bool(Pa,X_2)) -> hAPP_l248265089st_nat(takeWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(takeWhile_nat(Pa),Xs_1)))) # label(fact_716_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 108 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1052_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 109 (all X_2 all Xs_1 ((-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Xs_1) = hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(insert256706849le_alt,X_2),Xs_1)) & (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> Xs_1 = hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(insert256706849le_alt,X_2),Xs_1)))) # label(fact_770_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 110 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,B_1))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_2)),hAPP_f1593910865t_bool(B_1,X_2)))))) # label(fact_154_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 111 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_1)),hAPP_A1928120382l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,B_1))))) # label(fact_288_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 112 (all M all K_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1081_add__leD1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 113 (all X_2 all L_2 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(arrow_1495666017_mkbot(L_2),X_2)),arrow_1681063817le_Lin)))) # label(fact_27_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 114 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,hAPP_f372103450t_bool(cOMBK_1411148035t_bool,B_1)))))) # label(fact_226_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 115 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_1)),hAPP_f1865483825t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,B_1))))) # label(fact_272_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 116 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))))) # label(fact_670_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 117 (all P all Q all R hAPP_P606313927t_bool(hAPP_P1267694911t_bool(hAPP_f135580393t_bool(cOMBC_607108822t_bool,P),Q),R) = hAPP_P606313927t_bool(hAPP_P1267694911t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 118 (all Ys_1 all R_2 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),Ys_1)),hAPP_f1865483825t_bool(lex_Ar255587961le_alt,R_2)))) # label(fact_482_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 119 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_75_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 120 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_1)),hAPP_A568203993t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,B_1))))) # label(fact_201_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 121 (all X_2 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))) -> ((all Y_9 (hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_9),Xs_1) = Ys_1 -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_9)),R_2)))) -> -(all Zs (hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Zs) = Ys_1 -> -hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Zs)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2)))))))) # label(fact_475_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 122 (all X_39 all Xs_53 Xs_53 != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_39),Xs_53)) # label(fact_43_not__Cons__self2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 123 (all I_1 all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K)),J_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K)))))) # label(fact_1157_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 124 (all M M = hAPP_nat_nat(plus_plus_nat(M),zero_zero_nat)) # label(fact_1112_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 125 (all B_1_1 all B_2_1 is_bool(hAPP_list_bool_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 126 (all P all Q all R hAPP_f592646513l_bool(hAPP_f863359027l_bool(hAPP_f495827653l_bool(cOMBC_1136104858l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_f863359027l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 127 (all X_2 hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2))) # label(fact_345_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 128 (all Z_2 all Y_7 all X_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_2),Y_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_2),X_8))))) # label(fact_933_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 129 (all B_1_1 (is_fun1393352280t_bool(B_1_1) -> is_fun1393352280t_bool(collec1729629178le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 130 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B_1,X_2)))))) # label(fact_163_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 131 (all B_1_1 (is_fun158382675l_bool(B_1_1) -> is_fun158382675l_bool(collec418781817t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 132 (all Xs_1 all Ys_1 (nil_Ar126264853le_alt = Ys_1 <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1) = Xs_1)) # label(fact_404_self__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 133 (all P all Q all R hAPP_P864444517le_alt(P,hAPP_l391088160le_alt(Q,R)) = hAPP_l693571982le_alt(hAPP_f2001490223le_alt(hAPP_f1939049849le_alt(cOMBB_723746886le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_158) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 134 (all B_1_1 all B_2_1 (is_fun1236654035i_bool(B_1_1) -> is_fun288122577l_bool(pi_Arr990697634t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 135 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_1018_le__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 136 (all B_1_1 all B_2_1 is_fun2093718614t_bool(hAPP_f231379647t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___028) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 137 (all Aa all Ba all R_2 (is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(Ba) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),transi1256616594le_alt(R_2))) -> (Ba != Aa -> -(all Y_9 (is_Arr1861959080le_alt(Y_9) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_9)),transi1256616594le_alt(R_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_9),Ba)),R_2))))))))) # label(fact_862_rtranclE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 138 (all A all B (is_Arr1861959080le_alt(B) & is_Arr1861959080le_alt(A) -> (B != A -> (exists C_5 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,B),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,C_5),nil_Ar126264853le_alt))))) & is_Arr1861959080le_alt(C_5)))))) # label(fact_31_third__alt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 139 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,B_1))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B_1,X_2)))))) # label(fact_158_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 140 (all X_2 all Xs_1 ((exists Ys exists Zs (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Ys))) & Xs_1 = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs)))) <-> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_815_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 141 (all B_1_1 all B_2_1 is_fun760276937t_bool(hAPP_n1965810497t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 142 (all X_2 all Xs_1 ((hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(hAPP_f613335309t_bool(insert202184175t_bool,X_2),Xs_1) = Xs_1) & (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Xs_1) = hAPP_l1075146559t_bool(hAPP_f613335309t_bool(insert202184175t_bool,X_2),Xs_1)))) # label(fact_768_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 143 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,hAPP_f256804927l_bool(cOMBK_69806648l_bool,B_1)))))) # label(fact_253_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 144 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(hAPP_n2038854252t_bool(take_f1937952705t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))))) # label(fact_979_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 145 (exists X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),top_to2076077793t_bool)) & is_Arr1861959080le_alt(X_1))) # label(fact_447_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 146 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B_1,X_2)))))) # label(fact_148_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 147 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_1028_less__SucI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 148 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_1)),hAPP_n295497947l_bool(B_1,X_1))))) -> hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,B_1))))) # label(fact_213_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 149 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B_1,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))))) # label(fact_52_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 150 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_2)),hAPP_P1861769507t_bool(B_1,X_2)))))) # label(fact_160_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 151 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat)) # label(fact_1131_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 152 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Ys))) & Xs_1 = hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs)))))) # label(fact_871_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 153 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,hAPP_f1328016200t_bool(cOMBK_856666543ol_nat,B_1)))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_2)),B_1))))) # label(fact_110_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 154 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(M_2),N_2))))) # label(fact_1174_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 155 (all N_2 all K all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),K)),hAPP_nat_nat(minus_minus_nat(N_2),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))))) # label(fact_1137_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 156 (all P all Q hAPP_f5761716t_bool(hAPP_f14382104t_bool(cOMBK_1914291077t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___156) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 157 (all X_1 all Xa all Xb_1 (hBOOL(hAPP_P606313927t_bool(X_1,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Xa),Xb_1))) <-> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(produc212588606t_bool(X_1),Xa),Xb_1)))) # label(fact_327_curry__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 158 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_1)),hAPP_n588788980t_bool(B_1,X_1))))) -> hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,B_1))))) # label(fact_199_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 159 (all X_2 hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool))) # label(fact_378_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 160 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) <-> (exists Ys exists Zs (hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Ys))))))) # label(fact_816_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 161 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_Arr1861959080le_alt(hAPP_f666924118le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__031) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 162 (all N_5 all Xs_4 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_5),hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Xs_4)) = hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_5),Xs_4))) # label(fact_619_drop__tl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 163 (all Ca all P_1 all Q_2 (Q_2 = P_1 -> (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Ca),P_1)) <-> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Ca),Q_2))))) # label(fact_484_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 164 (all B_1_1 all B_2_1 (is_fun158382675l_bool(B_2_1) -> is_bool(hAPP_f250445784l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_058) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 165 (all Ys_1 all Xs_1 (Xs_1 = nil_Ar126264853le_alt <-> Ys_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))) # label(fact_405_self__append__conv2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 166 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),R_2)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ca)),transi1256616594le_alt(R_2)))))) # label(fact_638_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 167 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P324742453l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,B_1))))) # label(fact_300_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 168 (all P all Q hAPP_f996881846t_bool(hAPP_f372103450t_bool(cOMBK_1411148035t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___142) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 169 (all P all Q all R hAPP_f318645548t_bool(hAPP_l1288188215t_bool(P,R),Q) = hAPP_l1747810175t_bool(hAPP_f311173987t_bool(hAPP_f66177535t_bool(cOMBC_672290030t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_137) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 170 (all X_10 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10))) # label(fact_908_order__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 171 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),set_fu1865467835t_bool(Xs_1))) -> hBOOL(hAPP_f965095724l_bool(Pa,X_1))))) -> hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),Ys_1)) = hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),Ys_1)))) # label(fact_807_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 172 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_Arr43961803e_indi(hAPP_f1693298207e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_048) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 173 (all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) <-> hBOOL(hAPP_nat_bool(A_1,X_2)))) # label(fact_314_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 174 (all N (N != zero_zero_nat -> (exists M_1 N = hAPP_nat_nat(suc,M_1)))) # label(fact_1185_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 175 (all Y_2 all Ys_1 all Xs_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1)),Xs_1)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))) -> -(all Y_9 all Ys (hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_9),Ys) = Xs_1 -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_2),Y_9)),R_2)) -> -hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Ys_1),Ys)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2)))))))) # label(fact_547_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 176 (all B_1_1 all B_2_1 (is_fun279392540l_bool(B_2_1) -> is_fun279392540l_bool(hAPP_f111185985l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_071) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 177 (all Z_3 all Ca all P_1 ((all A_7 all B_6 (P_1 = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_l1284365004t_bool(hAPP_l1538437917t_bool(Ca,A_7),B_6))))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_P1861769507t_bool(hAPP_f906821569t_bool(produc2091914181t_bool,Ca),P_1))))) # label(fact_559_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 178 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),Xs_1)))) -> hBOOL(hAPP_A1785763630i_bool(Pa,X_2)) & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_682_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 179 (all B_1_1 (is_fun279392540l_bool(B_1_1) -> is_fun279392540l_bool(collec1553055422t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 180 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A_1),B_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B_1))))) # label(fact_944_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 181 (all X_2 all Xs_1 ((hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> Xs_1 = hAPP_l1493873365le_alt(hAPP_P734992695le_alt(insert178756925le_alt,X_2),Xs_1)) & (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> hAPP_l1493873365le_alt(hAPP_P734992695le_alt(insert178756925le_alt,X_2),Xs_1) = hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Xs_1)))) # label(fact_764_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 182 (all Us_1 all Vs_1 all Xs_1 all Ys_1 all R_2 (Xs_1 = Ys_1 & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Us_1),Vs_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) | Us_1 = Vs_1 & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Us_1)),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),Vs_1))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))) # label(fact_466_append__listrel1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 183 (all B_1_1 all B_2_1 is_bool(hAPP_f1976794890l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_060) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 184 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_Arr1861959080le_alt(hAPP_f1054274129le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 185 (all X_2 (hBOOL(hAPP_A862370221t_bool(top_to2076077793t_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_387_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 186 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_2)),hAPP_P1606644490l_bool(B_1,X_2)))))) # label(fact_174_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 187 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)))) # label(fact_1050_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 188 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,B_1)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),B_1))))) # label(fact_109_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 189 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> (-hBOOL(hAPP_f312250286l_bool(Pa,X_2)) -> hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),Ys_1)) = hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),Xs_1)))) # label(fact_721_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 190 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> (-hBOOL(hAPP_P1327827171t_bool(Pa,X_2)) -> hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),Xs_1) = hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),Ys_1))))) # label(fact_718_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 191 (all P all Q (is_fun288122577l_bool(P) -> P = hAPP_P139894920l_bool(hAPP_f695414965l_bool(cOMBK_1193272835le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_141) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 192 (all P all Q all R hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,P),Q),R) = hAPP_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 193 (all K all M_2 all N_2 (M_2 = N_2 <-> hAPP_nat_nat(plus_plus_nat(K),M_2) = hAPP_nat_nat(plus_plus_nat(K),N_2))) # label(fact_1088_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 194 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))))) # label(fact_974_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 195 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun1097062475t_bool(hAPP_A1159885342t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_007) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 196 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_2)),hAPP_f1663053423t_bool(B_1,X_2))) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1))))) # label(fact_78_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 197 (all Xs_1 (Xs_1 != nil_Pr2088511415le_alt -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hd_Pro1524751780le_alt(Xs_1)),set_Pr604701398le_alt(Xs_1))))) # label(fact_752_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 198 (all I_1 all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(Pa,N_1)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I_1)))))) # label(fact_1184_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 199 (all J_2 all K all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_1),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K)),I_1)))) # label(fact_1161_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 200 (all Xs_1 (nil_Ar126264853le_alt = Xs_1 <-> hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_1) = nil_Ar126264853le_alt)) # label(fact_461_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 201 (all M all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(plus_plus_nat(M),J))))) # label(fact_1065_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 202 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,hAPP_f14382104t_bool(cOMBK_1914291077t_bool,B_1)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_2)),B_1))))) # label(fact_106_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 203 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,A_1),B_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),B_1))))) # label(fact_941_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 204 (all Xs_1 all X_2 (Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt) <-> hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt))) # label(fact_623_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 205 (all B_1_1 all B_2_1 is_bool(hAPP_f899439636l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 206 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),set_fu335223357t_bool(L_1))) -> (hBOOL(hAPP_f312250286l_bool(Q_1,X_1)) <-> hBOOL(hAPP_f312250286l_bool(Pa,X_1)))))) -> hAPP_l210315413t_bool(dropWh23362493t_bool(Q_1),K) = hAPP_l210315413t_bool(dropWh23362493t_bool(Pa),L_1)))) # label(fact_842_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 207 (all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),transi992120749le_alt(R_2))) -> (Ba != Aa -> -(all Y_9 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Y_9)),transi992120749le_alt(R_2))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_9),Ba)),R_2))))))) # label(fact_861_rtranclE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 208 (all B_1_1 all B_2_1 is_fun1097062475t_bool(hAPP_P1599728724t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_097) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 209 (all B_1_1 all B_2_1 is_fun1097062475t_bool(hAPP_n291670979t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_024) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 210 (all Xs_1 all R_2 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),nil_Ar126264853le_alt)),hAPP_f1865483825t_bool(lex_Ar255587961le_alt,R_2)))) # label(fact_481_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 211 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),set_Pr604701398le_alt(Xs_1))) -> hBOOL(hAPP_P606313927t_bool(Pa,X_1))))) -> hAPP_l1766111573le_alt(dropWh1907450966le_alt(Pa),hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),Ys_1)) = hAPP_l1766111573le_alt(dropWh1907450966le_alt(Pa),Ys_1))) # label(fact_799_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 212 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_1)),B_1))))) -> hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,hAPP_f81007726t_bool(cOMBK_2130565512t_bool,B_1)))))) # label(fact_225_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 213 (all X_25 all Xs_28 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_28),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_25),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(rotate1322903650le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_25),Xs_28)) & nil_Ar126264853le_alt = hAPP_l726444215le_alt(rotate1322903650le_alt,nil_Ar126264853le_alt))) # label(fact_442_rotate__simps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 214 (all Xs_1 all Ys_1 hAPP_l726444215le_alt(list_c380068407le_alt(hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Ys_1),hAPP_f1608056749le_alt(cOMBK_1696648346le_alt,hAPP_l568342716le_alt(hAPP_f1294513379le_alt(cOMBC_1058495865le_alt,append1166636842le_alt),Ys_1))),Xs_1) = hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))) # label(fact_513_tl__append) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 215 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1))))) # label(fact_964_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 216 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),set_Pr1404309362le_alt(L_1))) -> (hBOOL(hAPP_P1327827171t_bool(Q_1,X_1)) <-> hBOOL(hAPP_P1327827171t_bool(Pa,X_1))))) -> hAPP_l1493873365le_alt(dropWh1604595954le_alt(Pa),L_1) = hAPP_l1493873365le_alt(dropWh1604595954le_alt(Q_1),K)))) # label(fact_839_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 217 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> (exists Ys exists Zs (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Ys))))))) # label(fact_865_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 218 (all Xs_1 all Ys_1 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1) = nil_Ar126264853le_alt <-> nil_Ar126264853le_alt = Ys_1 & nil_Ar126264853le_alt = Xs_1)) # label(fact_406_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.65 219 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,B_1)))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),B_1))))) # label(fact_103_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 220 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_1),B_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B_1))))) # label(fact_955_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 221 (all N_13 exists Xs_17 N_13 = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_17)) # label(fact_579_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 222 (all Ca all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A_1),B_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),B_1))))) # label(fact_914_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 223 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B_1,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))))) # label(fact_66_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 224 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) <-> (exists Ys exists Zs hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) = Xs_1))) # label(fact_832_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 225 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_1011_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 226 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_2),Xs_1) = Xs_1)) # label(fact_699_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 227 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(butlas995342418e_indi,Xs_1)))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_691_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 228 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,A_1),B_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),B_1))))) # label(fact_962_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 229 (all P all Q all R hAPP_bool_bool(P,hAPP_P606313927t_bool(Q,R)) = hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f600409331t_bool(cOMBB_433601099le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Arrow_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 230 (all X_2 all Xs_1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1))) # label(fact_771_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 231 (all B_1_1 is_fun961089132t_bool(last_f2112695026t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 232 (all X all Y (is_Pro1725146340le_alt(Y) & is_Pro1725146340le_alt(X) -> -hBOOL(hAPP_P606313927t_bool(hAPP_P1267694911t_bool(fequal454353832le_alt,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpu) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 233 (all Z_3 all Ca all P_1 ((all A_7 all B_6 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_l1328583473l_bool(hAPP_l395992834l_bool(Ca,A_7),B_6))))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_P139894920l_bool(hAPP_f86548619l_bool(produc998313258l_bool,Ca),P_1))))) # label(fact_560_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 234 (all P_1 all G all F all Q_2 (is_Pro1725146340le_alt(Q_2) -> ((all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) = Q_2 -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(G,X_1),Y_9)) <-> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F,X_1),Y_9)))))) -> (P_1 = Q_2 -> (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,G),Q_2)) <-> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F),P_1))))))) # label(fact_507_split__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 235 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) <-> (exists Ys exists Zs Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs))))) # label(fact_829_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 236 (all R_1 all S_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f580451669i_bool(hAPP_f712459161i_bool(cOMBC_1781321570l_bool,member1493247163e_indi),R_1)),hAPP_f580451669i_bool(hAPP_f712459161i_bool(cOMBC_1781321570l_bool,member1493247163e_indi),S_1))) <-> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,R_1),S_1)))) # label(fact_926_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 237 (all Xs_1 all X_2 all Ys_1 all Y_2 (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(X_2) -> (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt)) <-> Y_2 = X_2 & Xs_1 = Ys_1))) # label(fact_414_append1__eq__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 238 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 239 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) <-> (exists Ys exists Zs Xs_1 = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs))))) # label(fact_833_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 240 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),hAPP_A60074736l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,B_1))))) # label(fact_302_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 241 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun158382675l_bool(hAPP_A1112981887l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_014) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 242 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,hAPP_f11902820l_bool(cOMBK_39620975ol_nat,B_1)))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_2)),B_1))))) # label(fact_120_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 243 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_A490104565t_bool(hAPP_A101171597t_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_P2082381915t_bool(hAPP_f1783389935t_bool(produc51145731t_bool,Ca),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)))))) # label(fact_520_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 244 (all P all Q all R hAPP_A862370221t_bool(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_A862370221t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 245 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N)))) # label(fact_1072_le__add2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 246 (all Xs_1 (Xs_1 != nil_bool -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hd_bool(Xs_1)),set_bool(Xs_1))))) # label(fact_748_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 247 (all Ca all A_1 all B_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_1))))) # label(fact_909_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 248 (all Aa all R_2 hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Aa)),transi1256616594le_alt(R_2)))) # label(fact_632_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 249 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M)))) # label(fact_1168_diff__less__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 250 (all B_1_1 all B_2_1 is_bool(hAPP_f651410150l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 251 (all K_2 all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),K_2))))) # label(fact_1064_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 252 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A_1),B_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),B_1))))) # label(fact_961_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 253 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_fun279392540l_bool(hAPP_P229966473l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__093) # label(hypothesis) # label(non_clause). [assumption]. 2.20/2.66 254 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) <-> (exists K_1 hAPP_nat_nat(plus_plus_nat(M_2),K_1) = N_2))) # label(fact_1074_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 255 (all A_10 all List_4 hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_10),List_4) != nil_Ar126264853le_alt) # label(fact_37_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 256 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> N_2 != M_2 & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1045_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 257 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1236654035i_bool(hAPP_b1337486384i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf_017) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 258 (all X_2 all A_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) <-> hBOOL(hAPP_A1785763630i_bool(A_1,X_2)))) # label(fact_317_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 259 (all Pa all Aa all Ba (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(Aa),Ba))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))) & (all D (Aa = hAPP_nat_nat(plus_plus_nat(Ba),D) -> hBOOL(hAPP_nat_bool(Pa,D)))))) # label(fact_1101_nat__diff__split) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 260 (all I_2 all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2) = hAPP_nat_nat(plus_plus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)))) # label(fact_1158_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 261 (all Pa ((exists A_7 exists B_6 hBOOL(hAPP_P1327827171t_bool(Pa,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)))) <-> (exists X1 hBOOL(hAPP_P1327827171t_bool(Pa,X1))))) # label(fact_134_split__paired__Ex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 262 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),B_1))))) # label(fact_128_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 263 (all N_2 all M_2 hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(ord_min_nat,N_2))),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,N_2)),M_2)) # label(fact_1175_min__Suc1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 264 (all X_2 all Xs_1 (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Xs_1) = hAPP_l1075146559t_bool(hAPP_f613335309t_bool(insert202184175t_bool,X_2),Xs_1))) # label(fact_777_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 265 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) <-> hAPP_nat_nat(minus_minus_nat(M_2),N_2) = zero_zero_nat)) # label(fact_1130_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 266 (all X all Y (hBOOL(hAPP_P606313927t_bool(hAPP_P1267694911t_bool(fequal454353832le_alt,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpu) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 267 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(butlas1157436197t_bool,Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))))) # label(fact_694_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 268 (all Ca all A_1 all B_1 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_1),B_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),B_1))))) # label(fact_917_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 269 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_1)),hAPP_f1628730575t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,B_1))))) # label(fact_184_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 270 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_1)),hAPP_f228695594t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,B_1))))) # label(fact_268_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 271 (all P all Q P = hAPP_f1628730575t_bool(hAPP_f81007726t_bool(cOMBK_2130565512t_bool,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__117) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 272 (all X_2 hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool))) # label(fact_380_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 273 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) & hBOOL(hAPP_A862370221t_bool(Pa,X_1)))) -> (exists Ys exists X_1 (is_Arr1861959080le_alt(X_1) & (all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Ys))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa)))) & hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & (exists Zs hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs)) = Xs_1))))) # label(fact_906_split__list__first__prop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 274 (all M all N (zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M),N) -> (hAPP_nat_nat(minus_minus_nat(N),M) = zero_zero_nat -> N = M))) # label(fact_1146_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 275 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B_1,X_2))) -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1))))) # label(fact_84_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 276 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f1624277646l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,B_1))))) # label(fact_280_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 277 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_1)),hAPP_f5761716t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,B_1))))) # label(fact_277_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 278 (all P all Q (is_fun279392540l_bool(P) -> hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_107) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 279 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_2)),hAPP_P1606644490l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1))))) # label(fact_63_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 280 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 281 (all Q all P (-hBOOL(Q) | hBOOL(hAPP_bool_bool(fconj(P),Q)) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 282 (all B_1 all A_6 all A_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_6),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(A_1,B_1)),pi_Arr990697634t_bool(A_6,B_1))))) # label(fact_921_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 283 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1126_not__less0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 284 (all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> -(all X_1 all Xs_17 (is_Arr1861959080le_alt(X_1) -> (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs_17) = Xs_1 -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_2)),R_2)) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_17),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))))))))) # label(fact_546_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 285 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B_1,X_2)))))) # label(fact_179_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 286 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(hAPP_n2038854252t_bool(drop_f642150681t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))))) # label(fact_675_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 287 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Ys))) & Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs)))))) # label(fact_866_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 288 (all X_2 all Xs_1 (hBOOL(hAPP_l982832318l_bool(distin1691228364t_bool,Xs_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(dropWh1133555834t_bool(hAPP_f111185985l_bool(hAPP_f1982584345l_bool(cOMBB_310009925t_bool,fNot),hAPP_f863359027l_bool(hAPP_f495827653l_bool(cOMBC_1136104858l_bool,fequal1258273448t_bool),X_2))),hAPP_l1075146559t_bool(rev_fu1041356345t_bool,Xs_1)) = hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),hAPP_l1075146559t_bool(rev_fu1041356345t_bool,hAPP_l1075146559t_bool(takeWh1512678354t_bool(hAPP_f111185985l_bool(hAPP_f1982584345l_bool(cOMBB_310009925t_bool,fNot),hAPP_f863359027l_bool(hAPP_f495827653l_bool(cOMBC_1136104858l_bool,fequal1258273448t_bool),X_2))),Xs_1)))))) # label(fact_656_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 289 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_1)),B_1)))) -> hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,hAPP_f1328016200t_bool(cOMBK_856666543ol_nat,B_1)))))) # label(fact_240_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 290 (all A_1 pi_Arr990697634t_bool(A_1,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool) # label(fact_353_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 291 (all X_2 all Xs_1 (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Xs_1) = hAPP_l1660244757t_bool(hAPP_f726713198t_bool(insert1665396998t_bool,X_2),Xs_1))) # label(fact_778_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 292 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_1145_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 293 (all X_2 all Xs_1 all Y_2 all Ys_1 all R_2 (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Y_2) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),hAPP_f1865483825t_bool(lex_Ar255587961le_alt,R_2))) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(lex_Ar255587961le_alt,R_2))) & X_2 = Y_2 | hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_1) & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2))))) # label(fact_509_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 294 (all P_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,P_1),R_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,P_1),transi992120749le_alt(R_2))))) # label(fact_633_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 295 (all X_2 all U all V all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X_2),U)),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X_2),V))),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) -> ((all A_7 (is_Arr1861959080le_alt(A_7) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),A_7)),R_2)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,U),V)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2)))))) # label(fact_436_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 296 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P2136891882t_bool(hAPP_f1984771213t_bool(produc1527919682t_bool,Ca),P_1))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A1862272720t_bool(hAPP_A1470764750t_bool(Ca,X_1),Y_9))))))))) # label(fact_563_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 297 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_1),B_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),B_1))))) # label(fact_942_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 298 (exists X_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),top_to1576102282i_bool)) & is_Arr43961803e_indi(X_1))) # label(fact_446_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 299 (all I_2 all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(plus_plus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2))) # label(fact_1154_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 300 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_Arr1861959080le_alt(Z_4) & is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ys_1),Zs_1)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Zs_1)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))))) # label(fact_781_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 301 (all N_2 all X_2 all Xs_1 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = hAPP_n1875670159le_alt(nat_ca14895078le_alt(nil_Ar126264853le_alt,hAPP_f402821245le_alt(hAPP_f548810715le_alt(cOMBB_903467948lt_nat,hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2)),hAPP_l382792410le_alt(hAPP_f2068969285le_alt(cOMBC_1511969967le_alt,take_A1601602045le_alt),Xs_1))),N_2)) # label(fact_902_take__Cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 302 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1047_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 303 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,hAPP_f1809347209t_bool(cOMBK_1632198563le_alt,B_1)))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_2)),B_1))))) # label(fact_91_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 304 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),set_Ar219761597e_indi(L_1))) -> (hBOOL(hAPP_A1785763630i_bool(Pa,X_1)) <-> hBOOL(hAPP_A1785763630i_bool(Q_1,X_1)))))) -> hAPP_l54953109e_indi(dropWh601337149e_indi(Q_1),K) = hAPP_l54953109e_indi(dropWh601337149e_indi(Pa),L_1)))) # label(fact_840_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 305 (all M all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(plus_plus_nat(J),M))))) # label(fact_1066_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 306 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) <-> (exists Ys exists Zs (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Ys))) & Xs_1 = hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)))))) # label(fact_818_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 307 (all R_1 all S_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,hAPP_f1642286869t_bool(hAPP_f1297597679t_bool(cOMBC_188453282l_bool,member1020705648le_alt),R_1)),hAPP_f1642286869t_bool(hAPP_f1297597679t_bool(cOMBC_188453282l_bool,member1020705648le_alt),S_1))) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,R_1),S_1)))) # label(fact_925_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 308 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),Xs_1)))) -> hBOOL(hAPP_P606313927t_bool(Pa,X_2)) & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))))) # label(fact_687_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 309 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) | M_2 = N_2)) # label(fact_1044_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 310 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Zs))) & hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs)) = Xs_1)))) # label(fact_880_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 311 (all M all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N))) # label(fact_1196_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 312 (all X_2 hBOOL(hAPP_A862370221t_bool(top_to2076077793t_bool,X_2))) # label(fact_350_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 313 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> (exists K_1 hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_2),K_1)) = N_2))) # label(fact_1092_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 314 (all B_1_1 all B_2_1 is_bool(hAPP_P1327827171t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 315 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(hAPP_n1200821448t_bool(take_f1428279094t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_978_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 316 (all Aa hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),top_to1714702858l_bool))) # label(fact_987_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 317 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A_1),B_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B_1))))) # label(fact_953_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 318 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f210572555l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,B_1))))) # label(fact_193_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 319 (all M all N (M = N | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1041_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 320 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> (exists Ys exists Zs (Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Ys))))))) # label(fact_869_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 321 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_fun_bool_bool(hAPP_P324742453l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__092) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 322 (all X_5 all Y_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_5),Y_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5)) -> X_5 = Y_4))) # label(fact_936_order__antisym) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 323 (all Aa (is_fun961089132t_bool(Aa) -> (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa)) -> Aa = top_to565915683t_bool))) # label(fact_997_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 324 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_1)),hAPP_P1861769507t_bool(B_1,X_1))))) -> hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,B_1))))) # label(fact_200_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 325 (all B_1_1 all B_2_1 is_bool(hAPP_f879361201l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 326 (all Pa all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(Pa,Ba)) -> ((all Y_9 all Z_4 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_9),Z_4)),R_2)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Z_4),Ba)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(Pa,Z_4)) -> hBOOL(hAPP_l1386638586t_bool(Pa,Y_9)))))) -> hBOOL(hAPP_l1386638586t_bool(Pa,Aa)))))) # label(fact_857_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 327 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> (-hBOOL(hAPP_f965095724l_bool(Pa,X_2)) -> hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,hAPP_l1660244757t_bool(dropWh1552197947t_bool(Pa),Xs_1)),Ys_1) = hAPP_l1660244757t_bool(dropWh1552197947t_bool(Pa),hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),Ys_1))))) # label(fact_760_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 328 (all F ((all I hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I))),hAPP_nat_nat(F,I)))) -> (exists I all K_1 hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(I),K_1)) = hAPP_nat_nat(F,I)))) # label(fact_1097_weak__decr__stable) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 329 (all P all Q all R hAPP_f2001490223le_alt(P,hAPP_l1869074853le_alt(Q,R)) = hAPP_l1406283231le_alt(hAPP_f469186021le_alt(hAPP_f1933751673le_alt(cOMBB_1193902096le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_162) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 330 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))))) # label(fact_1070_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 331 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_1)),hAPP_P1606644490l_bool(B_1,X_1))))) -> hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,B_1))))) # label(fact_296_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 332 (all Pa hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_410_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 333 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,hAPP_f952375653l_bool(cOMBK_751995742le_alt,B_1)))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_2)),B_1))))) # label(fact_121_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 334 (all Aa (is_fun1236654035i_bool(Aa) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa)) <-> top_to1576102282i_bool = Aa))) # label(fact_996_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 335 (all Xs_1 all R_2 ((all X_1 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),X_1)),R_2))) -> -hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Xs_1)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))))) # label(fact_362_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 336 (all X_2 hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool))) # label(fact_370_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 337 (all X_2 all R_2 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),nil_Ar126264853le_alt)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2)))) # label(fact_355_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 338 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_1),B_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),B_1))))) # label(fact_951_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 339 (all B_1_1 all B_2_1 is_fun961089132t_bool(hAPP_l1284365004t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa_023) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 340 (all B_1_1 (is_fun288122577l_bool(B_1_1) -> is_fun288122577l_bool(collec1063742455t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 341 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,B_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_2)),hAPP_P2082381915t_bool(B_1,X_2)))))) # label(fact_141_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 342 (all Pa nil_Ar126264853le_alt = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),nil_Ar126264853le_alt)) # label(fact_491_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 343 (all Pa all Xs_1 all Ys_1 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_1) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,nil_Ar126264853le_alt),nil_Ar126264853le_alt)) -> ((all X_1 all Xs_17 all Y_9 all Ys (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_17) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Xs_17),Ys)) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs_17)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Ys))))))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Xs_1),Ys_1)))))) # label(fact_549_list__induct2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 344 (all Pa all Xs_1 all Y_2 all Ys_1 (-hBOOL(hAPP_A862370221t_bool(Pa,Y_2)) & Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1)) <-> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1) = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1))) # label(fact_480_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 345 (all Pa all Ax all Ay all Bx all By all R_2 (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ax),Ay)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Bx),By))),transi580536954le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Bx),By)) -> ((all A_7 all B_6 all Aa_1 all Ba_1 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(Ba_1) & is_Arr1861959080le_alt(Aa_1) & is_Arr1861959080le_alt(A_7) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa_1),Ba_1))),R_2)) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa_1),Ba_1)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Bx),By))),transi580536954le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Aa_1),Ba_1)) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,A_7),B_6))))))) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Ax),Ay)))))) # label(fact_899_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 346 (all B_1_1 is_fun961089132t_bool(hd_fun730195372t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 347 (all X_2 (hBOOL(top_top_bool) <-> hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2)))) # label(fact_385_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 348 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,A_1),B_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),B_1))))) # label(fact_950_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 349 (all Xs_1 all Pa all X_2 ((hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1)) & (-hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)))) # label(fact_490_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 350 (exists X_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),top_to522745736l_bool)) & is_fun760276937t_bool(X_1))) # label(fact_449_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 351 (all B_1_1 all B_2_1 is_bool(hAPP_f2115479956l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__prod_Itc__Arrow____Order____M) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 352 (all Pa (is_fun279392540l_bool(Pa) -> collec1553055422t_bool(Pa) = Pa)) # label(fact_326_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 353 (all Aa (is_fun961089132t_bool(Aa) -> (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa)) <-> Aa = top_to565915683t_bool))) # label(fact_991_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 354 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_1)),hAPP_f239852716t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,B_1))))) # label(fact_196_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 355 (all I (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_A1677245848t_bool(p,I))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_A1677245848t_bool(p_1,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 356 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> (exists Ys exists Zs (hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Zs))))))) # label(fact_882_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 357 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),hAPP_nat_nat(suc,M_2))))) # label(fact_1037_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 358 (all B_1 all G all F all A_1 ((all W (is_Pro1725146340le_alt(W) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,W),A_1)) -> (hBOOL(hAPP_P606313927t_bool(F,W)) <-> hBOOL(hAPP_P606313927t_bool(G,W)))))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,G),pi_Pro666468413t_bool(A_1,B_1))) <-> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,B_1)))))) # label(fact_303_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 359 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_2)),hAPP_P1711233733t_bool(B_1,X_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1))))) # label(fact_69_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 360 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_A2091627584i_bool(hAPP_A1965262040i_bool(Ca,A_7),B_6)))))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_P1875867302i_bool(hAPP_f1425186181i_bool(produc89849422i_bool,Ca),P_1)))))) # label(fact_557_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 361 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),B_1))))) # label(fact_98_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 362 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1098_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 363 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,hAPP_f340261009t_bool(cOMBK_545135096l_bool,B_1)))))) # label(fact_244_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 364 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_1)),hAPP_P1861769507t_bool(B_1,X_1))))) -> hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,B_1))))) # label(fact_282_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 365 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),hAPP_b1048178734l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,B_1))))) # label(fact_208_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 366 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_1)),hAPP_P1905961381l_bool(B_1,X_1))))) -> hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,B_1))))) # label(fact_210_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 367 (all Pa (is_fun1236654035i_bool(Pa) -> collec1611109369e_indi(Pa) = Pa)) # label(fact_325_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 368 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(hAPP_n2132365064le_alt(take_P1280951759le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))))) # label(fact_981_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 369 (all Xs_36 all Ys_13 (Xs_36 = Ys_13 -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),Ys_13) = Xs_36)) # label(fact_409_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 370 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(L_1))) -> (hBOOL(hAPP_bool_bool(Q_1,X_1)) <-> hBOOL(hAPP_bool_bool(Pa,X_1)))))) -> hAPP_l1189022293t_bool(dropWhile_bool(Q_1),K) = hAPP_l1189022293t_bool(dropWhile_bool(Pa),L_1)))) # label(fact_841_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 371 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f839832464l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,B_1))))) # label(fact_270_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 372 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),hAPP_b1812770943l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,B_1))))) # label(fact_294_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 373 (all B_1_1 is_Arr43961803e_indi(last_A1892550853e_indi(B_1_1))) # label(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 374 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> (exists Ys exists Zs Xs_1 = hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs))))) # label(fact_885_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 375 (all B_1_1 all B_2_1 is_bool(hAPP_f2076022549l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 376 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))))) # label(fact_1060_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 377 (all B_1_1 is_fun1097062475t_bool(last_f1633249093t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnb) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 378 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B_1,X_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1))))) # label(fact_47_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.66 379 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(butlas1472553170t_bool,Xs_1)))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_693_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 380 (all Ys_1 all Pa all Xs_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),set_Pr1404309362le_alt(Xs_1))) -> hBOOL(hAPP_P1327827171t_bool(Pa,X_1)))) -> hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),Ys_1)) = hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),Ys_1)))) # label(fact_802_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 381 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),hAPP_A1112981887l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,B_1))))) # label(fact_216_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 382 (all Nat hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1182_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 383 (all P all Q all R hAPP_l578398296l_bool(hAPP_f170721165l_bool(hAPP_f1056253543l_bool(cOMBB_1058319106le_alt,P),Q),R) = hAPP_P1610428353l_bool(P,hAPP_l391088160le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_146) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 384 (all B_1_1 all B_2_1 is_bool(hAPP_f1806001137l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 385 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(L_1))) -> (hBOOL(hAPP_nat_bool(Q_1,X_1)) <-> hBOOL(hAPP_nat_bool(Pa,X_1))))) -> hAPP_l248265089st_nat(dropWhile_nat(Pa),L_1) = hAPP_l248265089st_nat(dropWhile_nat(Q_1),K)))) # label(fact_837_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 386 (all X_2 all Xs_1 all Y_2 all Ys_1 all R_2 (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Y_2) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) <-> X_2 = Y_2 & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) | Xs_1 = Ys_1 & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2))))) # label(fact_468_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 387 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> Xs_1 = hAPP_l1660244757t_bool(hAPP_f726713198t_bool(insert1665396998t_bool,X_2),Xs_1))) # label(fact_705_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 388 (all P all Q all R hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(P,R),Q) = hAPP_P1327827171t_bool(hAPP_f1642286869t_bool(hAPP_f1297597679t_bool(cOMBC_188453282l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_138) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 389 (all B_1_1 is_fun961089132t_bool(set_Pr604701398le_alt(B_1_1))) # label(gsy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 390 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,hAPP_f420098683t_bool(cOMBK_964928722t_bool,B_1)))))) # label(fact_232_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 391 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,hAPP_f1739666797l_bool(cOMBK_8746725le_alt,B_1)))))) # label(fact_247_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 392 (all U all X_2 all Y_2 all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),R_2)) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,U),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Aa),X_2))),hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,U),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Ba),Y_2)))),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))))) # label(fact_431_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 393 (all B_1_1 all B_2_1 (is_fun158382675l_bool(B_1_1) & is_fun1097062475t_bool(B_2_1) -> is_bool(hAPP_f312250286l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_049) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 394 (all P all Q all R hAPP_P229966473l_bool(P,hAPP_A702847159le_alt(Q,R)) = hAPP_A187815023l_bool(hAPP_f1539445765l_bool(hAPP_f1688983057l_bool(cOMBB_84213429le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__136) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 395 (all Xs_1 all Ys_1 all R_2 all X_2 all Y_2 (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(R_2,X_2),Y_2)) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(R_2),Xs_1),Ys_1)) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(R_2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1)))))) # label(fact_585_listrelp_OCons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 396 (all B_1_1 all B_2_1 is_fun760276937t_bool(hAPP_P19446482t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_095) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 397 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,B_1)))))) # label(fact_257_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 398 (all R_1 all S_1 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),R_1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),S_1))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)))) # label(fact_931_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 399 (all B_1_1 all B_2_1 is_bool(hAPP_f354239713l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____075) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 400 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_2)),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)))) # label(fact_1054_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 401 (all B_1_1 all B_2_1 is_bool(hAPP_f1837019376l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_054) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 402 (all M all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K_2))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J)),hAPP_nat_nat(plus_plus_nat(K_2),M)))) # label(fact_1178_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 403 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,B_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B_1,X_2)))))) # label(fact_139_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 404 (all N all M ((zero_zero_nat = M -> N = hAPP_nat_nat(plus_plus_nat(M),N)) & (zero_zero_nat != M -> hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N)) = hAPP_nat_nat(plus_plus_nat(M),N)))) # label(fact_1199_add__eq__if) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 405 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) <-> (exists Ys exists Zs Xs_1 = hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs))))) # label(fact_830_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 406 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) <-> N_2 = M_2 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1032_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 407 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B_1,X_2)))))) # label(fact_147_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 408 (all P all Q all R hAPP_P1327827171t_bool(hAPP_P163071551t_bool(P,R),Q) = hAPP_P1327827171t_bool(hAPP_P163071551t_bool(hAPP_f2139078121t_bool(cOMBC_1470522126t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 409 (all R_1 all X_2 all Y_2 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(in_rel617948260le_alt(R_1),X_2),Y_2)) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_1)))) # label(fact_19_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 410 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_A1664620203t_bool(hAPP_A210478249t_bool(Ca,A_7),B_6)))))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_P1711233733t_bool(hAPP_f1708325453t_bool(produc315582749t_bool,Ca),P_1)))))) # label(fact_556_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 411 (all X_2 hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool))) # label(fact_367_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 412 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B_1,X_2))) -> -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1))))) # label(fact_51_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 413 (all P all Q all R hAPP_P1056860425le_alt(hAPP_l693571982le_alt(P,R),hAPP_l391088160le_alt(Q,R)) = hAPP_l391088160le_alt(hAPP_f1514103381le_alt(hAPP_f1564521144le_alt(cOMBS_1399042523le_alt,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 414 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_2)),hAPP_A1928120382l_bool(B_1,X_2))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1))))) # label(fact_55_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 415 (all X all Y (Y != X | hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(fequal1160105444le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 416 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_Arr1861959080le_alt(hAPP_f1800079444le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_047) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 417 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),hAPP_b1703662281t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,B_1))))) # label(fact_203_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 418 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_1_1) -> is_fun279392540l_bool(pi_Pro666468413t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 419 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),hAPP_A1112981887l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,B_1))))) # label(fact_298_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 420 (all X_2 all Xs_1 all Ys_1 all Zs_1 (Ys_1 = nil_Ar126264853le_alt & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1) = Zs_1 | (exists Ys_12 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Ys_12) = Ys_1 & Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_12),Zs_1))) <-> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),Zs_1))) # label(fact_413_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 421 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun961089132t_bool(hAPP_f515126293t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___085) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 422 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_1),B_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B_1))))) # label(fact_947_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 423 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1))))) # label(fact_952_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 424 (all A_1 ((all X_1 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))) -> A_1 = top_top_fun_nat_bool)) # label(fact_452_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 425 (all N_10 all X_18 all Xs_20 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_10),X_18)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_18),Xs_20)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_18),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_10),X_18)),Xs_20))) # label(fact_584_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 426 (all Xs_15 (Xs_15 != nil_Ar126264853le_alt -> last_A57386030le_alt(Xs_15) = hd_Arr805754088le_alt(hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_15)))) # label(fact_592_hd__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 427 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))))) -> -(all Ys all X_1 (is_Arr1861959080le_alt(X_1) -> ((exists Zs Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs))) -> (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) -> -(all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Ys))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa)))))))))) # label(fact_863_split__list__first__propE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 428 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),B_1))))) -> hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,B_1)))))) # label(fact_228_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 429 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),hAPP_A1952883197l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,B_1))))) # label(fact_207_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 430 (all F1 all F2 F1 = hAPP_l726444215le_alt(list_c380068407le_alt(F1,F2),nil_Ar126264853le_alt)) # label(fact_132_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 431 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)))) # label(fact_1003_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 432 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),hAPP_f244157820i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,B_1))))) # label(fact_274_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 433 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> (-hBOOL(hAPP_A1785763630i_bool(Pa,X_2)) -> hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,hAPP_l54953109e_indi(dropWh601337149e_indi(Pa),Xs_1)),Ys_1) = hAPP_l54953109e_indi(dropWh601337149e_indi(Pa),hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),Ys_1))))) # label(fact_756_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 434 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_1)),hAPP_P1905961381l_bool(B_1,X_1))))) -> hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,B_1))))) # label(fact_292_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 435 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> (exists Ys exists Zs hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs)) = Xs_1))) # label(fact_884_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 436 (all Pa hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),nil_Ar126264853le_alt) = partit327648526le_alt(Pa,nil_Ar126264853le_alt)) # label(fact_390_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 437 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_1)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))))) # label(fact_689_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 438 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,B_1))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_2)),hAPP_n2095207769l_bool(B_1,X_2)))))) # label(fact_164_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 439 (all Xs_1 all Ys_1 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1) = Ys_1 <-> nil_Ar126264853le_alt = Xs_1)) # label(fact_408_append__self__conv2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 440 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (M != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_1042_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 441 (all X all Y (is_fun760276937t_bool(Y) & is_fun760276937t_bool(X) -> -hBOOL(hAPP_f965095724l_bool(hAPP_f1577179519l_bool(fequal785189517t_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 442 (all K_2 all L all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),L)))))) # label(fact_1063_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 443 (all Xs_33 all Ys_9 (Ys_9 != nil_Ar126264853le_alt -> last_A57386030le_alt(Ys_9) = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_33),Ys_9)))) # label(fact_417_last__appendR) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 444 (all M all K_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_2)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)))) # label(fact_1080_add__leD2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 445 (all F all Aa all Ba (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F,Aa),Ba)))) # label(fact_533_splitD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 446 (all B_1_1 all B_2_1 is_bool(hAPP_f570668343l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_063) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 447 (all M all N hAPP_nat_nat(plus_plus_nat(N),M) = hAPP_nat_nat(plus_plus_nat(M),N)) # label(fact_1091_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 448 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,B_1)))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),B_1))))) # label(fact_90_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 449 (all B_1_1 (is_fun961089132t_bool(B_1_1) -> is_fun961089132t_bool(transi1256616594le_alt(B_1_1)))) # label(gsy_c_Transitive__Closure_Ortrancl_000tc__Arrow____Order____Mirabelle____tpnfnnb) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 450 (all P all Q all R hAPP_l1869074853le_alt(hAPP_f1790240989le_alt(hAPP_f1792349771le_alt(cOMBC_1330649024le_alt,P),Q),R) = hAPP_f216801278le_alt(hAPP_l489874441le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_152) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 451 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun961089132t_bool(hAPP_b1703662281t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 452 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,hAPP_f898562478t_bool(cOMBK_607931107t_bool,B_1)))))) # label(fact_227_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 453 (all Aa (is_fun279392540l_bool(Aa) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa)) <-> top_to1853035173l_bool = Aa))) # label(fact_993_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 454 (all S_1 all R_1 ((all X_1 all Xa (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Xa)),R_1)) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Xa)),S_1)))) <-> S_1 = R_1)) # label(fact_310_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 455 (all As (As != nil_fu507235289t_bool -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,last_f2112695026t_bool(As)),set_fu1384968698t_bool(As))))) # label(fact_731_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 456 (all X_2 hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2))) # label(fact_349_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 457 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,ord_min_nat),N_2))),M_2)) # label(fact_1176_min__Suc2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 458 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_1)),hAPP_n295497947l_bool(B_1,X_1))))) -> hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,B_1))))) # label(fact_295_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 459 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),hAPP_P1875867302i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,B_1))))) # label(fact_183_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 460 (all N zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N)) # label(fact_1115_min__0L) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 461 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_1)),hAPP_P2136891882t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,B_1))))) # label(fact_262_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 462 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_2)),hAPP_P1905961381l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1))))) # label(fact_59_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 463 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_1)),hAPP_f239852716t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,B_1))))) # label(fact_278_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 464 (all X_23 hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_23),X_23))) # label(fact_544_equal__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 465 (all F produc335266950le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,F)) = F) # label(fact_498_curry__split) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 466 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun158382675l_bool(hAPP_b517355696l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 467 (all X all Y (X != Y -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))))) # label(fact_1013_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 468 (all X_2 all Xs_1 (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) & hBOOL(hAPP_l54057324t_bool(distin1553582624le_alt,Xs_1)) <-> hBOOL(hAPP_l54057324t_bool(distin1553582624le_alt,hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Xs_1))))) # label(fact_709_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 469 (all Aa all List all A_8 all List_2 (is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(A_8) -> (List = List_2 & Aa = A_8 <-> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_8),List_2) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),List)))) # label(fact_42_list_Oinject) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 470 (all R_2 all X_1 all Xa (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Xa)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) <-> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(hAPP_f1267389329t_bool(cOMBB_747702273le_alt,cOMBC_1635684702l_bool),hAPP_f156764033l_bool(hAPP_f778758417l_bool(cOMBB_2112722489le_alt,hAPP_f1688983057l_bool(cOMBB_84213429le_alt,member1441201108le_alt)),produc1400112471le_alt))),R_2)),X_1),Xa)))) # label(fact_574_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 471 (all A_12 all B_9 all A_11 all B_8 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_11),B_8) = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_12),B_9) -> -(A_12 = A_11 -> B_8 != B_9))) # label(fact_17_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 472 (all X_2 all Xs_1 (hBOOL(hAPP_l2034560823i_bool(distin1358019435e_indi,Xs_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),hAPP_l54953109e_indi(rev_Ar2090626622e_indi,hAPP_l54953109e_indi(takeWh273131493e_indi(hAPP_f580451669i_bool(hAPP_f1250179763i_bool(cOMBB_1141363506e_indi,fNot),hAPP_A313542399i_bool(hAPP_f585152361i_bool(cOMBC_1428934564i_bool,fequal1196706959e_indi),X_2))),Xs_1))) = hAPP_l54953109e_indi(dropWh601337149e_indi(hAPP_f580451669i_bool(hAPP_f1250179763i_bool(cOMBB_1141363506e_indi,fNot),hAPP_A313542399i_bool(hAPP_f585152361i_bool(cOMBC_1428934564i_bool,fequal1196706959e_indi),X_2))),hAPP_l54953109e_indi(rev_Ar2090626622e_indi,Xs_1))))) # label(fact_653_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 473 (all X all Y (is_fun1097062475t_bool(X) & is_fun1097062475t_bool(Y) -> -hBOOL(hAPP_f312250286l_bool(hAPP_f1577576703l_bool(fequal1596628751t_bool,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____t) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 474 (all F (is_fun961089132t_bool(F) -> hAPP_f791205069t_bool(produc2022255647t_bool,hAPP_f231379647t_bool(hAPP_f1460305297t_bool(cOMBB_2048157563le_alt,hAPP_f724700817t_bool(cOMBB_164218871le_alt,F)),produc1400112471le_alt)) = F)) # label(fact_494_split__eta) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 475 (all P all Q (is_fun1236654035i_bool(P) -> hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___149) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 476 (all Aa (is_fun1236654035i_bool(Aa) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa)) -> Aa = top_to1576102282i_bool))) # label(fact_1002_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 477 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) <-> (exists Ys exists Zs (Xs_1 = hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs)) & -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Ys))))))) # label(fact_817_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 478 (all Z_1 all X_6 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_1))))) # label(fact_935_order__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 479 (all C_2 all A_3 all B_3 (B_3 = A_3 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),B_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),A_3))))) # label(fact_957_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 480 (all B_1 all A_6 all A_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_6),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(A_1,B_1)),pi_fun150026276t_bool(A_6,B_1))))) # label(fact_922_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 481 (all J all I_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J),I_2)),I_2))) # label(fact_1068_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 482 (all X_2 hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2))) # label(fact_346_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 483 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_86_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 484 (all N_9 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_9),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_604_drop__Nil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 485 (all N_2 (zero_zero_nat = N_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,zero_zero_nat))))) # label(fact_1170_less__Suc0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 486 (all M all N (M = hAPP_nat_nat(plus_plus_nat(M),N) -> zero_zero_nat = N)) # label(fact_1103_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 487 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,B_1)))))) # label(fact_239_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 488 (all X_2 all Xs_1 (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) & hBOOL(hAPP_l1795316048t_bool(distin856461956le_alt,Xs_1)) <-> hBOOL(hAPP_l1795316048t_bool(distin856461956le_alt,hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Xs_1))))) # label(fact_715_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 489 (all B_1_1 all B_2_1 is_bool(hAPP_f597137892l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_056) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 490 (all Xs_1 all Ys_1 all R_2 all N_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),lexn_A1157915829le_alt(R_2,N_2))) -> N_2 = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1) & hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_1) = N_2)) # label(fact_578_lexn__length) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 491 (all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Ca),P_1)) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) -> -hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Ca,X_1),Y_9)))))))) # label(fact_553_splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 492 (all P all Q all R hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 493 (all X_2 all Y_2 all R_2 ((all A_7 all B_6 (B_6 = A_7 | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,B_6),A_7)),R_2)) | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)),R_2)))) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,X_2),Y_2)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))) | Y_2 = X_2 | hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Y_2),X_2)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))))) # label(fact_360_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 494 (all X_2 all Xs_1 (hBOOL(hAPP_l89806901l_bool(distin22312297t_bool,Xs_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> hAPP_l1660244757t_bool(rev_fu1957290812t_bool,hAPP_l1660244757t_bool(tl_fun38025093t_bool,hAPP_l1660244757t_bool(dropWh1552197947t_bool(hAPP_f146009813l_bool(hAPP_f356431923l_bool(cOMBB_871930928t_bool,fNot),hAPP_f1577179519l_bool(hAPP_f1688301673l_bool(cOMBC_2105056416l_bool,fequal785189517t_bool),X_2))),Xs_1))) = hAPP_l1660244757t_bool(takeWh1309019107t_bool(hAPP_f146009813l_bool(hAPP_f356431923l_bool(cOMBB_871930928t_bool,fNot),hAPP_f1577179519l_bool(hAPP_f1688301673l_bool(cOMBC_2105056416l_bool,fequal785189517t_bool),X_2))),hAPP_l1660244757t_bool(rev_fu1957290812t_bool,Xs_1))))) # label(fact_648_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 495 (all B_1_1 all B_2_1 is_bool(hAPP_f1067427061l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___086) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 496 (all F all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(produc212588606t_bool(F),Aa),Ba)) <-> hBOOL(hAPP_P606313927t_bool(F,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_335_curry__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 497 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(butlas1888624491le_alt,Xs_1)))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))))) # label(fact_696_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 498 (all P all Q all R hAPP_l391088160le_alt(hAPP_f216801278le_alt(hAPP_f1349184697le_alt(cOMBB_1818168801le_alt,P),Q),R) = hAPP_l391088160le_alt(P,hAPP_l726444215le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_130) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 499 (all Y_15 (nil_Ar126264853le_alt != Y_15 -> -(all A_7 all List_1 (is_Arr1861959080le_alt(A_7) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_7),List_1) != Y_15)))) # label(fact_88_list_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 500 (all B_1_1 all B_2_1 is_fun961089132t_bool(hAPP_n588788980t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 501 (all X_4 all Y_3 (Y_3 = X_4 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)))) # label(fact_969_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 502 (all M all N hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N))) # label(fact_1084_add__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 503 (all X_2 all Y_2 (Y_2 = X_2 <-> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_2),Y_2)))) # label(fact_543_equal__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 504 (all P all Q (is_fun_bool_bool(P) -> hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 505 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),hAPP_b1703662281t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,B_1))))) # label(fact_285_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 506 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),hAPP_f1552576127i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,B_1))))) # label(fact_279_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 507 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1023_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 508 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,B_1))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_2)),hAPP_f1593910865t_bool(B_1,X_2))) -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1))))) # label(fact_81_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 509 (all B_1_1 all B_2_1 is_bool(hAPP_l2034560823i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 510 (all B_1_1 all B_2_1 (is_fun279392540l_bool(B_2_1) -> is_bool(hAPP_f1749234559l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_070) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 511 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> (-hBOOL(hAPP_f312250286l_bool(Pa,X_2)) -> hAPP_l210315413t_bool(dropWh23362493t_bool(Pa),hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),Ys_1)) = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,hAPP_l210315413t_bool(dropWh23362493t_bool(Pa),Xs_1)),Ys_1)))) # label(fact_758_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 512 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),transi1256616594le_alt(R_2))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ca)),transi1256616594le_alt(R_2)))))) # label(fact_640_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 513 (all Xs_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Xs_1))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))) # label(fact_470_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 514 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),set_Ar219761597e_indi(L_1))) -> (hBOOL(hAPP_A1785763630i_bool(Pa,X_1)) <-> hBOOL(hAPP_A1785763630i_bool(Q_1,X_1)))))) -> hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),L_1) = hAPP_l54953109e_indi(takeWh273131493e_indi(Q_1),K)))) # label(fact_849_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 515 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> (-hBOOL(hAPP_f965095724l_bool(Pa,X_2)) -> hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),Ys_1)) = hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),Xs_1)))) # label(fact_723_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 516 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))))) -> -(all Ys all X_1 (is_Arr1861959080le_alt(X_1) -> ((exists Zs Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs))) -> -hBOOL(hAPP_A862370221t_bool(Pa,X_1))))))) # label(fact_809_split__list__propE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 517 (all R_2 hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(R_2),nil_Ar126264853le_alt),nil_Ar126264853le_alt))) # label(fact_586_listrelp_ONil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 518 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_l1661879987l_bool(hAPP_l1824974724l_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_P1606644490l_bool(hAPP_f2122673039l_bool(produc2129949100l_bool,Ca),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)))))) # label(fact_527_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 519 (all X_2 all Xs_1 (hBOOL(hAPP_l2034560823i_bool(distin1358019435e_indi,hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Xs_1))) <-> hBOOL(hAPP_l2034560823i_bool(distin1358019435e_indi,Xs_1)) & -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_710_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 520 (all P all Q all R hAPP_f1457563459t_bool(P,hAPP_A1505516597le_alt(Q,R)) = hAPP_A1664620203t_bool(hAPP_f231379647t_bool(hAPP_f1460305297t_bool(cOMBB_2048157563le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___131) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 521 (all M all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_2)),hAPP_nat_nat(suc,J)) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K_2))))) # label(fact_1177_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 522 (all R_1 all S_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),R_1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),S_1))) <-> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,R_1),S_1)))) # label(fact_929_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 523 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_74_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 524 (all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) = N) # label(fact_1195_diff__Suc__1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 525 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ba),Ca)),R_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ca)),transi992120749le_alt(R_2)))))) # label(fact_637_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 526 (all Aa (is_fun288122577l_bool(Aa) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa)) -> Aa = top_to522745736l_bool))) # label(fact_998_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 527 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_1127_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 528 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)))) # label(fact_1046_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 529 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_1)),hAPP_f1593910865t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,B_1))))) # label(fact_276_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 530 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_fun961089132t_bool(X_1) & is_fun961089132t_bool(Y_9) & is_fun961089132t_bool(Z_4) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),set_fu1384968698t_bool(Xs_1))) -> (hBOOL(hAPP_f336430449l_bool(hAPP_P80514697l_bool(member636962260t_bool,hAPP_f1065005691t_bool(hAPP_f1544433597t_bool(produc32696407t_bool,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f336430449l_bool(hAPP_P80514697l_bool(member636962260t_bool,hAPP_f1065005691t_bool(hAPP_f1544433597t_bool(produc32696407t_bool,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f336430449l_bool(hAPP_P80514697l_bool(member636962260t_bool,hAPP_f1065005691t_bool(hAPP_f1544433597t_bool(produc32696407t_bool,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f2076022549l_bool(hAPP_P1136391889l_bool(member1457870584t_bool,hAPP_l869099372t_bool(hAPP_l1146224941t_bool(produc1867223169t_bool,Xs_1),Ys_1)),hAPP_f1802593209l_bool(lexord485014854t_bool,R_2))) -> (hBOOL(hAPP_f2076022549l_bool(hAPP_P1136391889l_bool(member1457870584t_bool,hAPP_l869099372t_bool(hAPP_l1146224941t_bool(produc1867223169t_bool,Ys_1),Zs_1)),hAPP_f1802593209l_bool(lexord485014854t_bool,R_2))) -> hBOOL(hAPP_f2076022549l_bool(hAPP_P1136391889l_bool(member1457870584t_bool,hAPP_l869099372t_bool(hAPP_l1146224941t_bool(produc1867223169t_bool,Xs_1),Zs_1)),hAPP_f1802593209l_bool(lexord485014854t_bool,R_2))))))) # label(fact_788_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 531 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))))) # label(fact_596_rtrancl__listrel1__if__listrel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 532 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_Pro1725146340le_alt(hAPP_A702847159le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__prod_It) # label(hypothesis) # label(non_clause). [assumption]. 2.20/2.67 533 (all X_2 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Ys_1))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))) # label(fact_463_listrel1I2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 534 (all A_1 pi_fun150026276t_bool(A_1,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool) # label(fact_352_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 535 (all P all Q (is_fun_bool_bool(P) -> hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_144) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 536 (all X_2 all Xs_1 ((exists Ys exists Zs (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Zs))) & hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)) = Xs_1)) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))))) # label(fact_827_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 537 (all Zs_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2)))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ys_1),Zs_1)),hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Zs_1)),hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2))))))) # label(fact_625_listrel__rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.67 538 (all X_2 all Xs_1 (hBOOL(hAPP_l89806901l_bool(distin22312297t_bool,hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Xs_1))) <-> hBOOL(hAPP_l89806901l_bool(distin22312297t_bool,Xs_1)) & -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))))) # label(fact_714_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 539 (all B_1_1 all B_2_1 is_bool(hAPP_f236193164l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_064) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 540 (all P all Q hAPP_f856106132t_bool(hAPP_f932544453t_bool(cOMBK_1773325549t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 541 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(suc,zero_zero_nat))) = N)) # label(fact_1116_Suc__pred) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 542 (all B_1_1 all B_2_1 is_bool(hAPP_f1276380911l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_042) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 543 (all P all Q all R hAPP_A1785763630i_bool(hAPP_f580451669i_bool(hAPP_f1250179763i_bool(cOMBB_1141363506e_indi,P),Q),R) = hAPP_bool_bool(P,hAPP_A1785763630i_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order___103) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 544 (all X_2 all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> hAPP_l726444215le_alt(dropWh156852662le_alt(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fNot),hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,fequal1160105444le_alt),X_2))),hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_l726444215le_alt(takeWh536362254le_alt(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fNot),hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,fequal1160105444le_alt),X_2))),Xs_1)))))) # label(fact_650_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 545 (all N all M hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) = zero_zero_nat) # label(fact_1111_diff__add__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 546 (all M all N all K_2 all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L)) -> (hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K_2),N) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_1062_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 547 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) <-> (exists Ys exists Zs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Ys))) & Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)))))) # label(fact_810_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 548 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),set_Pr604701398le_alt(Xs_1))) -> hBOOL(hAPP_P606313927t_bool(Pa,X_1))))) -> hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),Ys_1)) = hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),Ys_1)))) # label(fact_808_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 549 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,hAPP_f1622901481t_bool(cOMBK_1786248882t_bool,B_1)))))) # label(fact_231_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 550 (all P all Q (is_fun1393352280t_bool(P) -> P = hAPP_f239852716t_bool(hAPP_f1438487600t_bool(cOMBK_488408421t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___147) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 551 (all X_2 all A_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) <-> hBOOL(hAPP_bool_bool(A_1,X_2)))) # label(fact_318_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 552 (all P all Q (-hBOOL(hAPP_bool_bool(fconj(P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 553 (all Nat_3 hAPP_nat_nat(suc,Nat_3) != zero_zero_nat) # label(fact_1139_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 554 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,hAPP_f898562478t_bool(cOMBK_607931107t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_2)),B_1))))) # label(fact_97_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 555 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N)))) # label(fact_1100_zero__less__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 556 (all Xs_7 all I_4 all X_13 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_7),I_4),X_13)) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_7)) # label(fact_614_length__list__update) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 557 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 558 (all X_11 all Xs_2 hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_11),Xs_2)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_2)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_11),nil_Ar126264853le_alt))) # label(fact_628_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 559 (all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> ((all X_1 (is_Arr1861959080le_alt(X_1) -> (Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Ys_1) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_2)),R_2))))) -> -(all Zs (Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Zs) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Zs),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))))))) # label(fact_478_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 560 (all P all Q (is_fun_bool_bool(P) -> P = hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_118) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 561 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Xs_1)))) | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Ys_1)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1))))))) # label(fact_739_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 562 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,B_1)))))) # label(fact_260_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 563 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),set_fu1865467835t_bool(L_1))) -> (hBOOL(hAPP_f965095724l_bool(Q_1,X_1)) <-> hBOOL(hAPP_f965095724l_bool(Pa,X_1)))))) -> hAPP_l1660244757t_bool(dropWh1552197947t_bool(Q_1),K) = hAPP_l1660244757t_bool(dropWh1552197947t_bool(Pa),L_1)))) # label(fact_844_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 564 (all Xs_14 all X_17 all Ys_3 all Y_12 hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_14),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_17),Ys_3))),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_14)),Y_12) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_14),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_12),Ys_3))) # label(fact_594_list__update__length) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 565 (all I_2 all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I_2))))) # label(fact_1093_less__add__Suc2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 566 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),B_1))))) # label(fact_119_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 567 (all B_1_1 all B_2_1 (is_fun288122577l_bool(B_2_1) -> is_bool(hAPP_f777333846l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_045) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 568 (all B_1_1 all B_2_1 is_bool(hAPP_f2042909150l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_072) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 569 (all P_2 (is_Pro1725146340le_alt(P_2) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) != P_2)))) # label(fact_307_PairE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 570 (all Xs_1 set_Ar1565008694le_alt(hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1)) = set_Ar1565008694le_alt(Xs_1)) # label(fact_668_set__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 571 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),R_2)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),transi1256616594le_alt(R_2))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ca)),transi1256616594le_alt(R_2)))))) # label(fact_636_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 572 (all A_1 (is_fun_bool_bool(A_1) -> ((all X_1 (is_bool(X_1) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)))) -> top_to1647826457l_bool = A_1))) # label(fact_454_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 573 (all R_2 all X_1 all Xa (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,X_1),Xa)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))) <-> hBOOL(hAPP_l377001987t_bool(hAPP_l1437188439t_bool(listre831694736le_alt(hAPP_f311173987t_bool(hAPP_f66177535t_bool(cOMBC_672290030t_bool,hAPP_f1152779391t_bool(hAPP_f991870303t_bool(cOMBB_353715312le_alt,cOMBC_1740746827l_bool),hAPP_f370419053l_bool(hAPP_f1953650287l_bool(cOMBB_283473102le_alt,hAPP_f1056253543l_bool(cOMBB_1058319106le_alt,member1020705648le_alt)),produc237774329le_alt))),R_2)),X_1),Xa)))) # label(fact_573_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 574 (all B_1_1 is_fun760276937t_bool(last_f1417039043t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oind) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 575 (all B_1_1 all B_2_1 is_bool(hAPP_f68732431l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 576 (all Pa all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(Pa,Ba)) -> ((all Y_9 all Z_4 (is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(Z_4) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_9),Z_4)),R_2)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Z_4),Ba)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(Pa,Z_4)) -> hBOOL(hAPP_A862370221t_bool(Pa,Y_9))))))) -> hBOOL(hAPP_A862370221t_bool(Pa,Aa)))))) # label(fact_858_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 577 (all N_8 all X_12 hAPP_A832564074le_alt(replic351609551le_alt(N_8),X_12) = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_8),X_12))) # label(fact_616_rev__replicate) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 578 (all X_1 hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) = hAPP_n1699378549t_bool(ord_less_nat,X_1)) # label(fact_1006_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 579 (all X_2 hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),top_to2076077793t_bool))) # label(fact_368_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 580 (all B_1_1 all B_2_1 is_bool(hAPP_f1525366679l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_041) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 581 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(L_1))) -> (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) <-> hBOOL(hAPP_A862370221t_bool(Q_1,X_1)))))) -> hAPP_l726444215le_alt(dropWh156852662le_alt(Q_1),K) = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),L_1)))) # label(fact_838_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 582 (all X_2 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool))) # label(fact_366_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 583 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_1),B_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B_1))))) # label(fact_946_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 584 (all P all Q (is_fun961089132t_bool(P) -> P = hAPP_P1861769507t_bool(hAPP_f1783828715t_bool(cOMBK_1901607710le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_129) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 585 (all X_2 all Xs_1 ((exists Ys exists Zs (Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Zs))))) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))))) # label(fact_820_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 586 (all X_2 all U all V all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,X_2),U)),hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,X_2),V))),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))) -> ((all A_7 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),A_7)),R_2))) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,U),V)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2)))))) # label(fact_435_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 587 (all B_1_1 (is_fun961089132t_bool(B_1_1) -> is_fun2093718614t_bool(in_rel1305177154le_alt(B_1_1)))) # label(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 588 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N)))) # label(fact_1165_Suc__diff__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 589 (all Ys_1 all Xs_1 all Us_1 all Vs_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2)) -> (Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Vs_1)) -> (Ys_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Vs_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))))) # label(fact_472_listrel1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 590 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f210572555l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,B_1))))) # label(fact_275_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 591 (all M all N (N = M -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1020_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 592 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_A490104565t_bool(hAPP_A101171597t_bool(Ca,A_7),B_6)))))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_P2082381915t_bool(hAPP_f1783389935t_bool(produc51145731t_bool,Ca),P_1)))))) # label(fact_555_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 593 (all L_2 all X_2 all Y_2 (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Y_2) -> (X_2 != Y_2 -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_1539419881_below,L_2),X_2),Y_2)),arrow_1681063817le_Lin)))))) # label(fact_21_below__Lin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 594 (all As (As != nil_Pr2088511415le_alt -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,last_P736051166le_alt(As)),set_Pr604701398le_alt(As))))) # label(fact_733_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 595 (all P all Q (is_fun279392540l_bool(P) -> P = hAPP_n1674354836l_bool(hAPP_f11902820l_bool(cOMBK_39620975ol_nat,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 596 (all M all N M = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N)) # label(fact_1109_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 597 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_1) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1))) # label(fact_538_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 598 (all Y_2 all X_2 all Xs_1 (is_Arr43961803e_indi(Y_2) & is_Arr43961803e_indi(X_2) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),set_Ar219761597e_indi(hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Xs_1)))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),set_Ar219761597e_indi(Xs_1))) | X_2 = Y_2))) # label(fact_662_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 599 (all N_7 all Xs_6 hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_7),Xs_6)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_7),hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_6))) # label(fact_617_drop__butlast) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 600 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun1393352280t_bool(hAPP_f1663053423t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___079) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 601 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),Xs_1)))) -> hBOOL(hAPP_f312250286l_bool(Pa,X_2)) & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_684_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 602 (all Y_2 all X_2 all Xs_1 (is_fun1097062475t_bool(Y_2) & is_fun1097062475t_bool(X_2) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Y_2),set_fu335223357t_bool(hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Xs_1)))) -> X_2 = Y_2 | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Y_2),set_fu335223357t_bool(Xs_1)))))) # label(fact_664_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 603 (all X all Y X = hAPP_P1056860425le_alt(hAPP_P864444517le_alt(if_Pro1306781203le_alt(fTrue),X),Y)) # label(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 604 (all P all Q P = hAPP_A408086601le_alt(hAPP_f1608056749le_alt(cOMBK_1696648346le_alt,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 605 (all X_2 all Xs_1 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1)) & (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> Xs_1 = hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1)))) # label(fact_762_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 606 (all S_1 all R_1 (is_fun961089132t_bool(S_1) & is_fun961089132t_bool(R_1) -> (R_1 = S_1 <-> (all X_1 all Xa (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Xa) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1)) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1)))))))) # label(fact_311_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 607 (all P all Q (is_fun_bool_bool(P) -> hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 608 (all Xs_1 (nil_fu81264926t_bool != Xs_1 -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hd_fun191074571t_bool(Xs_1)),set_fu335223357t_bool(Xs_1))))) # label(fact_749_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 609 (all M_2 all N_2 hAPP_nat_nat(minus_minus_nat(M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(minus_minus_nat(M_2),N_2))) # label(fact_1151_diff__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 610 (all P all Q all R hAPP_n1875670159le_alt(hAPP_f402821245le_alt(hAPP_f548810715le_alt(cOMBB_903467948lt_nat,P),Q),R) = hAPP_l726444215le_alt(P,hAPP_n1875670159le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 611 (all N hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat) # label(fact_1150_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 612 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) <-> zero_zero_nat = M_2 | (exists J_1 (hAPP_nat_nat(suc,J_1) = M_2 & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N_2)))))) # label(fact_1169_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 613 (all X_2 all Xs_1 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),hAPP_l248265089st_nat(rev_nat,hAPP_l248265089st_nat(takeWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),Xs_1))) = hAPP_l248265089st_nat(dropWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_l248265089st_nat(rev_nat,Xs_1))))) # label(fact_651_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 614 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_1140_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 615 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) <-> (exists Ys exists Zs hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs)) = Xs_1))) # label(fact_834_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 616 (all M all N hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N)) # label(fact_1085_add__Suc__shift) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 617 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f839832464l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__036) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 618 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,B_1)))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),B_1))))) # label(fact_127_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 619 (all P all Q all R hAPP_f2014742713t_bool(P,hAPP_A1664620203t_bool(Q,R)) = hAPP_A1664620203t_bool(hAPP_f825175477t_bool(hAPP_f57507985t_bool(cOMBB_1171600517le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 620 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> Xs_1 = hAPP_l210315413t_bool(hAPP_f1812326636t_bool(insert1946138248t_bool,X_2),Xs_1))) # label(fact_703_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 621 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun1236654035i_bool(hAPP_A2091627584i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 622 (all P all Q all R hAPP_A1941004017t_bool(hAPP_A621939144t_bool(P,R),Q) = hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_132) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 623 (all Aa (is_fun158382675l_bool(Aa) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa)) <-> Aa = top_to1714702858l_bool))) # label(fact_994_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 624 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M)))) # label(fact_1073_le__add1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 625 (all I_7 all Xs_8 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_8)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,I_7),Xs_8))))) # label(fact_610_distinct__drop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 626 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1048_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 627 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M)))))) # label(fact_1119_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 628 (all X_2 all Xs_1 (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1))) # label(fact_775_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 629 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),set_fu1384968698t_bool(L_1))) -> (hBOOL(hAPP_f592646513l_bool(Pa,X_1)) <-> hBOOL(hAPP_f592646513l_bool(Q_1,X_1)))))) -> hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),L_1) = hAPP_l1075146559t_bool(takeWh1512678354t_bool(Q_1),K)))) # label(fact_852_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 630 (all Xs_1 all X_2 all Ys_1 all Y_2 all R_2 (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(X_2) -> (Ys_1 = Xs_1 & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2)) | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) & Y_2 = X_2 <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt))),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),nil_Ar126264853le_alt)))),hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))))) # label(fact_440_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 631 (all B_1 all A_6 all A_1 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_6),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(A_1,B_1)),pi_Pro666468413t_bool(A_6,B_1))))) # label(fact_920_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 632 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun_bool_bool(hAPP_A822657487l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_005) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 633 (all X_2 all Y_2 all L_2 all Z_3 (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(Z_3) & is_Arr1861959080le_alt(X_2) -> (Z_3 != X_2 & (Y_2 = Z_3 -> Y_2 != X_2) & (Y_2 != Z_3 -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_2))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(arrow_1644373103_mktop(L_2),Z_3)))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 634 (all I_5 all Y_10 hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(nil_Ar126264853le_alt),I_5),Y_10) = nil_Ar126264853le_alt) # label(fact_613_list__update__code_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 635 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),set_fu1865467835t_bool(L_1))) -> (hBOOL(hAPP_f965095724l_bool(Q_1,X_1)) <-> hBOOL(hAPP_f965095724l_bool(Pa,X_1)))))) -> hAPP_l1660244757t_bool(takeWh1309019107t_bool(Pa),L_1) = hAPP_l1660244757t_bool(takeWh1309019107t_bool(Q_1),K)))) # label(fact_853_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 636 (all X_2 all A_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) <-> hBOOL(hAPP_P1327827171t_bool(A_1,X_2)))) # label(fact_315_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 637 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_2)),hAPP_A187815023l_bool(B_1,X_2))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1))))) # label(fact_60_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 638 (all B_1_1 all B_2_1 is_bool(hAPP_f1382465777l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_087) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 639 (all R_2 hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,hAPP_f1865483825t_bool(listre760726333le_alt,R_2)),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))) # label(fact_905_listrel__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 640 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun279392540l_bool(hAPP_b1812770943l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 641 (all Pa all Ax all Ay all Bx all By all R_2 (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ax),Ay)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Bx),By))),transi580536954le_alt(R_2))) -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Ax),Ay)) -> ((all A_7 all B_6 all Aa_1 all Ba_1 (is_Arr1861959080le_alt(Ba_1) & is_Arr1861959080le_alt(Aa_1) & is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ax),Ay)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6))),transi580536954le_alt(R_2))) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa_1),Ba_1))),R_2)) -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,A_7),B_6)) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Aa_1),Ba_1))))))) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,Bx),By)))))) # label(fact_901_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 642 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f1624277646l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_052) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 643 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_1)),hAPP_P2082381915t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,B_1))))) # label(fact_263_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 644 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,hAPP_f1609079369t_bool(cOMBK_1369841150le_alt,B_1)))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_2)),B_1))))) # label(fact_93_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 645 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,B_1))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_2)),hAPP_n295497947l_bool(B_1,X_2)))))) # label(fact_173_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 646 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),set_Ar219761597e_indi(Xs_1))) -> hBOOL(hAPP_A1785763630i_bool(Pa,X_1))))) -> hAPP_l54953109e_indi(dropWh601337149e_indi(Pa),Ys_1) = hAPP_l54953109e_indi(dropWh601337149e_indi(Pa),hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),Ys_1)))) # label(fact_794_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 647 (all P all Q all R hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) = hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 648 (all P all Q (is_fun158382675l_bool(P) -> P = hAPP_P1606644490l_bool(hAPP_f681285561l_bool(cOMBK_1786282629le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_155) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 649 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> N = M))) # label(fact_1022_le__antisym) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 650 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A_1),B_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B_1))))) # label(fact_966_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 651 (all Pa all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(Pa,Aa)) -> ((all Y_9 all Z_4 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Y_9)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_9),Z_4)),R_2)) -> (hBOOL(hAPP_l1386638586t_bool(Pa,Y_9)) -> hBOOL(hAPP_l1386638586t_bool(Pa,Z_4)))))) -> hBOOL(hAPP_l1386638586t_bool(Pa,Ba)))))) # label(fact_855_rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 652 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_1)),hAPP_P2136891882t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,B_1))))) # label(fact_180_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 653 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_1),B_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),B_1))))) # label(fact_963_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 654 (all N_2 all M_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2))) <-> N_2 = M_2))) # label(fact_1030_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 655 (all Xs_1 all R_2 ((all X_1 (is_Arr1861959080le_alt(X_1) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),X_1)),R_2)))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Xs_1)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))) # label(fact_363_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 656 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_948_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 657 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f856106132t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,B_1))))) # label(fact_189_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 658 (all B_1_1 is_bool(hd_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 659 (all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1))) <-> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)))) # label(fact_615_distinct__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 660 (all B_1_1 all B_2_1 (is_fun2093718614t_bool(B_2_1) -> is_fun2093718614t_bool(hAPP_f825175477t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___026) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 661 (all Pa all X_2 all Xs_1 partit327648526le_alt(Pa,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,hAPP_f746471349le_alt(hAPP_f628327744le_alt(cOMBS_1294827559le_alt,hAPP_f1291559232le_alt(hAPP_f749699165le_alt(cOMBB_1450165017le_alt,cOMBS_1399042523le_alt),hAPP_f469186021le_alt(hAPP_f1933751673le_alt(cOMBB_1193902096le_alt,hAPP_f1939049849le_alt(cOMBB_723746886le_alt,if_Pro1306781203le_alt(hAPP_A862370221t_bool(Pa,X_2)))),hAPP_f1790240989le_alt(hAPP_f1013417831le_alt(cOMBB_2052911494le_alt,produc237774329le_alt),hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2))))),hAPP_f1790240989le_alt(hAPP_f1792349771le_alt(cOMBC_1330649024le_alt,hAPP_f1318121625le_alt(hAPP_f634775919le_alt(cOMBB_576205818le_alt,cOMBB_1818168801le_alt),produc237774329le_alt)),hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2)))),partit327648526le_alt(Pa,Xs_1))) # label(fact_483_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 662 (all K all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K),M_2)),hAPP_nat_nat(plus_plus_nat(K),N_2))))) # label(fact_1075_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 663 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_Pro1725146340le_alt(hAPP_b55004359le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 664 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),B_1))))) -> hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,B_1)))))) # label(fact_224_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 665 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_fun158382675l_bool(hAPP_f1577576703l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_053) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 666 (all P all Q hAPP_P2082381915t_bool(hAPP_f880868799t_bool(cOMBK_1550261278le_alt,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 667 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_l1542188220l_bool(hAPP_l1352613953l_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_P1905961381l_bool(hAPP_f786857743l_bool(produc1170920579l_bool,Ca),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)))))) # label(fact_526_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 668 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P324742453l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,B_1))))) # label(fact_218_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 669 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(L_1))) -> (hBOOL(hAPP_A862370221t_bool(Q_1,X_1)) <-> hBOOL(hAPP_A862370221t_bool(Pa,X_1)))))) -> hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),L_1) = hAPP_l726444215le_alt(takeWh536362254le_alt(Q_1),K)))) # label(fact_847_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 670 (all R_1 all X_2 all Y_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_1)) <-> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(in_rel1305177154le_alt(R_1),X_2),Y_2)))) # label(fact_20_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 671 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N))) # label(fact_1086_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 672 (all B_1_1 all B_2_1 is_bool(hAPP_f1111021425l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 673 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_2)),hAPP_f996881846t_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_72_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 674 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1393352280t_bool(hAPP_b30302907t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 675 (all X_33 all Xs_46 (is_Arr1861959080le_alt(X_33) -> (Xs_46 = nil_Ar126264853le_alt -> X_33 = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_33),Xs_46))) & (nil_Ar126264853le_alt != Xs_46 -> last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_33),Xs_46)) = last_A57386030le_alt(Xs_46)))) # label(fact_344_last_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 676 (all Aa (is_fun1393352280t_bool(Aa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,top_to2076077793t_bool),Aa)) <-> top_to2076077793t_bool = Aa))) # label(fact_995_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 677 (all Xs_1 (hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs_1)) <-> nil_Ar126264853le_alt = Xs_1)) # label(fact_337_List_Onull__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 678 (all P (is_bool(P) -> fFalse = P | P = fTrue)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 679 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_2)),hAPP_f1865483825t_bool(B_1,X_2))) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1))))) # label(fact_77_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 680 (all P (is_bool(P) -> fTrue = P | fFalse = P)) # label(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 681 (all R_1 all S_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,R_1),S_1)) <-> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),R_1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),S_1))))) # label(fact_928_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 682 (all Z_3 all Ca all P_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_P1905961381l_bool(hAPP_f786857743l_bool(produc1170920579l_bool,Ca),P_1))) -> -(all X_1 all Y_9 (P_1 = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_l1542188220l_bool(hAPP_l1352613953l_bool(Ca,X_1),Y_9))))))) # label(fact_570_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 683 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) & is_Arr1861959080le_alt(X_1))) <-> (exists Ys exists X_1 exists Zs (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & (all Xa (is_Arr1861959080le_alt(Xa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Zs))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa))))) & hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs)) = Xs_1 & is_Arr1861959080le_alt(X_1))))) # label(fact_892_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 684 (all B_1_1 all B_2_1 is_bool(hAPP_f903371257l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__fun_Itc__Arrow____Order____Mi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 685 (all P all Q all R hAPP_f2013399995l_bool(hAPP_A297543629l_bool(P,R),Q) = hAPP_A862370221t_bool(hAPP_f2014742713t_bool(hAPP_f1382209403t_bool(cOMBC_1745481870l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_104) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 686 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1019_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 687 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hAPP_nat_nat(suc,N) = M))) # label(fact_1039_le__SucE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.68 688 (all P all Q (is_fun961089132t_bool(P) -> hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_106) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 689 (all Aa all Ba all A_8 all B_7 (is_Arr1861959080le_alt(B_7) & is_Arr1861959080le_alt(A_8) & is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Aa) -> (B_7 = Ba & Aa = A_8 <-> hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_8),B_7)))) # label(fact_16_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 690 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_1)),B_1))))) -> hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,hAPP_f1362748656t_bool(cOMBK_208474378t_bool,B_1)))))) # label(fact_235_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 691 (all Ca all A_1 all B_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A_1),B_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Ca),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Ca),B_1))))) # label(fact_910_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 692 (all X_2 all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> hAPP_l726444215le_alt(takeWh536362254le_alt(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fNot),hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,fequal1160105444le_alt),X_2))),hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1)) = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(dropWh156852662le_alt(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fNot),hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,fequal1160105444le_alt),X_2))),Xs_1)))))) # label(fact_641_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 693 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,B_1))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_2)),hAPP_A568203993t_bool(B_1,X_2)))))) # label(fact_161_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 694 (all B_1_1 (is_fun1393352280t_bool(B_1_1) -> is_fun279392540l_bool(order_835987853le_alt(B_1_1)))) # label(gsy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 695 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_l1328583473l_bool(hAPP_l395992834l_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_P139894920l_bool(hAPP_f86548619l_bool(produc998313258l_bool,Ca),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)))))) # label(fact_525_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 696 (all Xs_22 (Xs_22 != nil_Ar126264853le_alt -> hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_22) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Xs_22)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hd_Arr805754088le_alt(Xs_22)),nil_Ar126264853le_alt)))) # label(fact_575_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 697 (all B_1_1 all B_2_1 (is_fun1236654035i_bool(B_2_1) -> is_fun1236654035i_bool(hAPP_f580451669i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__030) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 698 (all X_2 all U all V all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,U),V)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X_2),U)),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X_2),V))),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))) # label(fact_419_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 699 (all K_2 all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2))))) # label(fact_1021_le__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 700 (all B_1_1 all B_2_1 is_bool(hAPP_f1478750961l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow___) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 701 (all I_2 all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K_2)),I_2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I_2)),K_2))) # label(fact_1152_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 702 (all Pa all Ax all Ay all Bx all By all R_2 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ax),Ay)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Bx),By))),transi54034710le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Bx),By)) -> ((all A_7 all B_6 all Aa_1 all Ba_1 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa_1),Ba_1))),R_2)) -> (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa_1),Ba_1)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Bx),By))),transi54034710le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Aa_1),Ba_1)) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,A_7),B_6)))))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Ax),Ay)))))) # label(fact_898_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 703 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) & hBOOL(hAPP_f592646513l_bool(Pa,X_2)))) # label(fact_685_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 704 (all X_30 all Xs_43 (Xs_43 != nil_Ar126264853le_alt -> last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_30),Xs_43)) = last_A57386030le_alt(Xs_43))) # label(fact_358_last__ConsR) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 705 (all Ys_1 all Pa all Xs_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1))) -> hBOOL(hAPP_nat_bool(Pa,X_1)))) -> hAPP_l248265089st_nat(dropWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(dropWhile_nat(Pa),Ys_1))) # label(fact_791_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 706 (all X_2 all Xs_1 ((exists Ys exists Zs hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs)) = Xs_1) <-> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_831_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 707 (all Xs_1 all Ys_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),transi1256616594le_alt(R_2))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2))))))) # label(fact_621_rtrancl__listrel1__ConsI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 708 (all Pa all Xs_1 all Yes all No (partit327648526le_alt(Pa,Xs_1) = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Yes),No) -> (all X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(No))) -> -hBOOL(hAPP_A862370221t_bool(Pa,X_1)))) & (all X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Yes))) -> hBOOL(hAPP_A862370221t_bool(Pa,X_1)))))) # label(fact_780_partition__P) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 709 (all F all G ((all X_1 all Y_9 hAPP_l391088160le_alt(hAPP_l1869074853le_alt(F,X_1),Y_9) = hAPP_P1056860425le_alt(G,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9))) -> G = hAPP_f1078809103le_alt(produc748227559le_alt,F))) # label(fact_502_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 710 (all Ys_19 Ys_19 = hAPP_l726444215le_alt(splice360969192le_alt(nil_Ar126264853le_alt),Ys_19)) # label(fact_137_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 711 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,hAPP_f1438487600t_bool(cOMBK_488408421t_bool,B_1)))))) # label(fact_237_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 712 (all F all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F,Aa),Ba)) <-> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_489_split__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 713 (all X_2 all Xs_1 ((exists Ys exists Zs (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Zs))))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))))) # label(fact_819_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 714 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(hAPP_n2132365064le_alt(drop_P13505143le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))))) # label(fact_677_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 715 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Ys))) & hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs)) = Xs_1)))) # label(fact_868_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 716 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,hAPP_f584002568l_bool(cOMBK_532713098ol_nat,B_1)))))) # label(fact_245_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 717 (all Xs_1 all Y_2 all Ys_1 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1) = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Ys_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),nil_Ar126264853le_alt)) = Xs_1)) # label(fact_629_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 718 (all B_1_1 all B_2_1 is_bool(hAPP_f336430449l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 719 (all Xs_1 all R_2 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),Xs_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))) # label(fact_465_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 720 (all Xs_42 (nil_Ar126264853le_alt != Xs_42 -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_42)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,last_A57386030le_alt(Xs_42)),nil_Ar126264853le_alt)) = Xs_42)) # label(fact_391_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 721 (all X_29 all Xs_39 all Ys_16 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_29),Xs_39)),Ys_16) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_29),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_39),Ys_16))) # label(fact_399_append__Cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 722 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))))) -> -(all Ys all X_1 all Zs (is_Arr1861959080le_alt(X_1) -> (Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs)) -> (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) -> -(all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Zs))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa)))))))))) # label(fact_864_split__list__last__propE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 723 (all P all Q all R hAPP_l1701840224le_alt(hAPP_f1291559232le_alt(hAPP_f749699165le_alt(cOMBB_1450165017le_alt,P),Q),R) = hAPP_f1564521144le_alt(P,hAPP_l1406283231le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_164) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 724 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_1)),hAPP_n2095207769l_bool(B_1,X_1))))) -> hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,B_1))))) # label(fact_204_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 725 (all P all Q all R hAPP_f653880381t_bool(P,hAPP_A1553574765l_bool(Q,R)) = hAPP_A572596845t_bool(hAPP_f1324249913t_bool(hAPP_f1267389329t_bool(cOMBB_747702273le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___154) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 726 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,hAPP_f695414965l_bool(cOMBK_1193272835le_alt,B_1)))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_2)),B_1))))) # label(fact_116_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 727 (all A1 all A2 all R_2 (is_Arr1861959080le_alt(A2) & is_Arr1861959080le_alt(A1) -> ((exists A_7 exists B_6 exists C_5 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) & A_7 = A1 & C_5 = A2 & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,B_6),C_5)),R_2)) & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),transi1256616594le_alt(R_2))) & is_Arr1861959080le_alt(C_5))) | (exists A_7 (A2 = A_7 & A1 = A_7 & is_Arr1861959080le_alt(A_7))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A1),A2)),transi1256616594le_alt(R_2)))))) # label(fact_904_rtrancl_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 728 (all B_1_1 is_Arr1861959080le_alt(last_A57386030le_alt(B_1_1))) # label(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 729 (all P all Q (is_fun1393352280t_bool(P) -> P = hAPP_P1711233733t_bool(hAPP_f1609079369t_bool(cOMBK_1369841150le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 730 (all P all Q (is_fun279392540l_bool(P) -> hAPP_P1905961381l_bool(hAPP_f952375653l_bool(cOMBK_751995742le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_133) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 731 (all F all G hAPP_f1078809103le_alt(produc748227559le_alt,hAPP_f1790240989le_alt(hAPP_f1792349771le_alt(cOMBC_1330649024le_alt,hAPP_f1318121625le_alt(hAPP_f634775919le_alt(cOMBB_576205818le_alt,cOMBB_1818168801le_alt),hAPP_f1790240989le_alt(hAPP_f1013417831le_alt(cOMBB_2052911494le_alt,produc237774329le_alt),F))),G)) = produc1449729469le_alt(F,G)) # label(fact_595_map__pair__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 732 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun1236654035i_bool(hAPP_A313542399i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 733 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),B_1))))) # label(fact_129_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 734 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> zero_zero_nat != N)) # label(fact_1121_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 735 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_1)),B_1))))) -> hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,hAPP_f932544453t_bool(cOMBK_1773325549t_bool,B_1)))))) # label(fact_230_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 736 (all Pa all Ax all Ay all Bx all By all R_2 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ax),Ay)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Bx),By))),transi54034710le_alt(R_2))) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Ax),Ay)) -> ((all A_7 all B_6 all Aa_1 all Ba_1 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ax),Ay)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6))),transi54034710le_alt(R_2))) -> (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa_1),Ba_1))),R_2)) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,A_7),B_6)) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Aa_1),Ba_1)))))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Pa,Bx),By)))))) # label(fact_900_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 737 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_1)),hAPP_f996881846t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,B_1))))) # label(fact_267_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 738 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),hAPP_f1948454017i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,B_1))))) # label(fact_269_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 739 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> hAPP_l54953109e_indi(hAPP_A974963564e_indi(insert915800584e_indi,X_2),Xs_1) = Xs_1)) # label(fact_701_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 740 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,hAPP_f256804927l_bool(cOMBK_69806648l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),B_1))))) # label(fact_123_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 741 (all X all Y all Z hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z))) # label(fact_1090_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 742 (all Aa all X_2 all Ba all Y_2 all R_2 (is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Aa) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),X_2)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Ba),Y_2))),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) <-> Ba = Aa & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),R_2))))) # label(fact_342_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 743 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_fun1393352280t_bool(hAPP_f228695594t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__034) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 744 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),hAPP_b517355696l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,B_1))))) # label(fact_299_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 745 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,B_1)))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),B_1))))) # label(fact_118_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 746 (all P all Q all R hAPP_f170721165l_bool(P,hAPP_l1869074853le_alt(Q,R)) = hAPP_l1629075165l_bool(hAPP_f370419053l_bool(hAPP_f1953650287l_bool(cOMBB_283473102le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_159) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 747 (all P all Q (is_bool(P) -> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 748 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool))) # label(fact_364_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 749 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B_1,X_2)))))) # label(fact_168_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 750 (all Z_3 all Ca all P_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_P1861769507t_bool(hAPP_f906821569t_bool(produc2091914181t_bool,Ca),P_1))) -> -(all X_1 all Y_9 (P_1 = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Z_3),hAPP_l1284365004t_bool(hAPP_l1538437917t_bool(Ca,X_1),Y_9))))))) # label(fact_568_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 751 (all P all Q (is_fun288122577l_bool(P) -> P = hAPP_n2095207769l_bool(hAPP_f584002568l_bool(cOMBK_532713098ol_nat,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 752 (all P all Q (is_bool(P) -> P = hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 753 (all N_2 all K all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_2),K)),hAPP_nat_nat(minus_minus_nat(N_2),K))))))) # label(fact_1164_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 754 (all X_2 all Y_2 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_2),Y_2)) <-> X_2 = Y_2)) # label(fact_398_equal__list__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 755 (all B_1_1 all B_2_1 is_bool(hAPP_list_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 756 (all M_2 all K all F ((all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_1)),hAPP_nat_nat(F,N_1))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_2)),K)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_2),K)))))) # label(fact_1095_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 757 (all N_6 all Xs_5 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_6),hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_5)) = hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_6),Xs_5))) # label(fact_618_butlast__drop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 758 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_2)),hAPP_A568203993t_bool(B_1,X_2))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1))))) # label(fact_50_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 759 (all B_1_1 is_fun1393352280t_bool(set_Ar1565008694le_alt(B_1_1))) # label(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 760 (all I_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N)) -> hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I_2)) = I_2)) # label(fact_1134_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 761 (all X_2 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool))) # label(fact_375_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 762 (all Xs_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),nil_Ar126264853le_alt)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> nil_Ar126264853le_alt = Xs_1)) # label(fact_528_listrel__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 763 (all N N = hAPP_nat_nat(plus_plus_nat(zero_zero_nat),N)) # label(fact_1114_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 764 (all Y_2 all X_2 all Xs_1 (is_fun760276937t_bool(X_2) & is_fun760276937t_bool(Y_2) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Y_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Y_2),set_fu1865467835t_bool(Xs_1))) | X_2 = Y_2))) # label(fact_666_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 765 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(hAPP_n1429822280t_bool(drop_f1080688732t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))))) # label(fact_676_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 766 (all B_1_1 all B_2_1 is_fun158382675l_bool(hAPP_l1661879987l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa_021) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 767 (all Pa ((all X1 hBOOL(hAPP_P1327827171t_bool(Pa,X1))) <-> (all A_7 all B_6 hBOOL(hAPP_P1327827171t_bool(Pa,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 768 (all M zero_zero_nat = hAPP_nat_nat(minus_minus_nat(M),M)) # label(fact_1148_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 769 (all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Ca,A_7),B_6))))) -> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Ca),P_1))))) # label(fact_551_splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 770 (all Aa all Ba all A_8 all B_7 (Aa = A_8 & B_7 = Ba <-> hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_8),B_7) = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))) # label(fact_15_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 771 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_1099_le0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 772 (all Fa (hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,Fa)) <-> (all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) -> (all Xa (is_fun760276937t_bool(Xa) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Xa),arrow_1721807329e_Prof)) -> (all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> ((all I (is_Arr43961803e_indi(I) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A1677245848t_bool(Xa,I))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A1677245848t_bool(X_1,I)))))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_f412050202t_bool(Fa,X_1))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_f412050202t_bool(Fa,Xa))))))))))))))) # label(fact_32_IIA__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 773 (all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(Pa,N_1)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_1188_zero__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 774 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1097062475t_bool(hAPP_b1376601646t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_019) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 775 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun2093718614t_bool(hAPP_A210478249t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_002) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 776 (exists X_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),top_to565915683t_bool)) & is_Pro1725146340le_alt(X_1))) # label(fact_448_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 777 (all Y_6 all X_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6)) -> Y_6 = X_7))) # label(fact_934_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 778 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,B_1))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_2)),hAPP_A366518464l_bool(B_1,X_2)))))) # label(fact_175_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 779 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun961089132t_bool(hAPP_A568203993t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_010) # label(hypothesis) # label(non_clause). [assumption]. 2.20/2.69 780 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool))) # label(fact_373_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 781 (all X_35 all Xs_49 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_49)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_35),Xs_49))))) # label(fact_334_distinct__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 782 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_Arr43961803e_indi(hAPP_f1582908258e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___077) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 783 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_fun1097062475t_bool(X_1) & is_fun1097062475t_bool(Y_9) & is_fun1097062475t_bool(Z_4) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),set_fu335223357t_bool(Xs_1))) -> (hBOOL(hAPP_f927478261l_bool(hAPP_P1039044241l_bool(member1065824984t_bool,hAPP_f1925192252t_bool(hAPP_f1133021325t_bool(produc1096087521t_bool,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f927478261l_bool(hAPP_P1039044241l_bool(member1065824984t_bool,hAPP_f1925192252t_bool(hAPP_f1133021325t_bool(produc1096087521t_bool,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f927478261l_bool(hAPP_P1039044241l_bool(member1065824984t_bool,hAPP_f1925192252t_bool(hAPP_f1133021325t_bool(produc1096087521t_bool,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f1478750961l_bool(hAPP_P1320270217l_bool(member813910868t_bool,hAPP_l546743617t_bool(hAPP_l1806296521t_bool(produc1256910039t_bool,Xs_1),Ys_1)),hAPP_f1446256145l_bool(lexord46855665t_bool,R_2))) -> (hBOOL(hAPP_f1478750961l_bool(hAPP_P1320270217l_bool(member813910868t_bool,hAPP_l546743617t_bool(hAPP_l1806296521t_bool(produc1256910039t_bool,Ys_1),Zs_1)),hAPP_f1446256145l_bool(lexord46855665t_bool,R_2))) -> hBOOL(hAPP_f1478750961l_bool(hAPP_P1320270217l_bool(member813910868t_bool,hAPP_l546743617t_bool(hAPP_l1806296521t_bool(produc1256910039t_bool,Xs_1),Zs_1)),hAPP_f1446256145l_bool(lexord46855665t_bool,R_2))))))) # label(fact_787_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 784 (all N_2 all Pa (-hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(Pa,N_2)) -> (exists K_1 (hBOOL(hAPP_nat_bool(Pa,K_1)) & (all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) -> -hBOOL(hAPP_nat_bool(Pa,I)))) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_2))))))) # label(fact_1179_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 785 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,hAPP_f81007726t_bool(cOMBK_2130565512t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_2)),B_1))))) # label(fact_95_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 786 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B_1))))) # label(fact_943_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 787 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),set_fu1384968698t_bool(L_1))) -> (hBOOL(hAPP_f592646513l_bool(Q_1,X_1)) <-> hBOOL(hAPP_f592646513l_bool(Pa,X_1)))))) -> hAPP_l1075146559t_bool(dropWh1133555834t_bool(Pa),L_1) = hAPP_l1075146559t_bool(dropWh1133555834t_bool(Q_1),K)))) # label(fact_843_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 788 (all R_2 all S_2 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_2),S_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,hAPP_f1865483825t_bool(listre760726333le_alt,R_2)),hAPP_f1865483825t_bool(listre760726333le_alt,S_2))))) # label(fact_918_listrel__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 789 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(butlas1456493703le_alt,Xs_1)))) | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(butlas1456493703le_alt,Ys_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(butlas1456493703le_alt,hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),Ys_1))))))) # label(fact_737_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 790 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_2),Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))))) # label(fact_669_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 791 (all C_4 all B_5 all A_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_5)) -> (C_4 = B_5 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_4),A_5))))) # label(fact_937_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 792 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,hAPP_f372103450t_bool(cOMBK_1411148035t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_2)),B_1))))) # label(fact_96_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 793 (all Xs_1 all L_1 all Pa all X_2 (-hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1) = hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),L_1))))) # label(fact_392_takeWhile__tail) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 794 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> (-hBOOL(hAPP_P1327827171t_bool(Pa,X_2)) -> hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,hAPP_l1493873365le_alt(dropWh1604595954le_alt(Pa),Xs_1)),Ys_1) = hAPP_l1493873365le_alt(dropWh1604595954le_alt(Pa),hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),Ys_1))))) # label(fact_755_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 795 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A_1),B_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B_1))))) # label(fact_954_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 796 (all X_2 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> ((all Y_9 (is_Arr1861959080le_alt(Y_9) -> (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Xs_1) = Ys_1 -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_9)),R_2))))) -> -(all Zs (Ys_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Zs)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))))))) # label(fact_476_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 797 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1))))) # label(fact_87_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 798 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> (exists Ys exists Zs (Xs_1 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Zs))))))) # label(fact_874_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 799 (all X_2 all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),hAPP_f1662382841t_bool(lex_li678151430le_alt,R_2))) <-> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(lex_li678151430le_alt,R_2))) & Y_2 = X_2 | hAPP_l1071513828lt_nat(size_s1310206929le_alt,Xs_1) = hAPP_l1071513828lt_nat(size_s1310206929le_alt,Ys_1) & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)))) # label(fact_508_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 800 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,B_1))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_2)),hAPP_P2136891882t_bool(B_1,X_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1))))) # label(fact_67_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 801 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,B_1)))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),B_1))))) # label(fact_94_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 802 (all Ca all P_1 (hBOOL(hAPP_P1327827171t_bool(hAPP_f1331183759t_bool(produc1102988737t_bool,Ca),P_1)) -> -(all X_1 all Y_9 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Ca,X_1),Y_9)))))) # label(fact_552_splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 803 (all X_2 all Xs_1 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> hAPP_l248265089st_nat(rev_nat,hAPP_l248265089st_nat(tl_nat,hAPP_l248265089st_nat(dropWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),Xs_1))) = hAPP_l248265089st_nat(takeWhile_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_l248265089st_nat(rev_nat,Xs_1))))) # label(fact_642_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 804 (all C all A all B (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C)))))) # label(fact_1163_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 805 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,hAPP_f1739666797l_bool(cOMBK_8746725le_alt,B_1)))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_2)),B_1))))) # label(fact_117_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 806 (all I_2 all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K_2)),I_2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I_2)),K_2))) # label(fact_1153_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 807 (all M_2 all N_2 (N_2 = zero_zero_nat & zero_zero_nat = M_2 <-> zero_zero_nat = hAPP_nat_nat(plus_plus_nat(M_2),N_2))) # label(fact_1110_add__is__0) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 808 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,B_1)))))) # label(fact_234_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 809 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_2)),hAPP_f228695594t_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_73_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 810 (all X_2 all Xs_1 (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) & hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) <-> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1))))) # label(fact_708_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 811 (all Pa ((all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6))))) <-> (all X1 (is_Pro1725146340le_alt(X1) -> hBOOL(hAPP_P606313927t_bool(Pa,X1)))))) # label(fact_14_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 812 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(hAPP_n1429822280t_bool(take_f1669843892t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))))) # label(fact_980_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 813 (all P all Q (is_fun279392540l_bool(P) -> P = hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_116) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 814 (all A_1 ((all X_1 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1))) -> top_to772840767t_bool = A_1)) # label(fact_453_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 815 (all B_1_1 all B_2_1 is_bool(hAPP_f108029607l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 816 (all P all Q all R hAPP_l1869074853le_alt(hAPP_f1790240989le_alt(hAPP_f1013417831le_alt(cOMBB_2052911494le_alt,P),Q),R) = hAPP_l1869074853le_alt(P,hAPP_l726444215le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_140) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 817 (all Z_3 all Ca all P_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_P139894920l_bool(hAPP_f86548619l_bool(produc998313258l_bool,Ca),P_1))) -> -(all X_1 all Y_9 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Z_3),hAPP_l1328583473l_bool(hAPP_l395992834l_bool(Ca,X_1),Y_9))))))) # label(fact_569_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 818 (all X_2 all R_2 all Y_2 ((exists B_6 exists Z_4 hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,B_6),Z_4) = Y_2) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X_2),Y_2))),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))) # label(fact_434_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 819 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))) -> -(all X_1 all Y_9 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9)),R_2)) -> (all Us all Vs (Xs_1 = hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Us),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_1),Vs)) -> hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Us),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_9),Vs)) != Ys_1)))))) # label(fact_473_listrel1E) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 820 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) & is_fun1393352280t_bool(B_1_1) -> is_bool(hAPP_A862370221t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 821 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_2)),hAPP_P2082381915t_bool(B_1,X_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1))))) # label(fact_68_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.69 822 (all P all Q all R hAPP_f965095724l_bool(hAPP_f1577179519l_bool(hAPP_f1688301673l_bool(cOMBC_2105056416l_bool,P),Q),R) = hAPP_f965095724l_bool(hAPP_f1577179519l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 823 (all Pa all Xs_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) -> hBOOL(hAPP_A862370221t_bool(Pa,X_1))))) <-> nil_Ar126264853le_alt = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1))) # label(fact_734_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 824 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))))) # label(fact_1071_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 825 (all Xs_1 (Xs_1 != nil_Pr1357826771le_alt -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hd_Pro1848862016le_alt(Xs_1)),set_Pr1404309362le_alt(Xs_1))))) # label(fact_746_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 826 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),set_fu1384968698t_bool(Xs_1))) -> hBOOL(hAPP_f592646513l_bool(Pa,X_1))))) -> hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),Ys_1)) = hAPP_l1075146559t_bool(takeWh1512678354t_bool(Pa),hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),Ys_1)))) # label(fact_806_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 827 (all Ws (-hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Ws)) -> (exists Xs_17 exists Ys exists Zs exists Y_9 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_17),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),nil_Ar126264853le_alt)),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),nil_Ar126264853le_alt)),Zs)))) = Ws & is_Arr1861959080le_alt(Y_9))))) # label(fact_510_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 828 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f210572555l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___083) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 829 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(L_1))) -> (hBOOL(hAPP_bool_bool(Pa,X_1)) <-> hBOOL(hAPP_bool_bool(Q_1,X_1)))))) -> hAPP_l1189022293t_bool(takeWhile_bool(Pa),L_1) = hAPP_l1189022293t_bool(takeWhile_bool(Q_1),K)))) # label(fact_850_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 830 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) <-> (exists Ys exists Zs (hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Zs))))))) # label(fact_826_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 831 (all P all Q (is_bool(P) -> P = hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 832 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun760276937t_bool(hAPP_A2102641565t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_011) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 833 (all P_1 all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,P_1),R_2)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,P_1),transi1256616594le_alt(R_2))))) # label(fact_634_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 834 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,B_1))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_2)),hAPP_f239852716t_bool(B_1,X_2)))))) # label(fact_156_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 835 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> (-hBOOL(hAPP_f592646513l_bool(Pa,X_2)) -> hAPP_l1075146559t_bool(dropWh1133555834t_bool(Pa),hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),Ys_1)) = hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,hAPP_l1075146559t_bool(dropWh1133555834t_bool(Pa),Xs_1)),Ys_1)))) # label(fact_759_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 836 (all X_2 all Xs_1 (hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt) <-> Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt))) # label(fact_624_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 837 (all Ca all P_1 ((all A_7 all B_6 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(Ca,A_7),B_6)))) -> hBOOL(hAPP_P1327827171t_bool(hAPP_f1331183759t_bool(produc1102988737t_bool,Ca),P_1)))) # label(fact_550_splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 838 (all X_2 all Xs_1 (hBOOL(hAPP_l982832318l_bool(distin1691228364t_bool,hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Xs_1))) <-> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) & hBOOL(hAPP_l982832318l_bool(distin1691228364t_bool,Xs_1)))) # label(fact_713_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 839 (all X_2 all Z_3 all R_2 (is_Arr1861959080le_alt(Z_3) & is_Arr1861959080le_alt(X_2) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Z_3)),transi1256616594le_alt(R_2))) -> (X_2 != Z_3 -> -(all Y_9 (is_Arr1861959080le_alt(Y_9) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_9)),R_2)) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_9),Z_3)),transi1256616594le_alt(R_2)))))))))) # label(fact_860_converse__rtranclE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 840 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A_1,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,B_1)))))) # label(fact_259_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 841 (all A1 all A2 all R_2 ((exists A_7 (A_7 = A1 & A_7 = A2)) | (exists A_7 exists B_6 exists C_5 (A_7 = A1 & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)),transi992120749le_alt(R_2))) & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,B_6),C_5)),R_2)) & C_5 = A2)) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A1),A2)),transi992120749le_alt(R_2))))) # label(fact_903_rtrancl_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 842 (all Xs_27 all Ys_7 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_27) != hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_7) -> Ys_7 != Xs_27)) # label(fact_530_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 843 (all B_1_1 all B_2_1 is_bool(hAPP_l1795316048t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 844 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,B_1))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_2)),hAPP_f856106132t_bool(B_1,X_2))) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1))))) # label(fact_76_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 845 (all R_2 hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2)) = transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) # label(fact_603_listrel__rtrancl__eq__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 846 (all B_1_1 all B_2_1 is_bool(hAPP_f1534526009l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_057) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 847 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_1141_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 848 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_2)),hAPP_P139894920l_bool(B_1,X_2)))))) # label(fact_165_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 849 (all B_1_1 all B_2_1 is_fun279392540l_bool(hAPP_n1674354836l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 850 (all M_2 all N_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_2)))) # label(fact_1035_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 851 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_2)),hAPP_n295497947l_bool(B_1,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))))) # label(fact_62_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 852 (all X_2 all Xs_1 (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(insert256706849le_alt,X_2),Xs_1) = hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Xs_1))) # label(fact_779_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 853 (all B_1_1 all B_2_1 is_fun961089132t_bool(hAPP_P1861769507t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_100) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 854 (all B_1_1 all B_2_1 is_bool(hAPP_f1252760917l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_043) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 855 (all Pa all M_2 all N_2 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2))) -> ((M_2 = N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_2),M_2)))))) # label(fact_1017_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 856 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),hAPP_b1812770943l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,B_1))))) # label(fact_212_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 857 (all K_2 all L all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),L)))))) # label(fact_1079_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 858 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1861769507t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f354239713l_bool(hAPP_f720124009l_bool(member1139774916t_bool,F),pi_Pro623007021t_bool(A_1,hAPP_f952375653l_bool(cOMBK_751995742le_alt,B_1)))))) # label(fact_251_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 859 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(hAPP_n19406600le_alt(take_P580715755le_alt,N_2),Xs_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))))) # label(fact_975_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 860 (all Aa (is_fun288122577l_bool(Aa) -> (Aa = top_to522745736l_bool <-> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))))) # label(fact_992_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 861 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),hAPP_A1677245848t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,B_1))))) # label(fact_284_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 862 (all X_2 all Xs_1 (hBOOL(hAPP_l2060223415l_bool(distin1991771627t_bool,Xs_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> hAPP_l210315413t_bool(rev_fu1629171390t_bool,hAPP_l210315413t_bool(tl_fun413860871t_bool,hAPP_l210315413t_bool(dropWh23362493t_bool(hAPP_f1765205l_bool(hAPP_f152453811l_bool(cOMBB_1459698610t_bool,fNot),hAPP_f1577576703l_bool(hAPP_f1556356969l_bool(cOMBC_1576836772l_bool,fequal1596628751t_bool),X_2))),Xs_1))) = hAPP_l210315413t_bool(takeWh169821797t_bool(hAPP_f1765205l_bool(hAPP_f152453811l_bool(cOMBB_1459698610t_bool,fNot),hAPP_f1577576703l_bool(hAPP_f1556356969l_bool(cOMBC_1576836772l_bool,fequal1596628751t_bool),X_2))),hAPP_l210315413t_bool(rev_fu1629171390t_bool,Xs_1))))) # label(fact_646_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 863 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,B_1))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B_1,X_2)))))) # label(fact_157_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 864 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M)) # label(fact_1156_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 865 (all Xa_1 all Xb all Za all Zb all R_2 (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Xa_1),Xb)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Za),Zb))),transi580536954le_alt(R_2))) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Xa_1),Xb) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Za),Zb) -> -(all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Xa_1),Xb)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6))),R_2)) -> -hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Za),Zb))),transi580536954le_alt(R_2))))))))) # label(fact_897_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 866 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> hAPP_l1075146559t_bool(hAPP_f613335309t_bool(insert202184175t_bool,X_2),Xs_1) = Xs_1)) # label(fact_704_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 867 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_1)),hAPP_f1663053423t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,B_1))))) # label(fact_191_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 868 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),hAPP_A1677245848t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,B_1))))) # label(fact_202_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 869 (all F all Aa all Ba (hBOOL(hAPP_P1327827171t_bool(hAPP_f1331183759t_bool(produc1102988737t_bool,F),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(F,Aa),Ba)))) # label(fact_532_splitD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 870 (all A_1 (is_fun961089132t_bool(A_1) -> ((all X_1 (is_Pro1725146340le_alt(X_1) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)))) -> top_to565915683t_bool = A_1))) # label(fact_457_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 871 (all Y (zero_zero_nat != Y -> -(all Nat_1 Y != hAPP_nat_nat(suc,Nat_1)))) # label(fact_1187_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 872 (all Ys_1 all Pa all Xs_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),set_Pr1404309362le_alt(Xs_1))) -> hBOOL(hAPP_P1327827171t_bool(Pa,X_1)))) -> hAPP_l1493873365le_alt(dropWh1604595954le_alt(Pa),Ys_1) = hAPP_l1493873365le_alt(dropWh1604595954le_alt(Pa),hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Xs_1),Ys_1)))) # label(fact_793_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 873 (all B_1_1 all B_2_1 is_bool(hAPP_f196630486l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_040) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 874 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_fun279392540l_bool(hAPP_f1277514478l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__038) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 875 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,B_1))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_2)),hAPP_f856106132t_bool(B_1,X_2)))))) # label(fact_149_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 876 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_2)),hAPP_f228695594t_bool(B_1,X_2)))))) # label(fact_146_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 877 (all B_1_1 all B_2_1 is_Pro1725146340le_alt(hAPP_P1699981037le_alt(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_101) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 878 (all X all Y (hBOOL(hAPP_P1327827171t_bool(hAPP_P163071551t_bool(fequal673514820le_alt,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 879 (all B_1_1 all B_2_1 is_fun288122577l_bool(hAPP_l1328583473l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa_020) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 880 (all F all Aa all Ba (hBOOL(hAPP_P1327827171t_bool(F,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(produc231070560t_bool(F),Aa),Ba)))) # label(fact_328_curryI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 881 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,B_1))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_2)),hAPP_f1628730575t_bool(B_1,X_2))) -> -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1))))) # label(fact_71_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 882 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_2)),hAPP_n588788980t_bool(B_1,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))))) # label(fact_48_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 883 (all P all Q all R hAPP_l726444215le_alt(hAPP_l568342716le_alt(P,R),Q) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(hAPP_f1294513379le_alt(cOMBC_1058495865le_alt,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 884 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,B_1))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_2)),hAPP_f5761716t_bool(B_1,X_2)))))) # label(fact_155_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 885 (all X_2 hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),top_to2076077793t_bool))) # label(fact_377_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 886 (all X_34 all Xs_48 -hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_34),Xs_48)))) # label(fact_339_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 887 (all A_1 (is_fun1236654035i_bool(A_1) -> ((all X_1 (is_Arr43961803e_indi(X_1) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)))) -> A_1 = top_to1576102282i_bool))) # label(fact_455_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 888 (all X_2 all Xs_1 (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Xs_1) = hAPP_l54953109e_indi(hAPP_A974963564e_indi(insert915800584e_indi,X_2),Xs_1))) # label(fact_774_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 889 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_1_1) & is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 890 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,hAPP_f746617550l_bool(cOMBK_370033373t_bool,B_1)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),B_1))))) # label(fact_99_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 891 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> N = M))) # label(fact_1025_less__SucE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 892 (all B_1_1 all B_2_1 is_bool(hAPP_f1732944975l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_068) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 893 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(butlast_bool,Xs_1)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))))) # label(fact_692_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 894 (all Y_2 all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(Xs_1))) | (hBOOL(Y_2) <-> hBOOL(X_2)))) # label(fact_663_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 895 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) <-> (exists Ys exists Zs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Ys))) & Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs)))))) # label(fact_811_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 896 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(butlas309371216t_bool,Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))))) # label(fact_695_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 897 (all Xs_37 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_37),nil_Ar126264853le_alt) = Xs_37) # label(fact_403_append__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 898 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_1)),hAPP_P2082381915t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,B_1))))) # label(fact_181_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 899 (all Xs_1 set_Ar1565008694le_alt(hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_1)) = set_Ar1565008694le_alt(Xs_1)) # label(fact_697_set__rotate1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 900 (all X_2 all Xs_1 (hBOOL(hAPP_l54057324t_bool(distin1553582624le_alt,Xs_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> hAPP_l1493873365le_alt(dropWh1604595954le_alt(hAPP_f1642286869t_bool(hAPP_f62793075t_bool(cOMBB_1604919143le_alt,fNot),hAPP_P163071551t_bool(hAPP_f2139078121t_bool(cOMBC_1470522126t_bool,fequal673514820le_alt),X_2))),hAPP_l1493873365le_alt(rev_Pr464210035le_alt,Xs_1)) = hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),hAPP_l1493873365le_alt(rev_Pr464210035le_alt,hAPP_l1493873365le_alt(takeWh416411546le_alt(hAPP_f1642286869t_bool(hAPP_f62793075t_bool(cOMBB_1604919143le_alt,fNot),hAPP_P163071551t_bool(hAPP_f2139078121t_bool(cOMBC_1470522126t_bool,fequal673514820le_alt),X_2))),Xs_1)))))) # label(fact_652_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 901 (all B_1_1 all B_2_1 is_bool(hAPP_f599145828l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 902 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,hAPP_f589776703l_bool(cOMBK_1638246986le_alt,B_1)))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_2)),B_1))))) # label(fact_122_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 903 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(butlas1472553170t_bool,Xs_1)))) | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(butlas1472553170t_bool,Ys_1)))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(butlas1472553170t_bool,hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),Ys_1))))))) # label(fact_740_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 904 (all P all Q (is_fun288122577l_bool(P) -> P = hAPP_A1928120382l_bool(hAPP_f1739666797l_bool(cOMBK_8746725le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_126) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 905 (all Y_2 all X_2 all Xs_1 (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(X_2) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Y_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)))) -> X_2 = Y_2 | hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Y_2),set_Ar1565008694le_alt(Xs_1)))))) # label(fact_660_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 906 (all F all Aa all Ba (hBOOL(hAPP_P606313927t_bool(F,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))) -> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(produc212588606t_bool(F),Aa),Ba)))) # label(fact_329_curryI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 907 (all B_1_1 all B_2_1 is_bool(hAPP_f1508559628l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____074) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 908 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_1)),hAPP_P139894920l_bool(B_1,X_1))))) -> hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,B_1))))) # label(fact_287_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 909 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) -> (exists Ys exists Zs Xs_1 = hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs))))) # label(fact_889_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 910 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M)) # label(fact_1167_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 911 (all R_2 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),nil_Ar126264853le_alt)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2)))) # label(fact_539_listrel_ONil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 912 (all P all Q hAPP_P2136891882t_bool(hAPP_f1809347209t_bool(cOMBK_1632198563le_alt,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__prod_Itc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 913 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> (exists Ys exists Zs hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Ys),hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),Zs)) = Xs_1))) # label(fact_891_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 914 (all X_2 hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool))) # label(fact_371_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 915 -(all C_5 (is_Arr1861959080le_alt(C_5) -> -hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,C_5),nil_Ar126264853le_alt))))))) # label(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 916 (all M_2 all K all N_2 (hAPP_nat_nat(plus_plus_nat(M_2),K) = hAPP_nat_nat(plus_plus_nat(N_2),K) <-> N_2 = M_2)) # label(fact_1087_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 917 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun288122577l_bool(hAPP_A1928120382l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_006) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 918 (all P all Q all R hAPP_f312250286l_bool(hAPP_f1577576703l_bool(hAPP_f1556356969l_bool(cOMBC_1576836772l_bool,P),Q),R) = hAPP_f312250286l_bool(hAPP_f1577576703l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 919 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N_2),M_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1124_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 920 (all Pa all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1))))) # label(fact_411_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 921 (all P all Q (is_fun288122577l_bool(P) -> P = hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_128) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 922 (all B_1_1 all B_2_1 is_bool(hAPP_l1386638586t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 923 (all Xs_1 (nil_fu1891063196t_bool != Xs_1 -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hd_fun276684937t_bool(Xs_1)),set_fu1865467835t_bool(Xs_1))))) # label(fact_751_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 924 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_Pro1725146340le_alt(hAPP_A638717112le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__prod_I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 925 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B_1,X_2)))))) # label(fact_176_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 926 (all P_1 all F all G all Q_2 ((all X_1 all Y_9 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) = Q_2 -> hAPP_l391088160le_alt(hAPP_l1869074853le_alt(G,X_1),Y_9) = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(F,X_1),Y_9))) -> (P_1 = Q_2 -> hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,F),P_1) = hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,G),Q_2)))) # label(fact_506_split__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 927 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun760276937t_bool(hAPP_b317196972t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf_018) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 928 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_2)),hAPP_P139894920l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1))))) # label(fact_54_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 929 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_1)),hAPP_P1711233733t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,B_1))))) # label(fact_182_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 930 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_Pro1725146340le_alt(X_1) & is_Pro1725146340le_alt(Z_4) & is_Pro1725146340le_alt(Y_9) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),set_Pr604701398le_alt(Xs_1))) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f108029607l_bool(hAPP_P1336117749l_bool(member2144312714le_alt,hAPP_P1524963591le_alt(hAPP_P665560703le_alt(produc1593382163le_alt,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f117508401l_bool(hAPP_P1215479305l_bool(member1385125268le_alt,hAPP_l1646733722le_alt(hAPP_l1152370491le_alt(produc556103063le_alt,Xs_1),Ys_1)),hAPP_f1823567903t_bool(lexord1728804490le_alt,R_2))) -> (hBOOL(hAPP_f117508401l_bool(hAPP_P1215479305l_bool(member1385125268le_alt,hAPP_l1646733722le_alt(hAPP_l1152370491le_alt(produc556103063le_alt,Ys_1),Zs_1)),hAPP_f1823567903t_bool(lexord1728804490le_alt,R_2))) -> hBOOL(hAPP_f117508401l_bool(hAPP_P1215479305l_bool(member1385125268le_alt,hAPP_l1646733722le_alt(hAPP_l1152370491le_alt(produc556103063le_alt,Xs_1),Zs_1)),hAPP_f1823567903t_bool(lexord1728804490le_alt,R_2))))))) # label(fact_790_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 931 (all X all Y (Y != X | hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(fequal796301787le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 932 (all Aa hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),top_to565915683t_bool))) # label(fact_984_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 933 (all P all Q (is_bool(P) -> hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 934 (all M all N all K_2 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K_2)) # label(fact_1143_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 935 (all B_1_1 all B_2_1 is_bool(hAPP_f1306865520l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_069) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 936 (exists X_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) & is_bool(X_1))) # label(fact_445_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 937 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,hAPP_f681285561l_bool(cOMBK_1786282629le_alt,B_1)))))) # label(fact_255_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 938 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B_1,X_2)))))) # label(fact_177_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 939 (all P all Q all R hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f1982584345l_bool(cOMBB_310009925t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f592646513l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__prod_It) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 940 (all B_1_1 all B_2_1 is_bool(hAPP_l89806901l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 941 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) <-> (exists Ys exists Zs (Xs_1 = hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs)) & -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Zs))))))) # label(fact_821_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 942 (all M_2 all N_2 (hAPP_nat_nat(plus_plus_nat(M_2),N_2) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_2 = hAPP_nat_nat(suc,zero_zero_nat) & N_2 = zero_zero_nat | hAPP_nat_nat(suc,zero_zero_nat) = N_2 & zero_zero_nat = M_2)) # label(fact_1173_add__is__1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 943 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1424540178l_bool(hAPP_f452990795l_bool(member1870621557le_alt,F),pi_fun684211550le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1800079444le_alt(F,X_2)),hAPP_f239852716t_bool(B_1,X_2))) -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1))))) # label(fact_83_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 944 (all Pa (is_fun1393352280t_bool(Pa) -> collec1729629178le_alt(Pa) = Pa)) # label(fact_324_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 945 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> (exists Ys exists Zs Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs))))) # label(fact_887_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 946 (all B_1_1 is_fun_bool_bool(set_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 947 (all Xa_1 all Xb all Za all Zb all R_2 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xa_1),Xb)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Za),Zb))),transi54034710le_alt(R_2))) -> (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xa_1),Xb) != hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Za),Zb) -> -(all A_7 all B_6 (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xa_1),Xb)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6))),R_2)) -> -hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6)),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Za),Zb))),transi54034710le_alt(R_2)))))))) # label(fact_896_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 948 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_1)),hAPP_A366518464l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,B_1))))) # label(fact_297_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 949 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,hAPP_f681285561l_bool(cOMBK_1786282629le_alt,B_1)))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_2)),B_1))))) # label(fact_125_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 950 (all Xs_9 all Ys_2 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Ys_2)),hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_9)) = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_9),Ys_2))) # label(fact_609_rev__append) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 951 (all Xs_1 all Ys_1 all Zs_1 (Ys_1 = Zs_1 <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Zs_1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))) # label(fact_395_same__append__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 952 (all N hAPP_nat_nat(suc,N) != N) # label(fact_1007_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 953 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1))))) # label(fact_56_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 954 (all X all Y (Y != X | hBOOL(hAPP_f312250286l_bool(hAPP_f1577576703l_bool(fequal1596628751t_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____t) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 955 (all Aa hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),top_to1853035173l_bool))) # label(fact_986_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 956 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Ys))) & Xs_1 = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs)))))) # label(fact_870_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 957 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N))) # label(fact_1034_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 958 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Zs))) & hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs)) = Xs_1)))) # label(fact_879_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 959 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_1)))) | hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(butlas1262502241le_alt,Ys_1)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))))))) # label(fact_736_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 960 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1040_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 961 (all I_1 all J_2 all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K)),J_2)))) # label(fact_1166_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 962 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> (-hBOOL(hAPP_P606313927t_bool(Pa,X_2)) -> hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,hAPP_l1766111573le_alt(dropWh1907450966le_alt(Pa),Xs_1)),Ys_1) = hAPP_l1766111573le_alt(dropWh1907450966le_alt(Pa),hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),Ys_1))))) # label(fact_761_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 963 (all X all Y (is_Arr1861959080le_alt(Y) & is_Arr1861959080le_alt(X) -> -hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(fequal1160105444le_alt,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 964 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1))))) # label(fact_65_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 965 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_2)),hAPP_n1674354836l_bool(B_1,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))))) # label(fact_58_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 966 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) & is_fun1236654035i_bool(B_1_1) -> is_bool(hAPP_A1785763630i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 967 (all N N = hAPP_nat_nat(size_size_nat,N)) # label(fact_1191_nat__size) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 968 (all P all Q all R hAPP_f1539445765l_bool(P,hAPP_A1505516597le_alt(Q,R)) = hAPP_A1553574765l_bool(hAPP_f156764033l_bool(hAPP_f778758417l_bool(cOMBB_2112722489le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___153) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 969 (all Aa hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool))) # label(fact_983_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 970 (all N all J all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J),N)),K_2)))) # label(fact_1120_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 971 (all Xs_1 all X_2 all Ys_1 (is_Arr1861959080le_alt(X_2) -> (Ys_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),nil_Ar126264853le_alt)) <-> hAPP_l726444215le_alt(butlas1262502241le_alt,Ys_1) = Xs_1 & last_A57386030le_alt(Ys_1) = X_2 & nil_Ar126264853le_alt != Ys_1))) # label(fact_433_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 972 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_1038_le__SucI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 973 (all P all Q all R hAPP_f344580165t_bool(P,hAPP_A1677245848t_bool(Q,R)) = hAPP_A621939144t_bool(hAPP_f210227915t_bool(hAPP_f758198165t_bool(cOMBB_1769989562e_indi,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 974 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) <-> (exists M_1 N_2 = hAPP_nat_nat(suc,M_1)))) # label(fact_1171_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 975 (all Xs_1 all Ys_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),transi94963304le_alt(hAPP_f1662382841t_bool(listre635569361le_alt,R_2)))) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),transi94963304le_alt(hAPP_f1662382841t_bool(listre635569361le_alt,R_2))))))) # label(fact_622_rtrancl__listrel1__ConsI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 976 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> (-hBOOL(hAPP_A1785763630i_bool(Pa,X_2)) -> hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),Ys_1)) = hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),Xs_1)))) # label(fact_719_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 977 (all I_2 all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),J)),I_2))) # label(fact_1069_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 978 (all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))) -> ((all X_1 (hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_1),Ys_1) = Xs_1 -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_2)),R_2)))) -> -(all Zs (Xs_1 = hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Zs) -> -hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Zs),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2)))))))) # label(fact_477_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 979 (all Pa all Xs_1 hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1))),Xs_1)) # label(fact_593_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 980 (all G all F (is_fun961089132t_bool(G) -> ((all X_1 all Y_9 (is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F,X_1),Y_9)) <-> hBOOL(hAPP_P606313927t_bool(G,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9)))))) -> hAPP_f791205069t_bool(produc2022255647t_bool,F) = G))) # label(fact_503_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 981 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun1097062475t_bool(hAPP_A479848479t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_013) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 982 (all P all Q (is_fun961089132t_bool(P) -> P = hAPP_A568203993t_bool(hAPP_f393984045t_bool(cOMBK_673344138le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_108) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 983 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,B_1)))))) # label(fact_243_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 984 (all X_2 all Xs_1 (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) & hBOOL(hAPP_l2060223415l_bool(distin1991771627t_bool,Xs_1)) <-> hBOOL(hAPP_l2060223415l_bool(distin1991771627t_bool,hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Xs_1))))) # label(fact_712_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 985 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(butlas1888624491le_alt,Ys_1)))) | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(butlas1888624491le_alt,Xs_1)))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(hAPP_l1766111573le_alt(butlas1888624491le_alt,hAPP_l1766111573le_alt(hAPP_l1892800522le_alt(append308931554le_alt,Xs_1),Ys_1))))))) # label(fact_743_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 986 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> (exists Ys exists Zs Xs_1 = hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs))))) # label(fact_886_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 987 (all C_3 all A_4 all B_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),B_4)) -> (C_3 = B_4 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_3))))) # label(fact_938_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.70 988 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 989 (all R_1 all S_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),R_1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),S_1))) <-> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,R_1),S_1)))) # label(fact_930_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 990 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L))))) # label(fact_1133_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 991 (all B_1_1 all B_2_1 is_bool(hAPP_f927478261l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 992 (all Xs_47 (Xs_47 != nil_Ar126264853le_alt -> (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_47)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_47)))))) # label(fact_343_distinct__butlast) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 993 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1024_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 994 (all X_2 all Y_2 all R_2 ((all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> A_7 = B_6 | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,B_6),A_7)),R_2)) | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),R_2)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_2),X_2)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) | X_2 = Y_2)) # label(fact_361_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 995 (all I_2 all J all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),J)),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)))) # label(fact_1061_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 996 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_2_1) -> is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 997 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B_1,X_2))) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1))))) # label(fact_79_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 998 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),set_fu1865467835t_bool(Xs_1))) -> hBOOL(hAPP_f965095724l_bool(Pa,X_1))))) -> hAPP_l1660244757t_bool(dropWh1552197947t_bool(Pa),Ys_1) = hAPP_l1660244757t_bool(dropWh1552197947t_bool(Pa),hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),Ys_1)))) # label(fact_798_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 999 (exists A_7 exists B_6 exists C_5 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(C_5) & hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_7),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,B_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,C_5),nil_Ar126264853le_alt))))))) # label(fact_39_alt3) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1000 (all B_1_1 all B_2_1 is_bool(hAPP_l54057324t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1001 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(takeWhile_bool(Pa),Xs_1)))) -> hBOOL(hAPP_bool_bool(Pa,X_2)) & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))))) # label(fact_683_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1002 (all Fa ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) -> (all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> ((all I (is_Arr43961803e_indi(I) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A1677245848t_bool(X_1,I))))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_f412050202t_bool(Fa,X_1))))))))) <-> hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,Fa)))) # label(fact_33_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1003 (all P all Q all R hAPP_f1514103381le_alt(P,hAPP_l1869074853le_alt(Q,R)) = hAPP_l1869074853le_alt(hAPP_f746471349le_alt(hAPP_f1532338415le_alt(cOMBB_2017209238le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1004 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,B_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_2)),hAPP_P2136891882t_bool(B_1,X_2)))))) # label(fact_140_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1005 (all M all N hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N))) # label(fact_1083_add__Suc__right) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1006 (all A1 all A2 all R_2 (nil_Ar126264853le_alt = A1 & A2 = nil_Ar126264853le_alt | (exists X_1 exists Y_9 exists Xs_17 exists Ys (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs_17) = A1 & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Ys) = A2 & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9)),R_2)) & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_17),Ys)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) & is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(X_1))) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A1),A2)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))))) # label(fact_577_listrel_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1007 (all B_1_1 (is_fun961089132t_bool(B_1_1) -> is_fun2093718614t_bool(produc212588606t_bool(B_1_1)))) # label(gsy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oal) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1008 (all P all Q all R hAPP_l568342716le_alt(P,hAPP_A832564074le_alt(Q,R)) = hAPP_A408086601le_alt(hAPP_f1777336662le_alt(hAPP_f939319677le_alt(cOMBB_881934114le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_124) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1009 (all X_2 all Y_2 all L_2 all Z_3 (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(Z_3) & is_Arr1861959080le_alt(X_2) -> (Z_3 != Y_2 & (X_2 = Z_3 -> X_2 != Y_2) & (Z_3 != X_2 -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_2))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(arrow_1495666017_mkbot(L_2),Z_3)))))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1010 (all Xs_29 (Xs_29 != nil_Ar126264853le_alt -> -(all Ys all Y_9 (is_Arr1861959080le_alt(Y_9) -> Xs_29 != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),nil_Ar126264853le_alt)))))) # label(fact_438_rev__cases) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1011 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,B_1))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B_1,X_2)))))) # label(fact_153_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1012 (all P_2 -(all X_1 all Y_9 P_2 != hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9))) # label(fact_306_PairE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1013 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (exists K_1 N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1))))) # label(fact_1096_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1014 (all As (As != nil_nat -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,last_nat(As)),set_nat(As))))) # label(fact_726_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1015 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2)))))) # label(fact_630_listrel__reflcl__if__listrel1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1016 (all B_1_1 all B_2_1 is_bool(hAPP_f1351174655l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1017 (all Y_2 all Ys_1 all Xs_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1)),Xs_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> -(all Y_9 all Ys (is_Arr1861959080le_alt(Y_9) -> (Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Ys) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),Y_9)),R_2)) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ys_1),Ys)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))))))))) # label(fact_548_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1018 (all Ca all A_1 all B_1 (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A_1),B_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B_1))))) # label(fact_913_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1019 (all X_2 hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool))) # label(fact_381_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1020 (all X_2 all A_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) <-> hBOOL(hAPP_P606313927t_bool(A_1,X_2)))) # label(fact_319_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1021 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) <-> N_2 != zero_zero_nat)) # label(fact_1125_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1022 (all Xs_1 (Xs_1 != nil_Ar126264853le_alt <-> (exists Y_9 exists Ys (is_Arr1861959080le_alt(Y_9) & Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Ys))))) # label(fact_89_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1023 (all As (nil_fu81264926t_bool != As -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,last_f1633249093t_bool(As)),set_fu335223357t_bool(As))))) # label(fact_730_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1024 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),hAPP_P1875867302i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,B_1))))) # label(fact_265_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1025 (all X_2 all Xs_1 ((exists Ys exists Zs (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Zs))) & Xs_1 = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs)))) <-> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_824_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1026 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_fun961089132t_bool(hAPP_P1267694911t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__094) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1027 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,B_1))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_2)),hAPP_n1674354836l_bool(B_1,X_2)))))) # label(fact_169_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1028 (all P all Q all R hAPP_f1728064559t_bool(P,hAPP_l1629075165l_bool(Q,R)) = hAPP_l1288188215t_bool(hAPP_f1152779391t_bool(hAPP_f991870303t_bool(cOMBB_353715312le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_160) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1029 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),set_Pr1404309362le_alt(Xs_1))) -> (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f536389215l_bool(hAPP_P1580093797l_bool(member2066943042le_alt,hAPP_P47603675le_alt(hAPP_P2141504567le_alt(produc1326092875le_alt,X_1),Z_4)),R_2)))))) -> (hBOOL(hAPP_f1790426673l_bool(hAPP_P1303953929l_bool(member1501249940le_alt,hAPP_l993078710le_alt(hAPP_l139141107le_alt(produc1810286871le_alt,Xs_1),Ys_1)),hAPP_f471467367t_bool(lexord1965430054le_alt,R_2))) -> (hBOOL(hAPP_f1790426673l_bool(hAPP_P1303953929l_bool(member1501249940le_alt,hAPP_l993078710le_alt(hAPP_l139141107le_alt(produc1810286871le_alt,Ys_1),Zs_1)),hAPP_f471467367t_bool(lexord1965430054le_alt,R_2))) -> hBOOL(hAPP_f1790426673l_bool(hAPP_P1303953929l_bool(member1501249940le_alt,hAPP_l993078710le_alt(hAPP_l139141107le_alt(produc1810286871le_alt,Xs_1),Zs_1)),hAPP_f471467367t_bool(lexord1965430054le_alt,R_2))))))) # label(fact_784_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1030 (all F all X_2 all Xs_1 hAPP_l726444215le_alt(maps_A461338881le_alt(F),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(F,X_2)),hAPP_l726444215le_alt(maps_A461338881le_alt(F),Xs_1))) # label(fact_421_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1031 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f839832464l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,B_1))))) # label(fact_188_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1032 (all X_2 all Xs_1 (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) & hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1)) <-> hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1))))) # label(fact_711_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1033 (all U all X_2 all Y_2 all Aa all Ba all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),R_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,U),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),X_2))),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,U),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Ba),Y_2)))),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))))) # label(fact_432_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1034 (all R_1 all S_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1))))) # label(fact_923_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1035 (all B_1_1 all B_2_1 (is_fun1097062475t_bool(B_2_1) -> is_fun1236654035i_bool(hAPP_f1552576127i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_051) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1036 (all B_1_1 all B_2_1 is_bool(hAPP_l2060223415l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1037 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_2)),hAPP_A366518464l_bool(B_1,X_2))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1))))) # label(fact_64_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1038 (all X_2 all A_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) <-> hBOOL(hAPP_f312250286l_bool(A_1,X_2)))) # label(fact_322_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1039 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_1)),hAPP_P139894920l_bool(B_1,X_1))))) -> hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,B_1))))) # label(fact_205_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1040 (all Xs_1 all Ys_1 (nil_Ar126264853le_alt = Ys_1 <-> Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))) # label(fact_407_append__self__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1041 (all Xs_12 all I_8 all X_14 all Y_11 hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_12),I_8),X_14)),I_8),Y_11) = hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_12),I_8),Y_11)) # label(fact_599_list__update__overwrite) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1042 (all Xs_1 all Ys_1 all Zs_1 all Ts ((exists Us (Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs_1),Us) & Ts = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us),Ys_1) | Zs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Us) & hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us),Ts) = Ys_1)) <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs_1),Ts) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))) # label(fact_396_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1043 (all Aa all X_2 all Ba all Y_2 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,X_2),Y_2)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))) & Ba = Aa | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),R_2)) <-> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Aa),X_2)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Ba),Y_2))),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))))) # label(fact_341_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1044 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),B_1))))) -> hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,B_1)))))) # label(fact_238_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1045 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_2_1) -> is_fun_bool_bool(hAPP_f961197973l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__HOL__Obo) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1046 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Zs))) & hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) = Xs_1)))) # label(fact_878_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1047 (all Pa ((exists A_7 exists B_6 (hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6))) & is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7))) <-> (exists X1 (is_Pro1725146340le_alt(X1) & hBOOL(hAPP_P606313927t_bool(Pa,X1)))))) # label(fact_135_split__paired__Ex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1048 (all F1 all Aa all Ba (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F1),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))) <-> hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F1,Aa),Ba)))) # label(fact_487_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1049 (all Aa (is_fun1393352280t_bool(Aa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,top_to2076077793t_bool),Aa)) -> Aa = top_to2076077793t_bool))) # label(fact_1001_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1050 (exists X_1 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),top_top_fun_nat_bool))) # label(fact_443_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1051 (all Z_3 all Ca all P_1 ((all A_7 all B_6 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_l1661879987l_bool(hAPP_l1824974724l_bool(Ca,A_7),B_6))))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_P1606644490l_bool(hAPP_f2122673039l_bool(produc2129949100l_bool,Ca),P_1))))) # label(fact_562_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1052 (all F1 all Aa all Ba (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(F1,Aa),Ba)) -> hBOOL(hAPP_P1327827171t_bool(hAPP_f1331183759t_bool(produc1102988737t_bool,F1),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))))) # label(fact_517_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1053 (all P all Q all R hAPP_bool_bool(P,hAPP_bool_bool(Q,R)) = hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1054 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9)),R_2)) -> (all Us all Vs (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Vs)) = Xs_1 -> Ys_1 != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Vs))))))))) # label(fact_474_listrel1E) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1055 (all X_2 all A_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) <-> hBOOL(hAPP_f965095724l_bool(A_1,X_2)))) # label(fact_320_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1056 (all X_2 hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool))) # label(fact_379_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1057 (all Xs_31 all X_27 Xs_31 = hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_31),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_27),nil_Ar126264853le_alt)))) # label(fact_422_butlast__snoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1058 (all Ys_1 all Xs_1 all Us_1 all Vs_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)) -> (Xs_1 = hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Us_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Vs_1)) -> (hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Us_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Vs_1)) = Ys_1 -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))))))) # label(fact_471_listrel1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1059 (all P all Q all R hAPP_l726444215le_alt(hAPP_n2139729636le_alt(P,R),Q) = hAPP_n1875670159le_alt(hAPP_l382792410le_alt(hAPP_f2068969285le_alt(cOMBC_1511969967le_alt,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1060 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P324742453l_bool(hAPP_f1502595491l_bool(produc1995698397l_bool,Ca),P_1))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(X_1) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A822657487l_bool(hAPP_A1345295975l_bool(Ca,X_1),Y_9))))))))) # label(fact_567_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1061 (all P all Q (is_fun961089132t_bool(P) -> P = hAPP_n588788980t_bool(hAPP_f1328016200t_bool(cOMBK_856666543ol_nat,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1062 (all Ys_1 all Pa all Xs_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1))) -> hBOOL(hAPP_nat_bool(Pa,X_1)))) -> hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),hAPP_l248265089st_nat(takeWhile_nat(Pa),Ys_1)) = hAPP_l248265089st_nat(takeWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)))) # label(fact_800_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1063 (all I_2 all K_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J)) -> hAPP_nat_nat(minus_minus_nat(I_2),hAPP_nat_nat(minus_minus_nat(J),K_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_2),K_2)),J))) # label(fact_1162_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1064 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A_1,hAPP_f746617550l_bool(cOMBK_370033373t_bool,B_1)))))) # label(fact_229_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1065 (all Aa all Ba (is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Aa) -> (Aa != Ba -> (exists X_1 (is_fun961089132t_bool(X_1) & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),X_1)) & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),arrow_1681063817le_Lin))))))) # label(fact_34_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1066 (all B_1_1 is_Pro1725146340le_alt(hd_Pro1524751780le_alt(B_1_1))) # label(gsy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1067 (all X_2 all Xs_1 ((hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> Xs_1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_2),Xs_1)) & (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_2),Xs_1)))) # label(fact_763_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1068 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_A1664620203t_bool(hAPP_A210478249t_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_P1711233733t_bool(hAPP_f1708325453t_bool(produc315582749t_bool,Ca),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)))))) # label(fact_521_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1069 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> Xs_1 = hAPP_l1493873365le_alt(hAPP_P734992695le_alt(insert178756925le_alt,X_2),Xs_1))) # label(fact_700_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1070 (all P_a all Pa all A_8 all B_7 all Aa all Ba (is_Arr1861959080le_alt(B_7) & is_Arr1861959080le_alt(Ba) & is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(A_8) -> (Aa != Ba -> (B_7 != A_8 -> (Aa != B_7 -> (A_8 != Ba -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_a),arrow_1721807329e_Prof)) -> ((all I (is_Arr43961803e_indi(I) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_8),B_7)),hAPP_A1677245848t_bool(P_a,I)))))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_8),B_7)),hAPP_f412050202t_bool(f,P_a))))))))))))) # label(fact_23__C1_C) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1071 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f1624277646l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,B_1))))) # label(fact_198_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1072 (all Xs_1 (nil_Ar126264853le_alt != Xs_1 -> (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) -> hAPP_l726444215le_alt(takeWh536362254le_alt(hAPP_f2014742713t_bool(hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fNot),hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,fequal1160105444le_alt),last_A57386030le_alt(Xs_1)))),Xs_1) = hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_1)))) # label(fact_388_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1073 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f856106132t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,B_1))))) # label(fact_271_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1074 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (hBOOL(hAPP_f1707011108l_bool(hAPP_l1107171823l_bool(member1013148679le_alt,X_1),set_li1646995977le_alt(Xs_1))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Z_4)),R_2)))))) -> (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))) -> (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Ys_1),Zs_1)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Zs_1)),hAPP_f1662382841t_bool(lexord484930493le_alt,R_2))))))) # label(fact_782_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1075 (all P all Q (is_fun158382675l_bool(P) -> hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_150) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1076 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_1),B_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B_1))))) # label(fact_956_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1077 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2115479956l_bool(hAPP_f975710927l_bool(member24871799le_alt,F),pi_nat249006182le_alt(A_1,B_1))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_n324757596le_alt(F,X_2)),hAPP_n588788980t_bool(B_1,X_2)))))) # label(fact_159_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1078 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun158382675l_bool(hAPP_A366518464l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_008) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1079 (all B_1_1 all B_2_1 is_bool(hAPP_f799496074l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1080 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> (-hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1)),Ys_1) = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1))))) # label(fact_754_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1081 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_1144_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1082 (all Xs_40 all Ys_17 all Zs_3 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_40),Ys_17)),Zs_3) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_40),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_17),Zs_3))) # label(fact_397_append__assoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1083 (all P all Q (is_fun158382675l_bool(P) -> P = hAPP_n295497947l_bool(hAPP_f1879785608l_bool(cOMBK_2131602312ol_nat,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1084 (all B_1_1 all B_2_1 is_bool(hAPP_f16559284l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_067) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1085 (all X all Y (X != Y | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1086 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) <-> (exists Ys exists Zs (Xs_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Ys))))))) # label(fact_814_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1087 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B_1,X_2)))))) # label(fact_167_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1088 (all Pa all Aa all Ba (-((exists D (-hBOOL(hAPP_nat_bool(Pa,D)) & hAPP_nat_nat(plus_plus_nat(Ba),D) = Aa)) | -hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))) <-> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(Aa),Ba))))) # label(fact_1102_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1089 (all X_2 all Xs_1 ((-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Xs_1) = hAPP_l210315413t_bool(hAPP_f1812326636t_bool(insert1946138248t_bool,X_2),Xs_1)) & (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> Xs_1 = hAPP_l210315413t_bool(hAPP_f1812326636t_bool(insert1946138248t_bool,X_2),Xs_1)))) # label(fact_767_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1090 (all P all Q P = hAPP_f1865483825t_bool(hAPP_f1622901481t_bool(cOMBK_1786248882t_bool,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___134) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1091 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> (exists Ys exists Zs (hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Zs))))))) # label(fact_881_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1092 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1))) -> hBOOL(hAPP_bool_bool(Pa,X_1))))) -> hAPP_l1189022293t_bool(dropWhile_bool(Pa),Ys_1) = hAPP_l1189022293t_bool(dropWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)))) # label(fact_795_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1093 (all Aa all R_2 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Aa)),transi992120749le_alt(R_2)))) # label(fact_631_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1094 (all B_1_1 all B_2_1 is_Pro1725146340le_alt(hAPP_n324757596le_alt(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1095 (all B_1_1 all B_2_1 is_bool(hAPP_l377001987t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1096 (all Ys_1 all Xs_1 all Zs_1 (Zs_1 = Ys_1 <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs_1),Xs_1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),Xs_1))) # label(fact_394_append__same__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1097 (all Xs_50 Xs_50 = hAPP_l726444215le_alt(splice360969192le_alt(Xs_50),nil_Ar126264853le_alt)) # label(fact_138_splice__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1098 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,B_1)))))) # label(fact_261_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1099 (all Xs_26 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_26)) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_26)) # label(fact_534_length__rotate1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1100 (all P all Q all R hAPP_f777333846l_bool(hAPP_f461621971l_bool(P,R),Q) = hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___151) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1101 (all X all Y (is_fun961089132t_bool(Y) & is_fun961089132t_bool(X) -> X = Y | -hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(fequal1258273448t_bool,X),Y)))) # label(help_fequal_1_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1102 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_P2082381915t_bool(hAPP_f1783389935t_bool(produc51145731t_bool,Ca),P_1))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(Y_9) & is_Arr1861959080le_alt(X_1) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Z_3),hAPP_A490104565t_bool(hAPP_A101171597t_bool(Ca,X_1),Y_9))))))))) # label(fact_564_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1103 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun279392540l_bool(hAPP_A187815023l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_009) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1104 (all V_2 all Va hAPP_l726444215le_alt(splice360969192le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,V_2),Va)),nil_Ar126264853le_alt) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,V_2),Va)) # label(fact_131_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1105 (all M all K_2 all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_2)),hAPP_nat_nat(plus_plus_nat(N),K_2)) = hAPP_nat_nat(minus_minus_nat(M),N)) # label(fact_1105_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1106 (all B_1_1 is_fun288122577l_bool(set_fu1865467835t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1107 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) = hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1108 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1043_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1109 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A1862272720t_bool(hAPP_A1470764750t_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P2136891882t_bool(hAPP_f1984771213t_bool(produc1527919682t_bool,Ca),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)))))) # label(fact_519_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1110 (all Nat_5 all Nat_4 (hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_5) <-> Nat_5 = Nat_4)) # label(fact_1009_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1111 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,hAPP_f1622901481t_bool(cOMBK_1786248882t_bool,B_1)))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_2)),B_1))))) # label(fact_101_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1112 (all B_1_1 (is_fun1236654035i_bool(B_1_1) -> is_fun1236654035i_bool(collec1611109369e_indi(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1113 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))))) # label(fact_688_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1114 (all K all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hAPP_nat_nat(minus_minus_nat(J_2),I_1) = K <-> hAPP_nat_nat(plus_plus_nat(K),I_1) = J_2))) # label(fact_1155_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1115 (all X_2 all Xs_1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) & hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_1)) <-> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Xs_1))))) # label(fact_707_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1116 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),hAPP_f244157820i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,B_1))))) # label(fact_192_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1117 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A822657487l_bool(hAPP_A1345295975l_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P324742453l_bool(hAPP_f1502595491l_bool(produc1995698397l_bool,Ca),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)))))) # label(fact_523_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1118 (all P all Q all R hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1119 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),Xs_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) & hBOOL(hAPP_P1327827171t_bool(Pa,X_2)))) # label(fact_681_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1120 (all X_2 all Xs_1 (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> hAPP_l1189022293t_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),hAPP_l1189022293t_bool(rev_bool,Xs_1)) = hAPP_l1189022293t_bool(rev_bool,hAPP_l1189022293t_bool(tl_bool,hAPP_l1189022293t_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),Xs_1)))))) # label(fact_645_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1121 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),hAPP_f1277514478l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,B_1))))) # label(fact_301_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1122 (all P all Q (is_fun158382675l_bool(P) -> hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_145) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1123 (all P all Q (is_fun1236654035i_bool(P) -> P = hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___110) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1124 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(butlas1157436197t_bool,Ys_1)))) | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(butlas1157436197t_bool,Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(butlas1157436197t_bool,hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),Ys_1))))))) # label(fact_741_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1125 (all Xs_13 all X_16 all X_15 all I_10 all I_9 (I_10 != I_9 -> hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_13),I_10),X_16)),I_9),X_15) = hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_13),I_9),X_15)),I_10),X_16))) # label(fact_598_list__update__swap) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1126 (all X_2 all Xs_1 (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Xs_1) = hAPP_l1493873365le_alt(hAPP_P734992695le_alt(insert178756925le_alt,X_2),Xs_1))) # label(fact_773_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1127 (all I_2 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) -> (hAPP_nat_nat(suc,I_2) != K_2 -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> hAPP_nat_nat(suc,J_1) != K_2))))) # label(fact_1057_lessE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1128 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),set_Ar219761597e_indi(Xs_1))) -> hBOOL(hAPP_A1785763630i_bool(Pa,X_1))))) -> hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),Ys_1)) = hAPP_l54953109e_indi(takeWh273131493e_indi(Pa),hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Xs_1),Ys_1)))) # label(fact_803_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1129 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),set_Pr604701398le_alt(L_1))) -> (hBOOL(hAPP_P606313927t_bool(Pa,X_1)) <-> hBOOL(hAPP_P606313927t_bool(Q_1,X_1)))))) -> hAPP_l1766111573le_alt(takeWh1529274110le_alt(Pa),L_1) = hAPP_l1766111573le_alt(takeWh1529274110le_alt(Q_1),K)))) # label(fact_854_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1130 (all B_1_1 all B_2_1 (is_fun279392540l_bool(B_1_1) & is_fun961089132t_bool(B_2_1) -> is_bool(hAPP_f592646513l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___078) # label(hypothesis) # label(non_clause). [assumption]. 2.20/2.71 1131 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_fun1236654035i_bool(hAPP_f1948454017i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__035) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1132 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))))) # label(fact_977_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1133 (exists L_3 (is_fun961089132t_bool(L_3) & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin)))) # label(fact_40_linear__alt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.71 1134 (all Pa all Xs_1 (hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1) != nil_Ar126264853le_alt -> -hBOOL(hAPP_A862370221t_bool(Pa,hd_Arr805754088le_alt(hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1)))))) # label(fact_589_hd__dropWhile) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1135 (all X_2 all L_2 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(arrow_1644373103_mktop(L_2),X_2)),arrow_1681063817le_Lin)))) # label(fact_28_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1136 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),set_fu335223357t_bool(Xs_1))) -> hBOOL(hAPP_f312250286l_bool(Pa,X_1))))) -> hAPP_l210315413t_bool(dropWh23362493t_bool(Pa),Ys_1) = hAPP_l210315413t_bool(dropWh23362493t_bool(Pa),hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),Ys_1)))) # label(fact_796_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1137 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,hAPP_f1783828715t_bool(cOMBK_1901607710le_alt,B_1)))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_2)),B_1))))) # label(fact_111_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1138 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),hAPP_f1552576127i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,B_1))))) # label(fact_197_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1139 (all X_2 hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool))) # label(fact_369_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1140 (all Xs_1 (nil_Ar126264853le_alt = Xs_1 <-> hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) = nil_Ar126264853le_alt)) # label(fact_607_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1141 (all Xs_1 (nil_Ar126264853le_alt != Xs_1 -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hd_Arr805754088le_alt(Xs_1)),set_Ar1565008694le_alt(Xs_1))))) # label(fact_744_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1142 (all X_2 all Xs_1 (hBOOL(hAPP_l2034560823i_bool(distin1358019435e_indi,Xs_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> hAPP_l54953109e_indi(takeWh273131493e_indi(hAPP_f580451669i_bool(hAPP_f1250179763i_bool(cOMBB_1141363506e_indi,fNot),hAPP_A313542399i_bool(hAPP_f585152361i_bool(cOMBC_1428934564i_bool,fequal1196706959e_indi),X_2))),hAPP_l54953109e_indi(rev_Ar2090626622e_indi,Xs_1)) = hAPP_l54953109e_indi(rev_Ar2090626622e_indi,hAPP_l54953109e_indi(tl_Arr1614430599e_indi,hAPP_l54953109e_indi(dropWh601337149e_indi(hAPP_f580451669i_bool(hAPP_f1250179763i_bool(cOMBB_1141363506e_indi,fNot),hAPP_A313542399i_bool(hAPP_f585152361i_bool(cOMBC_1428934564i_bool,fequal1196706959e_indi),X_2))),Xs_1)))))) # label(fact_644_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1143 (all K_2 all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))))) # label(fact_1026_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1144 (all Aa hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,Aa),top_to2076077793t_bool))) # label(fact_988_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1145 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_1)),hAPP_f1593910865t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,B_1))))) # label(fact_194_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1146 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> (-hBOOL(hAPP_nat_bool(Pa,X_2)) -> hAPP_l248265089st_nat(dropWhile_nat(Pa),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(dropWhile_nat(Pa),Xs_1)),Ys_1)))) # label(fact_753_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1147 (all N all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3)) -> (exists M_1 hAPP_nat_nat(suc,M_1) = M_3))) # label(fact_1056_Suc__le__D) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1148 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) & is_fun288122577l_bool(B_1_1) -> is_bool(hAPP_f965095724l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__033) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1149 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),hAPP_b517355696l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,B_1))))) # label(fact_217_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1150 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),set_nat(Xs_1))) -> (hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Z_4)),R_2)))))) -> (hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Xs_1),Ys_1)),hAPP_f29979067t_bool(lexord_nat,R_2))) -> (hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Ys_1),Zs_1)),hAPP_f29979067t_bool(lexord_nat,R_2))) -> hBOOL(hAPP_f1919691607l_bool(hAPP_P1736545109l_bool(member910422074st_nat,hAPP_l318352527st_nat(hAPP_l1148138287st_nat(produc1869962435st_nat,Xs_1),Zs_1)),hAPP_f29979067t_bool(lexord_nat,R_2))))))) # label(fact_783_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1151 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun279392540l_bool(hAPP_f863359027l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___084) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1152 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,hAPP_f1874082285l_bool(cOMBK_1778599651le_alt,B_1)))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_2)),B_1))))) # label(fact_126_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1153 (all Xs_11 Xs_11 = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_11))) # label(fact_602_rev__rev__ident) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1154 (all P all Q all R hAPP_P606313927t_bool(P,hAPP_A702847159le_alt(Q,R)) = hAPP_A862370221t_bool(hAPP_f1457563459t_bool(hAPP_f724700817t_bool(cOMBB_164218871le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1155 (all N_2 all K all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> (hAPP_nat_nat(minus_minus_nat(N_2),K) = hAPP_nat_nat(minus_minus_nat(M_2),K) <-> M_2 = N_2)))) # label(fact_1135_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1156 (all Xs_30 all X_26 (is_Arr1861959080le_alt(X_26) -> last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_30),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_26),nil_Ar126264853le_alt))) = X_26)) # label(fact_423_last__snoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1157 (all F1 all F2 all Aa all List hAPP_l726444215le_alt(list_c380068407le_alt(F1,F2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),List)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(F2,Aa),List)) # label(fact_133_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1158 (all Xs_1 all Ys_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),R_2)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys_1))),hAPP_f1865483825t_bool(listre760726333le_alt,R_2)))))) # label(fact_512_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1159 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_1049_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1160 (all B_1_1 all B_2_1 is_bool(hAPP_f1424540178l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1161 (all A_1 (is_fun288122577l_bool(A_1) -> ((all X_1 (is_fun760276937t_bool(X_1) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)))) -> top_to522745736l_bool = A_1))) # label(fact_458_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1162 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(butlas309371216t_bool,Ys_1)))) | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(butlas309371216t_bool,Xs_1)))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(hAPP_l1660244757t_bool(butlas309371216t_bool,hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Xs_1),Ys_1))))))) # label(fact_742_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1163 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) & hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & is_Arr1861959080le_alt(X_1))) <-> (exists Ys exists X_1 (hBOOL(hAPP_A862370221t_bool(Pa,X_1)) & (all Xa (is_Arr1861959080le_alt(Xa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Ys))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa))))) & (exists Zs Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs))) & is_Arr1861959080le_alt(X_1))))) # label(fact_893_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1164 (all Pa all Xs_1 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1)),hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1)) = Xs_1) # label(fact_501_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1165 (all X_2 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),top_to772840767t_bool))) # label(fact_374_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1166 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(hAPP_l210315413t_bool(hAPP_n1200821448t_bool(drop_f176122846t_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))))) # label(fact_674_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1167 (all P all Q all R hAPP_A1785763630i_bool(hAPP_A313542399i_bool(P,R),Q) = hAPP_A1785763630i_bool(hAPP_A313542399i_bool(hAPP_f585152361i_bool(cOMBC_1428934564i_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1168 (all Ys_18 all Us_2 all Xs_41 all Xs1_1 all Zs_4 (Zs_4 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_41),Xs1_1) -> (Ys_18 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs1_1),Us_2) -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_41),Ys_18) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs_4),Us_2)))) # label(fact_393_append__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1169 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f570668343l_bool(hAPP_f2111526677l_bool(member1881985050ol_nat,F),pi_fun2080023171ol_nat(A_1,hAPP_f1362748656t_bool(cOMBK_208474378t_bool,B_1)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1416261241ol_nat(F,X_2)),B_1))))) # label(fact_105_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1170 (all I_3 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_3),Xs))))) # label(fact_982_distinct__take) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1171 (all P all Q all R hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q) = hAPP_bool_bool(hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1172 (all X_2 all Z_3 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Z_3)),transi992120749le_alt(R_2))) -> (Z_3 != X_2 -> -(all Y_9 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_9)),R_2)) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Y_9),Z_3)),transi992120749le_alt(R_2)))))))) # label(fact_859_converse__rtranclE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1173 (all F all Aa all Ba hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,F),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)) = hAPP_l391088160le_alt(hAPP_l1869074853le_alt(F,Aa),Ba)) # label(fact_488_split__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1174 (all M all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(plus_plus_nat(J),M))))) # label(fact_1076_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1175 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_1)),hAPP_f1865483825t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,B_1))))) # label(fact_190_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1176 (all Xs_1 all Pa all X_2 ((hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1)) = hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1))) & (-hBOOL(hAPP_A862370221t_bool(Pa,X_2)) -> hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)) = nil_Ar126264853le_alt))) # label(fact_420_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1177 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) & is_fun1097062475t_bool(B_1_1) -> is_fun961089132t_bool(hAPP_f412050202t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__039) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1178 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_fun1393352280t_bool(hAPP_P1711233733t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__090) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1179 (all Fa all I_1 (hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I_1)) <-> (all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) -> hAPP_A1677245848t_bool(X_1,I_1) = hAPP_f412050202t_bool(Fa,X_1)))))) # label(fact_41_dictator__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1180 (all B_1_1 all B_2_1 is_bool(hAPP_f1707011108l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1181 (all Q_1 all Pa all Z_3 (is_Pro1725146340le_alt(Z_3) -> (hBOOL(hAPP_bool_bool(Q_1,hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Pa),Z_3))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (Z_3 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) -> -hBOOL(hAPP_bool_bool(Q_1,hAPP_A862370221t_bool(hAPP_A1664620203t_bool(Pa,X_1),Y_9))))))))) # label(fact_505_splitE2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1182 (all X_2 all Xs_1 all Y_2 all Ys_1 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))) & Y_2 = X_2 | hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)) & Ys_1 = Xs_1 <-> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))))) # label(fact_467_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1183 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_1)),hAPP_f1663053423t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,B_1))))) # label(fact_273_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1184 (exists X_1 (is_fun1097062475t_bool(X_1) & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),top_to1714702858l_bool)))) # label(fact_451_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1185 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,B_1)))))) # label(fact_248_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1186 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1732944975l_bool(hAPP_f671616325l_bool(member1636995890le_alt,F),pi_fun380945313le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f1619707799le_alt(F,X_2)),hAPP_f1865483825t_bool(B_1,X_2)))))) # label(fact_150_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1187 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_Arr1861959080le_alt(hAPP_P1257947515le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1188 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),hAPP_f1277514478l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,B_1))))) # label(fact_219_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1189 (all N (N != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_1118_gr0I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1190 (all M all N all K_2 hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K_2)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K_2)) # label(fact_1089_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1191 (all R_1 all S_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,R_1),S_1)) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_f2014742713t_bool(hAPP_f1382209403t_bool(cOMBC_1745481870l_bool,member1071917752le_alt),R_1)),hAPP_f2014742713t_bool(hAPP_f1382209403t_bool(cOMBC_1745481870l_bool,member1071917752le_alt),S_1))))) # label(fact_924_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1192 (all C_1 all A_2 all B_2 (B_2 = A_2 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),C_1))))) # label(fact_958_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1193 (all Xs_1 all K all X_2 (nil_Ar126264853le_alt = hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(Xs_1),K),X_2) <-> nil_Ar126264853le_alt = Xs_1)) # label(fact_611_list__update__nonempty) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1194 (all Ys_14 Ys_14 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),Ys_14)) # label(fact_401_append__Nil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1195 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_Arr43961803e_indi(Z_4) & is_Arr43961803e_indi(Y_9) & is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),set_Ar219761597e_indi(Xs_1))) -> (hBOOL(hAPP_f1067427061l_bool(hAPP_P1563303057l_bool(member345815512e_indi,hAPP_A1350932668e_indi(hAPP_A1266156941e_indi(produc1208780001e_indi,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f1067427061l_bool(hAPP_P1563303057l_bool(member345815512e_indi,hAPP_A1350932668e_indi(hAPP_A1266156941e_indi(produc1208780001e_indi,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f1067427061l_bool(hAPP_P1563303057l_bool(member345815512e_indi,hAPP_A1350932668e_indi(hAPP_A1266156941e_indi(produc1208780001e_indi,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f1382465777l_bool(hAPP_P1068600713l_bool(member1461267796e_indi,hAPP_l2052497089e_indi(hAPP_l29767369e_indi(produc347570391e_indi,Xs_1),Ys_1)),hAPP_f554166545i_bool(lexord1102905201e_indi,R_2))) -> (hBOOL(hAPP_f1382465777l_bool(hAPP_P1068600713l_bool(member1461267796e_indi,hAPP_l2052497089e_indi(hAPP_l29767369e_indi(produc347570391e_indi,Ys_1),Zs_1)),hAPP_f554166545i_bool(lexord1102905201e_indi,R_2))) -> hBOOL(hAPP_f1382465777l_bool(hAPP_P1068600713l_bool(member1461267796e_indi,hAPP_l2052497089e_indi(hAPP_l29767369e_indi(produc347570391e_indi,Xs_1),Zs_1)),hAPP_f554166545i_bool(lexord1102905201e_indi,R_2))))))) # label(fact_785_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1196 (all B_1_1 all B_2_1 is_bool(hAPP_f1271753300l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1197 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1123_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1198 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_1),B_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B_1))))) # label(fact_968_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1199 (all P all Q all R hAPP_f1514103381le_alt(hAPP_l1701840224le_alt(P,R),hAPP_l1869074853le_alt(Q,R)) = hAPP_l1869074853le_alt(hAPP_f746471349le_alt(hAPP_f628327744le_alt(cOMBS_1294827559le_alt,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_157) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1200 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n1674354836l_bool(B_1,X_1))))) -> hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,B_1))))) # label(fact_209_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1201 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B_1,X_2))) -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1))))) # label(fact_85_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1202 (all Y_2 all X_2 all Xs_1 (is_fun961089132t_bool(X_2) & is_fun961089132t_bool(Y_2) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Y_2),set_fu1384968698t_bool(hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Xs_1)))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Y_2),set_fu1384968698t_bool(Xs_1))) | Y_2 = X_2))) # label(fact_665_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1203 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P1599728724t_bool(F,X_1)),hAPP_P1606644490l_bool(B_1,X_1))))) -> hBOOL(hAPP_f1508559628l_bool(hAPP_f984565261l_bool(member1329875721t_bool,F),pi_Pro1636653258t_bool(A_1,B_1))))) # label(fact_214_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1204 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Xs_1)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) & hBOOL(hAPP_A862370221t_bool(Pa,X_2)))) # label(fact_680_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1205 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_939_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1206 (all N all K_2 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) -> hAPP_nat_nat(minus_minus_nat(M),N) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K_2)),hAPP_nat_nat(minus_minus_nat(N),K_2))))) # label(fact_1136_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1207 (all X_2 all A_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) <-> hBOOL(hAPP_f592646513l_bool(A_1,X_2)))) # label(fact_321_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1208 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(A_7) & is_Arr1861959080le_alt(B_6) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_A822657487l_bool(hAPP_A1345295975l_bool(Ca,A_7),B_6)))))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Z_3),hAPP_P324742453l_bool(hAPP_f1502595491l_bool(produc1995698397l_bool,Ca),P_1)))))) # label(fact_558_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1209 (all Aa all Ba all L_2 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),L_2)) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),L_2))))) # label(fact_29_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1210 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_1)),hAPP_A187815023l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,B_1))))) # label(fact_211_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1211 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_2)),hAPP_n2095207769l_bool(B_1,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))))) # label(fact_53_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1212 (all K_2 all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K_2)),hAPP_nat_nat(plus_plus_nat(J),K_2))))) # label(fact_1078_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1213 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) -> hBOOL(hAPP_A862370221t_bool(Pa,X_1))))) -> hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Ys_1) = hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1)))) # label(fact_792_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1214 (all B_1_1 all B_2_1 is_bool(hAPP_f817604743l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1215 (all Xs_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Xs_1))),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))))) # label(fact_469_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1216 (all X_2 all Xs_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Zs))) & Xs_1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Zs)))))) # label(fact_875_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1217 (all B_1_1 all B_2_1 is_bool(hAPP_f167218729l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_066) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1218 (all B_1_1 all B_2_1 is_bool(hAPP_f536389215l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1219 (all X_24 all Xs_25 hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_24),Xs_25)) = Xs_25) # label(fact_535_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1220 (all N_12 all X_21 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_12),X_21)) = N_12) # label(fact_581_length__replicate) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1221 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_2_1) -> is_fun288122577l_bool(hAPP_f1577179519l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__037) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1222 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),hAPP_f1948454017i_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A_1,B_1))))) # label(fact_187_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1223 (all X_2 all Xs_1 ((hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> hAPP_l1660244757t_bool(hAPP_f726713198t_bool(insert1665396998t_bool,X_2),Xs_1) = Xs_1) & (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) -> hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Xs_1) = hAPP_l1660244757t_bool(hAPP_f726713198t_bool(insert1665396998t_bool,X_2),Xs_1)))) # label(fact_769_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1224 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f16559284l_bool(hAPP_f2142494605l_bool(member1846971697ol_nat,F),pi_fun1597968236ol_nat(A_1,hAPP_f932544453t_bool(cOMBK_1773325549t_bool,B_1)))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f816335862ol_nat(F,X_2)),B_1))))) # label(fact_100_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1225 (all X_2 (hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_384_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1226 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M))) # label(fact_1129_diff__le__self) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1227 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B_1,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))))) # label(fact_57_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1228 (all M all I_2 all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N)),I_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(minus_minus_nat(M),I_2)),hAPP_nat_nat(minus_minus_nat(N),I_2))) # label(fact_1104_min__diff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1229 (all B_1_1 (is_fun961089132t_bool(B_1_1) -> is_fun961089132t_bool(collec2096990994le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1230 (all B_1_1 all B_2_1 (is_Pro1725146340le_alt(B_2_1) -> is_fun1236654035i_bool(hAPP_P1875867302i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__091) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1231 (all Xs_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,nil_Ar126264853le_alt),Xs_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> Xs_1 = nil_Ar126264853le_alt)) # label(fact_529_listrel__Nil1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1232 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_2)),hAPP_P1861769507t_bool(B_1,X_2))) -> -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),A_1))))) # label(fact_49_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1233 (all Xs_1 hAPP_l726444215le_alt(list_c380068407le_alt(nil_Ar126264853le_alt,hAPP_f1777336662le_alt(hAPP_f939319677le_alt(cOMBB_881934114le_alt,hAPP_f1294513379le_alt(cOMBC_1058495865le_alt,append1166636842le_alt)),hAPP_l618618165le_alt(hAPP_f657005563le_alt(cOMBC_1919297930le_alt,cons_A1216297413le_alt),nil_Ar126264853le_alt))),Xs_1) = hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_1)) # label(fact_441_rotate1__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1234 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_2)),hAPP_f5761716t_bool(B_1,X_2))) -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1))))) # label(fact_82_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1235 (all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(rotate1322903650le_alt,Xs_1))) <-> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)))) # label(fact_462_distinct1__rotate) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1236 (all Pa all Q_1 all X_1 (hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,hAPP_f825175477t_bool(hAPP_f57507985t_bool(cOMBB_1171600517le_alt,hAPP_f27970449t_bool(cOMBB_2104979073le_alt,fconj(Pa))),Q_1)),X_1)) <-> hBOOL(Pa) & hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,Q_1),X_1)))) # label(fact_572_split__part) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1237 (all B_1_1 all B_2_1 is_fun1393352280t_bool(hAPP_f1457563459t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___029) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1238 (all P all Q P = hAPP_f1593910865t_bool(hAPP_f1362748656t_bool(cOMBK_208474378t_bool,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__143) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1239 (all X_2 all Xs_1 (hBOOL(hAPP_l1795316048t_bool(distin856461956le_alt,Xs_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(cons_P993230855le_alt,X_2),hAPP_l1766111573le_alt(rev_Pr295966039le_alt,hAPP_l1766111573le_alt(takeWh1529274110le_alt(hAPP_f515126293t_bool(hAPP_f600409331t_bool(cOMBB_433601099le_alt,fNot),hAPP_P1267694911t_bool(hAPP_f135580393t_bool(cOMBC_607108822t_bool,fequal454353832le_alt),X_2))),Xs_1))) = hAPP_l1766111573le_alt(dropWh1907450966le_alt(hAPP_f515126293t_bool(hAPP_f600409331t_bool(cOMBB_433601099le_alt,fNot),hAPP_P1267694911t_bool(hAPP_f135580393t_bool(cOMBC_607108822t_bool,fequal454353832le_alt),X_2))),hAPP_l1766111573le_alt(rev_Pr295966039le_alt,Xs_1))))) # label(fact_658_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1240 (all B_1_1 all B_2_1 (is_fun288122577l_bool(B_2_1) -> is_fun288122577l_bool(hAPP_f146009813l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_046) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1241 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_1)),hAPP_f5761716t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,B_1))))) # label(fact_195_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1242 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> (exists Ys exists Zs (Xs_1 = hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs)) & -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Zs))))))) # label(fact_877_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1243 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_fun760276937t_bool(X_1) & is_fun760276937t_bool(Y_9) & is_fun760276937t_bool(Z_4) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),set_fu1865467835t_bool(Xs_1))) -> (hBOOL(hAPP_f1806001137l_bool(hAPP_P1971325577l_bool(member739461844t_bool,hAPP_f1886133174t_bool(hAPP_f541777673t_bool(produc586224093t_bool,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f1806001137l_bool(hAPP_P1971325577l_bool(member739461844t_bool,hAPP_f1886133174t_bool(hAPP_f541777673t_bool(produc586224093t_bool,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f1806001137l_bool(hAPP_P1971325577l_bool(member739461844t_bool,hAPP_f1886133174t_bool(hAPP_f541777673t_bool(produc586224093t_bool,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f1111021425l_bool(hAPP_P215277193l_bool(member307575252t_bool,hAPP_l1347264831t_bool(hAPP_l1242990405t_bool(produc966439767t_bool,Xs_1),Ys_1)),hAPP_f2045380501l_bool(lexord2016448367t_bool,R_2))) -> (hBOOL(hAPP_f1111021425l_bool(hAPP_P215277193l_bool(member307575252t_bool,hAPP_l1347264831t_bool(hAPP_l1242990405t_bool(produc966439767t_bool,Ys_1),Zs_1)),hAPP_f2045380501l_bool(lexord2016448367t_bool,R_2))) -> hBOOL(hAPP_f1111021425l_bool(hAPP_P215277193l_bool(member307575252t_bool,hAPP_l1347264831t_bool(hAPP_l1242990405t_bool(produc966439767t_bool,Xs_1),Zs_1)),hAPP_f2045380501l_bool(lexord2016448367t_bool,R_2))))))) # label(fact_789_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1244 (all X all Y (-hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(fequal796301787le_alt,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1245 (all F all B_1 all A_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f53317332le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f236193164l_bool(hAPP_f652666381l_bool(member1535903113le_alt,F),pi_fun90241866le_alt(A_1,hAPP_f14382104t_bool(cOMBK_1914291077t_bool,B_1)))))) # label(fact_236_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1246 (all I_1 all Fa (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Fa),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) -> ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) -> (all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> (B_6 != A_7 -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_A1677245848t_bool(X_1,I_1))) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6)),hAPP_f412050202t_bool(Fa,X_1)))))))))) -> hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I_1))))) # label(fact_46_dictatorI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1247 (all Pa all Xs_1 ((exists X_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) & hBOOL(hAPP_A862370221t_bool(Pa,X_1)))) -> (exists Ys exists X_1 exists Zs (is_Arr1861959080le_alt(X_1) & hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs)) = Xs_1 & (all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),set_Ar1565008694le_alt(Zs))) -> -hBOOL(hAPP_A862370221t_bool(Pa,Xa)))) & hBOOL(hAPP_A862370221t_bool(Pa,X_1)))))) # label(fact_907_split__list__last__prop) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1248 (all B_1_1 is_fun1097062475t_bool(hd_fun191074571t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpu) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1249 (all B_1_1 all B_2_1 (is_fun2093718614t_bool(B_1_1) & is_Arr1861959080le_alt(B_2_1) -> is_fun1393352280t_bool(hAPP_A1664620203t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1250 (all X_2 all Xs_1 ((exists Ys exists Zs (hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Zs))))) <-> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))))) # label(fact_823_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1251 (all X_2 hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2))) # label(fact_347_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1252 (all X_2 (hBOOL(top_top_bool) <-> hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2)))) # label(fact_383_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1253 (all X_2 all Xs_1 ((hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> Xs_1 = hAPP_l54953109e_indi(hAPP_A974963564e_indi(insert915800584e_indi,X_2),Xs_1)) & (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) -> hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Xs_1) = hAPP_l54953109e_indi(hAPP_A974963564e_indi(insert915800584e_indi,X_2),Xs_1)))) # label(fact_765_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1254 (all P all Q (is_fun279392540l_bool(P) -> P = hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_139) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1255 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_1),B_1)) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),B_1))))) # label(fact_912_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1256 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,B_1)))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),B_1))))) # label(fact_104_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1257 (all Ys_5 all Xs_19 ((Xs_19 != nil_Ar126264853le_alt -> hd_Arr805754088le_alt(Xs_19) = hd_Arr805754088le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_19),Ys_5))) & (Xs_19 = nil_Ar126264853le_alt -> hd_Arr805754088le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_19),Ys_5)) = hd_Arr805754088le_alt(Ys_5)))) # label(fact_587_hd__append) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1258 (all Xs_52 all X_38 hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_38),Xs_52) != Xs_52) # label(fact_44_not__Cons__self) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1259 (all X all Y (is_Arr43961803e_indi(X) & is_Arr43961803e_indi(Y) -> -hBOOL(hAPP_A1785763630i_bool(hAPP_A313542399i_bool(fequal1196706959e_indi,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1260 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,hAPP_f589776703l_bool(cOMBK_1638246986le_alt,B_1)))))) # label(fact_252_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1261 (all B_1_1 all B_2_1 is_bool(hAPP_f1098788115l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1262 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),hAPP_A60074736l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,B_1))))) # label(fact_220_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1263 (all X all Y (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(fequal1258273448t_bool,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1264 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A_1,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,B_1)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),B_1))))) # label(fact_108_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1265 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_2)),hAPP_f1663053423t_bool(B_1,X_2)))))) # label(fact_151_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1266 (all F (is_fun961089132t_bool(F) -> F = hAPP_f791205069t_bool(produc2022255647t_bool,produc212588606t_bool(F)))) # label(fact_495_split__curry) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1267 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B_1,X_2))) -> -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1))))) # label(fact_80_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1268 (all P all Q (is_fun158382675l_bool(P) -> hAPP_A366518464l_bool(hAPP_f1874082285l_bool(cOMBK_1778599651le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_148) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1269 (all F all B_1 all A_1 ((all X_1 (is_Arr43961803e_indi(X_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),hAPP_A1952883197l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A_1,B_1))))) # label(fact_289_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1270 (all Xs_1 all Pa (hBOOL(hAPP_l1386638586t_bool(Pa,nil_Ar126264853le_alt)) -> ((all X_1 all Xs_17 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_l1386638586t_bool(Pa,Xs_17)) -> hBOOL(hAPP_l1386638586t_bool(Pa,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_17),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt))))))) -> hBOOL(hAPP_l1386638586t_bool(Pa,Xs_1))))) # label(fact_437_rev__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1271 (all Xs_1 all Ys_1 (Xs_1 = Ys_1 <-> hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Ys_1))) # label(fact_600_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1272 (all X_2 hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2))) # label(fact_348_top1I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1273 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f68732431l_bool(hAPP_f1556434125l_bool(member1366121996le_alt,F),pi_fun1792636103le_alt(A_1,hAPP_f420098683t_bool(cOMBK_964928722t_bool,B_1)))) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f1054274129le_alt(F,X_2)),B_1))))) # label(fact_102_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1274 (all As (As != nil_fu1891063196t_bool -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,last_f1417039043t_bool(As)),set_fu1865467835t_bool(As))))) # label(fact_732_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1275 (all As (As != nil_Ar1968865438e_indi -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,last_A1892550853e_indi(As)),set_Ar219761597e_indi(As))))) # label(fact_728_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1276 (all Z_3 all Ca all P_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_P1606644490l_bool(hAPP_f2122673039l_bool(produc2129949100l_bool,Ca),P_1))) -> -(all X_1 all Y_9 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Z_3),hAPP_l1661879987l_bool(hAPP_l1824974724l_bool(Ca,X_1),Y_9))))))) # label(fact_571_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1277 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_P1711233733t_bool(hAPP_f1708325453t_bool(produc315582749t_bool,Ca),P_1))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Z_3),hAPP_A1664620203t_bool(hAPP_A210478249t_bool(Ca,X_1),Y_9))))))))) # label(fact_565_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1278 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,B_1))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_2)),hAPP_P1711233733t_bool(B_1,X_2)))))) # label(fact_142_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1279 (all M all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(plus_plus_nat(M),J))))) # label(fact_1077_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1280 (all X_2 all Xs_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Xs_1))) <-> (exists Ys exists Zs (Xs_1 = hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Ys),hAPP_l1075146559t_bool(hAPP_f613335309t_bool(cons_f1416466313t_bool,X_2),Zs)) & -hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),set_fu1384968698t_bool(Zs))))))) # label(fact_825_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1281 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),set_fu335223357t_bool(L_1))) -> (hBOOL(hAPP_f312250286l_bool(Q_1,X_1)) <-> hBOOL(hAPP_f312250286l_bool(Pa,X_1)))))) -> hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),L_1) = hAPP_l210315413t_bool(takeWh169821797t_bool(Q_1),K)))) # label(fact_851_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1282 (all X_2 all Xs_1 (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))) <-> (exists Ys exists Zs (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Ys))) & Xs_1 = hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs)))))) # label(fact_813_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1283 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N)))) # label(fact_1004_lessI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1284 (all N hAPP_nat_nat(plus_plus_nat(one_one_nat),N) = hAPP_nat_nat(suc,N)) # label(fact_1194_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption]. 2.20/2.72 1285 (all Aa (is_fun279392540l_bool(Aa) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa)) -> Aa = top_to1853035173l_bool))) # label(fact_999_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1286 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_2)),hAPP_f1628730575t_bool(B_1,X_2)))))) # label(fact_144_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1287 (all B_1_1 all B_2_1 is_bool(hAPP_f785974231l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_044) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1288 (all N_2 all Pa (hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,N_1)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))))) -> hBOOL(hAPP_nat_bool(Pa,N_2))))) # label(fact_1186_nat__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1289 (all F all B_1 all A_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A_1)) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),B_1))))) -> hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A_1,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,B_1)))))) # label(fact_233_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1290 (all X_9 all Y_8 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9)))) # label(fact_932_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1291 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),transi992120749le_alt(R_2))) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ba),Ca)),transi992120749le_alt(R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ca)),transi992120749le_alt(R_2)))))) # label(fact_639_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1292 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,B_1))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_2)),hAPP_A1928120382l_bool(B_1,X_2)))))) # label(fact_166_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1293 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),hAPP_b1048178734l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,B_1))))) # label(fact_290_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1294 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (N != hAPP_nat_nat(suc,M) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))))) # label(fact_1027_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1295 (all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> (exists K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) & J = hAPP_nat_nat(plus_plus_nat(I_2),K_1))))) # label(fact_1180_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1296 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2))) <-> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1033_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1297 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun279392540l_bool(hAPP_A60074736l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_015) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1298 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,hAPP_f1879785608l_bool(cOMBK_2131602312ol_nat,B_1)))))) # label(fact_254_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1299 (all R_1 all S_1 (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1))) <-> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)))) # label(fact_927_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1300 (all P all Q all R hAPP_f592646513l_bool(hAPP_A187815023l_bool(P,R),Q) = hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_112) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1301 (all X all Y (-hBOOL(hAPP_P1327827171t_bool(hAPP_P163071551t_bool(fequal673514820le_alt,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1302 (all I_11 all X_22 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(I_11),X_22)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_22),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_22),hAPP_A832564074le_alt(replic351609551le_alt(I_11),X_22))) # label(fact_580_replicate__append__same) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1303 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> ((all A_7 all B_6 (is_Arr1861959080le_alt(B_6) & is_Arr1861959080le_alt(A_7) -> (P_1 = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_7),B_6) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_A1862272720t_bool(hAPP_A1470764750t_bool(Ca,A_7),B_6)))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_3),hAPP_P2136891882t_bool(hAPP_f1984771213t_bool(produc1527919682t_bool,Ca),P_1)))))) # label(fact_554_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1304 (all X_2 all Xs_1 (hBOOL(hAPP_l1795316048t_bool(distin856461956le_alt,Xs_1)) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> hAPP_l1766111573le_alt(rev_Pr295966039le_alt,hAPP_l1766111573le_alt(tl_Pro12277920le_alt,hAPP_l1766111573le_alt(dropWh1907450966le_alt(hAPP_f515126293t_bool(hAPP_f600409331t_bool(cOMBB_433601099le_alt,fNot),hAPP_P1267694911t_bool(hAPP_f135580393t_bool(cOMBC_607108822t_bool,fequal454353832le_alt),X_2))),Xs_1))) = hAPP_l1766111573le_alt(takeWh1529274110le_alt(hAPP_f515126293t_bool(hAPP_f600409331t_bool(cOMBB_433601099le_alt,fNot),hAPP_P1267694911t_bool(hAPP_f135580393t_bool(cOMBC_607108822t_bool,fequal454353832le_alt),X_2))),hAPP_l1766111573le_alt(rev_Pr295966039le_alt,Xs_1))))) # label(fact_649_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1305 (all B_1_1 all B_2_1 is_bool(hAPP_l982832318l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1306 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A1159885342t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f196630486l_bool(hAPP_f1212866771l_bool(member392258873t_bool,F),pi_Arr44017448t_bool(A_1,hAPP_f1874082285l_bool(cOMBK_1778599651le_alt,B_1)))))) # label(fact_256_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1307 (all Xs_1 (Xs_1 != nil_Ar1968865438e_indi -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hd_Arr465110667e_indi(Xs_1)),set_Ar219761597e_indi(Xs_1))))) # label(fact_747_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1308 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),set_Ar1565008694le_alt(Xs_1))) -> hBOOL(hAPP_A862370221t_bool(Pa,X_1))))) -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),Ys_1)) = hAPP_l726444215le_alt(takeWh536362254le_alt(Pa),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1)))) # label(fact_801_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1309 (all Q_1 all Pa all L_1 all K (K = L_1 -> ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),set_Pr604701398le_alt(L_1))) -> (hBOOL(hAPP_P606313927t_bool(Pa,X_1)) <-> hBOOL(hAPP_P606313927t_bool(Q_1,X_1)))))) -> hAPP_l1766111573le_alt(dropWh1907450966le_alt(Q_1),K) = hAPP_l1766111573le_alt(dropWh1907450966le_alt(Pa),L_1)))) # label(fact_845_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1310 (all X_2 all Pa all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(takeWhile_nat(Pa),Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) & hBOOL(hAPP_nat_bool(Pa,X_2)))) # label(fact_679_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1311 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1312 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f1418366331ol_nat(F,X_1)),hAPP_f1628730575t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1534526009l_bool(hAPP_f2069145881l_bool(member1258861596ol_nat,F),pi_fun770049925ol_nat(A_1,B_1))))) # label(fact_266_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1313 (all X_37 all Xs_51 all Y_14 all Ys_20 hAPP_l726444215le_alt(splice360969192le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_37),Xs_51)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_14),Ys_20)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_37),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_14),hAPP_l726444215le_alt(splice360969192le_alt(Xs_51),Ys_20)))) # label(fact_136_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1314 (all P all Q (hBOOL(Q) | -hBOOL(hAPP_bool_bool(fconj(P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1315 (all B_1_1 all B_2_1 is_bool(hAPP_f263022001l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Ol) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1316 (all X_3 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_3)))) # label(fact_971_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1317 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> M != N)) # label(fact_1015_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1318 (all Aa (is_fun158382675l_bool(Aa) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa)) -> Aa = top_to1714702858l_bool))) # label(fact_1000_top__le) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1319 (all Ca all Aa all Ba all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba)),R_2)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Ba),Ca)),transi992120749le_alt(R_2))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ca)),transi992120749le_alt(R_2)))))) # label(fact_635_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1320 (all X_2 all Xs_1 ((exists Ys exists Zs hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) = Xs_1) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))))) # label(fact_828_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1321 (all K_2 all M all N hAPP_nat_nat(minus_minus_nat(M),N) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K_2),M)),hAPP_nat_nat(plus_plus_nat(K_2),N))) # label(fact_1106_diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1322 (all P all Q all R hAPP_f592646513l_bool(hAPP_P229966473l_bool(P,R),Q) = hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__123) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1323 (all Xs_1 all X_2 all Ys_1 all Y_2 all R_2 (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))) & Y_2 = X_2 | Xs_1 = Ys_1 & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)) <-> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Xs_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),nil_li1922300522le_alt))),hAPP_l1891879573le_alt(hAPP_l1570526551le_alt(append1181015317le_alt,Ys_1),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),nil_li1922300522le_alt)))),hAPP_f1662382841t_bool(listre635569361le_alt,R_2))))) # label(fact_439_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1324 (all X_2 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Ys_1))),transi992120749le_alt(hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))))) # label(fact_626_rtrancl__listrel1__ConsI1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1325 (all X_2 all Xs_1 (-hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> hAPP_l210315413t_bool(hAPP_f1812326636t_bool(insert1946138248t_bool,X_2),Xs_1) = hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Xs_1))) # label(fact_776_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1326 (all Y_13 -(all A_7 all B_6 Y_13 != hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6))) # label(fact_308_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1327 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_2),Xs_1) = Xs_1)) # label(fact_698_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1328 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A_1,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,B_1)))))) # label(fact_249_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1329 (all Ys_6 all Xs_23 (nil_Ar126264853le_alt != Xs_23 -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Xs_23)),Ys_6) = hAPP_l726444215le_alt(tl_Arr1453005548le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_23),Ys_6)))) # label(fact_540_tl__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1330 (all X_2 all Xs_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),set_fu1865467835t_bool(Xs_1))) <-> (exists Ys exists Zs Xs_1 = hAPP_l1660244757t_bool(hAPP_l776124325t_bool(append1995644103t_bool,Ys),hAPP_l1660244757t_bool(hAPP_f726713198t_bool(cons_f1803648492t_bool,X_2),Zs))))) # label(fact_835_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1331 (all Z_3 all Ca all P_1 (is_Pro1725146340le_alt(P_1) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_P1875867302i_bool(hAPP_f1425186181i_bool(produc89849422i_bool,Ca),P_1))) -> -(all X_1 all Y_9 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_9) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Y_9) = P_1 -> -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_A2091627584i_bool(hAPP_A1965262040i_bool(Ca,X_1),Y_9))))))))) # label(fact_566_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1332 (all F all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(produc212588606t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P606313927t_bool(F,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_333_curryD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1333 (all P all Q (is_fun961089132t_bool(P) -> P = hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_111) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1334 (all Ca all P_1 all Q_2 (Q_2 = P_1 -> hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,Ca),P_1) = hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,Ca),Q_2))) # label(fact_485_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1335 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun_bool_bool(hAPP_b589554111l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1336 (all Ys_4 all Xs_18 (nil_Ar126264853le_alt != Xs_18 -> hd_Arr805754088le_alt(Xs_18) = hd_Arr805754088le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_18),Ys_4)))) # label(fact_588_hd__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1337 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2))) <-> N_2 = M_2))) # label(fact_1051_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1338 (all Y_2 all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Y_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Xs_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Y_2),set_Pr1404309362le_alt(Xs_1))) | X_2 = Y_2)) # label(fact_661_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1339 (all P all Q all R hAPP_l489874441le_alt(hAPP_f1318121625le_alt(hAPP_f634775919le_alt(cOMBB_576205818le_alt,P),Q),R) = hAPP_f1349184697le_alt(P,hAPP_l1869074853le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_161) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1340 (all B_1_1 all B_2_1 is_fun279392540l_bool(hAPP_l1542188220l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa_022) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1341 (all X all Y (Y != X | hBOOL(hAPP_A1785763630i_bool(hAPP_A313542399i_bool(fequal1196706959e_indi,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1342 (all P all Q all R hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f152453811l_bool(cOMBB_1459698610t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f312250286l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1343 (all Q_1 all Pa all L_1 all K (L_1 = K -> ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),set_Pr1404309362le_alt(L_1))) -> (hBOOL(hAPP_P1327827171t_bool(Pa,X_1)) <-> hBOOL(hAPP_P1327827171t_bool(Q_1,X_1))))) -> hAPP_l1493873365le_alt(takeWh416411546le_alt(Q_1),K) = hAPP_l1493873365le_alt(takeWh416411546le_alt(Pa),L_1)))) # label(fact_848_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1344 (all Xs_35 all Ys_11 ((Ys_11 != nil_Ar126264853le_alt -> hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_35),Ys_11)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_35),hAPP_l726444215le_alt(butlas1262502241le_alt,Ys_11))) & (Ys_11 = nil_Ar126264853le_alt -> hAPP_l726444215le_alt(butlas1262502241le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_35),Ys_11)) = hAPP_l726444215le_alt(butlas1262502241le_alt,Xs_35)))) # label(fact_415_butlast__append) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1345 (all N zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N),zero_zero_nat)) # label(fact_1113_min__0R) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1346 (all K all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K),M_2)),hAPP_nat_nat(plus_plus_nat(K),N_2))))) # label(fact_1067_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1347 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun288122577l_bool(hAPP_b1048178734l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1348 (all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Ys_1)),hAPP_f1865483825t_bool(listre760726333le_alt,R_2))) -> hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_1))) # label(fact_531_listrel__eq__len) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1349 (all P all Q all R hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f356431923l_bool(cOMBB_871930928t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f965095724l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Arrow__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1350 (all Xs_1 (nil_Ar126264853le_alt = Xs_1 <-> nil_Ar126264853le_alt = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1))) # label(fact_606_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1351 (all Xs_1 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,Xs_1),nil_Ar126264853le_alt)) <-> hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs_1)))) # label(fact_389_equal__Nil__null) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1352 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1353 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_1),B_1)) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B_1))))) # label(fact_967_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1354 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,hAPP_f393984045t_bool(cOMBK_673344138le_alt,B_1)))))) # label(fact_242_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1355 (all Zs_1 all Ys_1 all R_2 all Xs_1 ((all X_1 all Y_9 all Z_4 (is_bool(X_1) & is_bool(Z_4) & is_bool(Y_9) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1))) -> (hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_1),Y_9)),R_2)) -> (hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,Y_9),Z_4)),R_2)) -> hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_1),Z_4)),R_2))))))) -> (hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs_1),Ys_1)),hAPP_f1114274611l_bool(lexord_bool,R_2))) -> (hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Ys_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_2))) -> hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_2))))))) # label(fact_786_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1356 (all P all Q (is_bool(P) -> P = hAPP_A862370221t_bool(hAPP_b30302907t_bool(cOMBK_1646462604le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1357 (all B_1_1 is_fun279392540l_bool(set_fu1384968698t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnb) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1358 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2835579l_bool(hAPP_f1229756829l_bool(member379339614t_bool,F),pi_nat955432909t_bool(A_1,hAPP_f1879785608l_bool(cOMBK_2131602312ol_nat,B_1)))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_n291670979t_bool(F,X_2)),B_1))))) # label(fact_124_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1359 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A_1),B_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),B_1))))) # label(fact_949_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1360 (all F all Aa all Ba (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(produc231070560t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1327827171t_bool(F,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))))) # label(fact_332_curryD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1361 (all As (nil_Ar126264853le_alt != As -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,last_A57386030le_alt(As)),set_Ar1565008694le_alt(As))))) # label(fact_725_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1362 (all F hAPP_f1078809103le_alt(produc748227559le_alt,hAPP_f746471349le_alt(hAPP_f1532338415le_alt(cOMBB_2017209238le_alt,hAPP_f500394983le_alt(cOMBB_500037706le_alt,F)),produc237774329le_alt)) = F) # label(fact_493_split__eta) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1363 (all Pa all Xs_1 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_1)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(dropWh156852662le_alt(Pa),Xs_1))))) # label(fact_492_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1364 (all B_1_1 all B_2_1 is_bool(hAPP_f307807922l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__fun_Itc__prod_Itc__Arrow____O) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1365 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1525366679l_bool(hAPP_f586020557l_bool(member1055039380t_bool,F),pi_Arr1306565967t_bool(A_1,B_1))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(F,X_2)),hAPP_A187815023l_bool(B_1,X_2)))))) # label(fact_171_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1366 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A_1,hAPP_f340261009t_bool(cOMBK_545135096l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),B_1))))) # label(fact_114_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1367 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_n1965810497t_bool(F,X_1)),hAPP_n2095207769l_bool(B_1,X_1))))) -> hBOOL(hAPP_f903371257l_bool(hAPP_f1546082457l_bool(member1494731740t_bool,F),pi_nat1317494091t_bool(A_1,B_1))))) # label(fact_286_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1368 (all F all B_1 all A_1 ((all X_1 (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A1805174428t_bool(F,X_1)),hAPP_A1928120382l_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1271753300l_bool(hAPP_f1254328783l_bool(member1986685623t_bool,F),pi_Arr1600668070t_bool(A_1,B_1))))) # label(fact_206_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1369 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs_1))) -> hBOOL(hAPP_bool_bool(Pa,X_1))))) -> hAPP_l1189022293t_bool(takeWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),hAPP_l1189022293t_bool(takeWhile_bool(Pa),Ys_1)))) # label(fact_804_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1370 (all Xs_10 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_10)) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_10)) # label(fact_608_length__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1371 (all Xs_1 all Ys_1 all X_2 all Y_2 all R_2 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),R_2)) -> (hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,Xs_1),Ys_1)),hAPP_f1662382841t_bool(listre638180162le_alt,R_2))) -> hBOOL(hAPP_f1757554033l_bool(hAPP_P753566857l_bool(member1208501972le_alt,hAPP_l190821901le_alt(hAPP_l1508829665le_alt(produc26555607le_alt,hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_2),Xs_1)),hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,Y_2),Ys_1))),hAPP_f1662382841t_bool(listre638180162le_alt,R_2)))))) # label(fact_511_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1372 (all Ys_1 all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Ys_1)))) | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(butlast_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1))))))) # label(fact_735_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1373 (all B_1_1 all B_2_1 is_fun288122577l_bool(hAPP_P139894920l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_096) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1374 (all R_2 all A1 all A2 (nil_Ar126264853le_alt = A1 & A2 = nil_Ar126264853le_alt | (exists X_1 exists Y_9 exists Xs_17 exists Ys (is_Arr1861959080le_alt(X_1) & hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(R_2,X_1),Y_9)) & hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(R_2),Xs_17),Ys)) & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_9),Ys) = A2 & A1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs_17) & is_Arr1861959080le_alt(Y_9))) <-> hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(listre53232751le_alt(R_2),A1),A2)))) # label(fact_590_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1375 (all N_2 all X_2 all Xs_1 hAPP_n1875670159le_alt(nat_ca14895078le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1),hAPP_l382792410le_alt(hAPP_f2068969285le_alt(cOMBC_1511969967le_alt,drop_A186780501le_alt),Xs_1)),N_2) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1))) # label(fact_895_drop__Cons) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1376 (all Xs_1 (Xs_1 != nil_nat -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hd_nat(Xs_1)),set_nat(Xs_1))))) # label(fact_745_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1377 (all F (is_fun2093718614t_bool(F) -> F = produc212588606t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F)))) # label(fact_497_curry__split) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1378 (all P all Q all R hAPP_P1327827171t_bool(hAPP_f1642286869t_bool(hAPP_f62793075t_bool(cOMBB_1604919143le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1327827171t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__List__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1379 (all Q_1 all Pa all Z_3 (hBOOL(hAPP_P1327827171t_bool(Q_1,hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,Pa),Z_3))) -> -(all X_1 all Y_9 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_1),Y_9) = Z_3 -> -hBOOL(hAPP_P1327827171t_bool(Q_1,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(Pa,X_1),Y_9))))))) # label(fact_504_splitE2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1380 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> T != S)) # label(fact_1016_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1381 (all P all Q all R hAPP_f1634113933l_bool(hAPP_l578398296l_bool(P,R),Q) = hAPP_l1386638586t_bool(hAPP_f318645548t_bool(hAPP_f1728064559t_bool(cOMBC_1740746827l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_121) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1382 (all X_2 all Xs_1 ((exists Ys exists Zs (hAPP_l54953109e_indi(hAPP_l367315107e_indi(append153154761e_indi,Ys),hAPP_l54953109e_indi(hAPP_A974963564e_indi(cons_A104257774e_indi,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Zs))))) <-> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),set_Ar219761597e_indi(Xs_1))))) # label(fact_822_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1383 (all B_1_1 all B_2_1 is_bool(hAPP_f859154022l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_062) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1384 (all N hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat)) # label(fact_1193_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1385 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_f666924118le_alt(F,X_1)),hAPP_f228695594t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f899439636l_bool(hAPP_f2103233871l_bool(member1620122743le_alt,F),pi_fun462417760le_alt(A_1,B_1))))) # label(fact_186_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1386 (all X_2 all Xs_1 ((-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),Xs_1)) & (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1) = Xs_1))) # label(fact_766_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1387 (all A_1 (is_fun158382675l_bool(A_1) -> ((all X_1 (is_fun1097062475t_bool(X_1) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A_1)))) -> top_to1714702858l_bool = A_1))) # label(fact_460_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1388 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))))) # label(fact_1005_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1389 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun760276937t_bool(hAPP_f329301088t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___082) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1390 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M)) # label(fact_1159_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1391 (all Z_3 all Ca all Aa all Ba (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_A2091627584i_bool(hAPP_A1965262040i_bool(Ca,Aa),Ba))) -> hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Z_3),hAPP_P1875867302i_bool(hAPP_f1425186181i_bool(produc89849422i_bool,Ca),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)))))) # label(fact_522_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1392 (all P all Q (is_bool(P) -> P = hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn_102) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1393 (all X_31 all Xs_44 (is_Arr1861959080le_alt(X_31) -> (Xs_44 = nil_Ar126264853le_alt -> X_31 = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_31),Xs_44))))) # label(fact_357_last__ConsL) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1394 (all X_2 all Xs_1 ((exists Ys exists Zs (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Ys))) & Xs_1 = hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs)))) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))))) # label(fact_812_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1395 (all P all Q (is_fun279392540l_bool(P) -> hAPP_A187815023l_bool(hAPP_f589776703l_bool(cOMBK_1638246986le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_114) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1396 (all Xs_1 all R_2 -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),nil_Ar126264853le_alt)),hAPP_f1865483825t_bool(listre904073838le_alt,R_2)))) # label(fact_464_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1397 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N_2),Xs_1)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))))) # label(fact_673_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1398 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_1)),B_1))))) -> hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,hAPP_f880868799t_bool(cOMBK_1550261278le_alt,B_1)))))) # label(fact_222_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1399 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A_1),B_1)) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B_1))))) # label(fact_945_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1400 (all P all Q (is_bool(P) -> P = hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1401 (all I_1 all J_2 all F ((all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2)))))) # label(fact_1055_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1402 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A_1),B_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B_1))))) # label(fact_965_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1403 (all B_1_1 all B_2_1 is_bool(hAPP_f2835579l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__fun_Itc__fun_Itc__Arrow____Or) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1404 (all B_1_1 all B_2_1 is_bool(hAPP_f1790426673l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1405 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P339823136lt_nat(F,X_1)),B_1))))) -> hBOOL(hAPP_f2042909150l_bool(hAPP_f1073701219l_bool(member547554753lt_nat,F),pi_Pro264071722lt_nat(A_1,hAPP_f1809347209t_bool(cOMBK_1632198563le_alt,B_1)))))) # label(fact_221_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1406 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> (exists Ys exists Zs (hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs)) = Xs_1 & -hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Ys))))))) # label(fact_867_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1407 (all P all Q all R hAPP_f1663053423t_bool(hAPP_A572596845t_bool(P,R),Q) = hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_122) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1408 (all Nat hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat))) # label(fact_1189_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1409 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,A_1),B_1)) -> (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Ca),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,Ca),B_1))))) # label(fact_911_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1410 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B_1,X_2))) -> -hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1))))) # label(fact_70_PiE) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1411 (all B_1_1 all B_2_1 is_bool(hAPP_f1725204053l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_055) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1412 (all X_2 (hBOOL(top_top_bool) <-> hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2)))) # label(fact_382_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1413 (all B_1_1 all B_2_1 is_fun279392540l_bool(hAPP_P1905961381l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_099) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1414 (all P all Q all R hAPP_A862370221t_bool(hAPP_A1664620203t_bool(P,R),Q) = hAPP_A862370221t_bool(hAPP_A1664620203t_bool(hAPP_f825175477t_bool(cOMBC_1628726426t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1415 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_fun760276937t_bool(hAPP_A1805174428t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_004) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1416 (exists X_1 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),top_to772840767t_bool))) # label(fact_444_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1417 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun961089132t_bool(X_1) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),set_fu1384968698t_bool(Xs_1))) -> hBOOL(hAPP_f592646513l_bool(Pa,X_1))))) -> hAPP_l1075146559t_bool(dropWh1133555834t_bool(Pa),Ys_1) = hAPP_l1075146559t_bool(dropWh1133555834t_bool(Pa),hAPP_l1075146559t_bool(hAPP_l265951104t_bool(append923785710t_bool,Xs_1),Ys_1)))) # label(fact_797_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1418 (all X_19 all Xs_21 (is_Arr1861959080le_alt(X_19) -> hd_Arr805754088le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_19),Xs_21)) = X_19)) # label(fact_583_hd_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1419 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,B_1))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_2)),hAPP_f996881846t_bool(B_1,X_2)))))) # label(fact_145_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1420 (all X_2 all Y_2 all L_2 (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Y_2) -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> (Y_2 != X_2 -> (-hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_2)) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),X_2)),L_2))))))) # label(fact_30_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1421 (all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> Xs_1 = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_2),Xs_1))) # label(fact_702_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1422 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_n588788980t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f307807922l_bool(hAPP_f491986957l_bool(member107042095t_bool,F),pi_nat1370421354t_bool(A_1,hAPP_f11902820l_bool(cOMBK_39620975ol_nat,B_1)))))) # label(fact_250_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1423 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f2017347493l_bool(hAPP_f137298509l_bool(member1567747746le_alt,F),pi_Pro2035602019le_alt(A_1,hAPP_f880868799t_bool(cOMBK_1550261278le_alt,B_1)))) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_P1095651821le_alt(F,X_2)),B_1))))) # label(fact_92_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1424 (all M all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(M),N)) # label(fact_1142_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1425 (all Xs_38 all Zs_2 all X_28 all Xs1 all Ys_15 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_28),Xs1) = Ys_15 -> (Xs_38 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs1),Zs_2) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_28),Xs_38) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_15),Zs_2)))) # label(fact_400_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1426 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P1699981037le_alt(F,X_1)),B_1)))) -> hBOOL(hAPP_f1468796453l_bool(hAPP_f1867424333l_bool(member290075938le_alt,F),pi_Pro492447587le_alt(A_1,hAPP_f1783828715t_bool(cOMBK_1901607710le_alt,B_1)))))) # label(fact_241_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1427 (all Z_3 all Ca all P_1 ((all A_7 all B_6 (hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,A_7),B_6) = P_1 -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_l1542188220l_bool(hAPP_l1352613953l_bool(Ca,A_7),B_6))))) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Z_3),hAPP_P1905961381l_bool(hAPP_f786857743l_bool(produc1170920579l_bool,Ca),P_1))))) # label(fact_561_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1428 (all X_2 all Xs_1 (hBOOL(hAPP_l2060223415l_bool(distin1991771627t_bool,Xs_1)) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),hAPP_l210315413t_bool(rev_fu1629171390t_bool,hAPP_l210315413t_bool(takeWh169821797t_bool(hAPP_f1765205l_bool(hAPP_f152453811l_bool(cOMBB_1459698610t_bool,fNot),hAPP_f1577576703l_bool(hAPP_f1556356969l_bool(cOMBC_1576836772l_bool,fequal1596628751t_bool),X_2))),Xs_1))) = hAPP_l210315413t_bool(dropWh23362493t_bool(hAPP_f1765205l_bool(hAPP_f152453811l_bool(cOMBB_1459698610t_bool,fNot),hAPP_f1577576703l_bool(hAPP_f1556356969l_bool(cOMBC_1576836772l_bool,fequal1596628751t_bool),X_2))),hAPP_l210315413t_bool(rev_fu1629171390t_bool,Xs_1))))) # label(fact_655_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1429 (all B_1_1 all B_2_1 is_bool(hAPP_f1919691607l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Oli) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1430 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))))) # label(fact_1132_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1431 (all P all Q (is_fun1236654035i_bool(P) -> P = hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___127) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1432 (all L_2 all X_2 all Y_2 (is_Arr1861959080le_alt(X_2) & is_Arr1861959080le_alt(Y_2) -> (X_2 != Y_2 -> (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(arrow_230821333_above(L_2,X_2),Y_2)),arrow_1681063817le_Lin)))))) # label(fact_45_above__Lin) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1433 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) | hAPP_nat_nat(suc,N_2) = M_2)) # label(fact_1036_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1434 (all B_1_1 all B_2_1 (is_fun1393352280t_bool(B_2_1) -> is_bool(hAPP_f2013399995l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1435 (all X_2 (hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_386_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1436 (all X_2 all Xs_1 (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),set_fu335223357t_bool(Xs_1))) -> (exists Ys exists Zs hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Ys),hAPP_l210315413t_bool(hAPP_f1812326636t_bool(cons_f14678382t_bool,X_2),Zs)) = Xs_1))) # label(fact_888_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1437 (all Xs_16 (nil_Ar126264853le_alt != Xs_16 -> last_A57386030le_alt(hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_16)) = hd_Arr805754088le_alt(Xs_16))) # label(fact_591_last__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1438 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_1138_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1439 (all P all Q all R hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,P),Q),R) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_163) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1440 (all X_2 all Y_2 all R_2 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Y_2) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,X_2) & hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),hAPP_f1865483825t_bool(lexord1945649794le_alt,R_2))) <-> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,X_2),Y_2)),hAPP_f1865483825t_bool(lex_Ar255587961le_alt,R_2))))) # label(fact_541_lexord__lex) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1441 (all B_1_1 all B_2_1 is_bool(hAPP_f969456697l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1442 (all Xs_32 all Ys_8 ((Ys_8 = nil_Ar126264853le_alt -> last_A57386030le_alt(Xs_32) = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_32),Ys_8))) & (nil_Ar126264853le_alt != Ys_8 -> last_A57386030le_alt(Ys_8) = last_A57386030le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_32),Ys_8))))) # label(fact_418_last__append) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1443 (all Xs_1 all Ys_1 (Xs_1 = hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Ys_1) <-> hAPP_l726444215le_alt(rev_Ar2093961333le_alt,Xs_1) = Ys_1)) # label(fact_601_rev__swap) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1444 (all Ys_1 all Zs_1 all X_2 all Xs_1 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_1),Zs_1) <-> (exists Ys_12 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_12),Zs_1) = Xs_1 & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Ys_12) = Ys_1)) | hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1) = Zs_1 & nil_Ar126264853le_alt = Ys_1)) # label(fact_412_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1445 (all X all Y Y = hAPP_P1056860425le_alt(hAPP_P864444517le_alt(if_Pro1306781203le_alt(fFalse),X),Y)) # label(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1446 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,B_1)))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),B_1))))) # label(fact_113_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1447 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B_1,X_2)))))) # label(fact_172_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1448 (all X all Y (is_bool(X) & is_bool(Y) -> -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.73 1449 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2))))) # label(fact_1031_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1450 (all F1 all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F1,Aa),Ba)) -> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F1),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_518_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1451 (all B_1 all F all G all A_1 ((all W (is_Arr43961803e_indi(W) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,W),A_1)) -> hAPP_A1677245848t_bool(G,W) = hAPP_A1677245848t_bool(F,W)))) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A_1,B_1))) <-> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,G),pi_Arr990697634t_bool(A_1,B_1)))))) # label(fact_305_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1452 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_1014_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1453 (all B_1_1 is_Arr1861959080le_alt(hd_Arr805754088le_alt(B_1_1))) # label(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1454 (all I_2 all J all K_2 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),K_2)),J) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_2),J)),K_2)) # label(fact_1147_diff__commute) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1455 (all B_1_1 all B_2_1 (is_fun760276937t_bool(B_1_1) & is_Arr43961803e_indi(B_2_1) -> is_fun961089132t_bool(hAPP_A1677245848t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_016) # label(hypothesis) # label(non_clause). [assumption]. 2.20/2.74 1456 (all I_6 all V_1 hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(nil_Ar126264853le_alt),I_6),V_1) = nil_Ar126264853le_alt) # label(fact_612_list__update_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1457 (all Aa hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),top_to522745736l_bool))) # label(fact_985_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1458 (all P (is_bool(P) -> P = fFalse | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1459 (all B_1_1 is_bool(last_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1460 (all Xs_24 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_24)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(tl_Arr1453005548le_alt,Xs_24))))) # label(fact_537_distinct__tl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1461 (all X_2 hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool))) # label(fact_372_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1462 (all As (As != nil_bool -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,last_bool(As)),set_bool(As))))) # label(fact_729_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1463 (all Ys_1 all Pa all Xs_1 ((all X_1 (is_fun1097062475t_bool(X_1) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),set_fu335223357t_bool(Xs_1))) -> hBOOL(hAPP_f312250286l_bool(Pa,X_1))))) -> hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),Ys_1)) = hAPP_l210315413t_bool(hAPP_l583487011t_bool(append381950793t_bool,Xs_1),hAPP_l210315413t_bool(takeWh169821797t_bool(Pa),Ys_1)))) # label(fact_805_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1464 (all M_2 all N_2 (hAPP_nat_nat(plus_plus_nat(M_2),N_2) = hAPP_nat_nat(suc,zero_zero_nat) <-> N_2 = hAPP_nat_nat(suc,zero_zero_nat) & zero_zero_nat = M_2 | N_2 = zero_zero_nat & M_2 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1172_one__is__add) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1465 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(hAPP_l1493873365le_alt(butlas1456493703le_alt,Xs_1)))) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))))) # label(fact_690_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1466 (all X_2 all Xs_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Xs_1))) -> (exists Ys exists Zs (-hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_2),set_Pr1404309362le_alt(Zs))) & hAPP_l1493873365le_alt(hAPP_l1686876398le_alt(append1415857790le_alt,Ys),hAPP_l1493873365le_alt(hAPP_P734992695le_alt(cons_P893004579le_alt,X_2),Zs)) = Xs_1)))) # label(fact_876_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1467 (all B_1_1 (is_bool(B_1_1) -> is_fun_bool_bool(fconj(B_1_1)))) # label(gsy_c_fconj) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1468 (all N all M M = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N)) # label(fact_1108_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1469 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_2_1) -> is_fun2093718614t_bool(hAPP_f1617919085t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___080) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1470 (all F1 all Aa all Ba hAPP_l391088160le_alt(hAPP_l1869074853le_alt(F1,Aa),Ba) = hAPP_P1056860425le_alt(hAPP_f1078809103le_alt(produc748227559le_alt,F1),hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))) # label(fact_486_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1471 (all P all Q all R hAPP_A568203993t_bool(hAPP_A1625428400t_bool(P,R),Q) = hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_120) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1472 (all X_2 all Xs_1 (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs_1)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> hAPP_l1189022293t_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),hAPP_l1189022293t_bool(rev_bool,Xs_1)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_2),hAPP_l1189022293t_bool(rev_bool,hAPP_l1189022293t_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_2))),Xs_1)))))) # label(fact_654_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1473 (all N_3 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_3),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_972_take__Nil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1474 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M))))) # label(fact_1122_diff__less) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1475 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z))))) # label(fact_1059_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1476 (all X_2 all Xs_1 (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),set_Ar1565008694le_alt(Xs_1))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_2),Xs_1) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1))) # label(fact_772_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1477 (all X_2 all Xs_1 all I_1 all V hAPP_n1875670159le_alt(nat_ca14895078le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,V),Xs_1),hAPP_f402821245le_alt(hAPP_f548810715le_alt(cOMBB_903467948lt_nat,hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2)),hAPP_A1043896845le_alt(hAPP_f1956511609le_alt(cOMBC_1697899890le_alt,list_u1050032253le_alt(Xs_1)),V))),I_1) = hAPP_A832564074le_alt(hAPP_n49391885le_alt(list_u1050032253le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_2),Xs_1)),I_1),V)) # label(fact_894_list__update_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1478 (all Ys_1 all Pa all X_2 all Xs_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs_1))) -> (-hBOOL(hAPP_bool_bool(Pa,X_2)) -> hAPP_l1189022293t_bool(dropWhile_bool(Pa),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_1),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(dropWhile_bool(Pa),Xs_1)),Ys_1)))) # label(fact_757_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1479 (all Xs_1 all Ys_1 (Xs_1 = nil_Ar126264853le_alt & nil_Ar126264853le_alt = Ys_1 <-> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1) = nil_Ar126264853le_alt)) # label(fact_402_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1480 (all B_1_1 all B_2_1 is_bool(hAPP_f117508401l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1481 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A_1),B_1)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),B_1))))) # label(fact_940_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1482 (all X_36 hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_36),nil_Ar126264853le_alt) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_36),nil_Ar126264853le_alt)) # label(fact_312_insert__Nil) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1483 (all X_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))) -> (exists Ys exists Zs hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_2),Zs)) = Xs_1))) # label(fact_883_split__list) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1484 (all B_1_1 all B_2_1 (is_Arr43961803e_indi(B_2_1) -> is_fun288122577l_bool(hAPP_A1952883197l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_012) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1485 (all B_1_1 all B_2_1 is_bool(hAPP_f2017347493l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_073) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1486 (all P all Q all R hAPP_f1749234559l_bool(hAPP_f566237389l_bool(P,R),Q) = hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_135) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1487 (all B_1_1 all B_2_1 is_bool(hAPP_f560831258l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_065) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1488 (all M all K_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K_2))))) # label(fact_1160_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1489 (all X_2 all Xs_1 (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),set_Pr604701398le_alt(Xs_1))) -> Xs_1 = hAPP_l1766111573le_alt(hAPP_P1057207891le_alt(insert256706849le_alt,X_2),Xs_1))) # label(fact_706_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1490 (all P all Q (is_fun1393352280t_bool(P) -> P = hAPP_f1663053423t_bool(hAPP_f420098683t_bool(cOMBK_964928722t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___113) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1491 (all B_1 all F all G all A_1 ((all W (is_fun760276937t_bool(W) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,W),A_1)) -> hAPP_f412050202t_bool(F,W) = hAPP_f412050202t_bool(G,W)))) -> (hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A_1,B_1))) <-> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,G),pi_fun150026276t_bool(A_1,B_1)))))) # label(fact_304_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1492 (all A_9 all List_3 nil_Ar126264853le_alt != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_9),List_3)) # label(fact_38_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1493 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1276380911l_bool(hAPP_f1868812933l_bool(member26406738le_alt,F),pi_Arr55294401le_alt(A_1,hAPP_f393984045t_bool(cOMBK_673344138le_alt,B_1)))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(F,X_2)),B_1))))) # label(fact_112_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1494 (all Pa all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hBOOL(hAPP_nat_bool(Pa,J_2)) -> ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I))) -> hBOOL(hAPP_nat_bool(Pa,I))))) -> hBOOL(hAPP_nat_bool(Pa,I_1)))))) # label(fact_1053_inc__induct) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1495 (all B_1_1 is_fun1236654035i_bool(set_Ar219761597e_indi(B_1_1))) # label(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1496 (all B_1_1 is_fun760276937t_bool(hd_fun276684937t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1497 (all F all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,X_1),A_1)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P19446482t_bool(F,X_1)),B_1)))) -> hBOOL(hAPP_f799496074l_bool(hAPP_f105614477l_bool(member2043543687t_bool,F),pi_Pro531915080t_bool(A_1,hAPP_f695414965l_bool(cOMBK_1193272835le_alt,B_1)))))) # label(fact_246_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1498 (all F all B_1 all A_1 ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),B_1))))) -> hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A_1,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,B_1)))))) # label(fact_258_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1499 (all X_2 all N_2 all Xs_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_2),Xs_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),set_nat(Xs_1))))) # label(fact_973_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1500 (all B_1_1 all B_2_1 (is_fun961089132t_bool(B_1_1) & is_Pro1725146340le_alt(B_2_1) -> is_bool(hAPP_P606313927t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__089) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1501 (all R_2 all S_2 (hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_2),S_2)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_f310455147l_bool(ord_le340789135t_bool,hAPP_f1865483825t_bool(listre904073838le_alt,R_2)),hAPP_f1865483825t_bool(listre904073838le_alt,S_2))))) # label(fact_919_listrel1__mono) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1502 (all Y_2 all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) <-> Y_2 = X_2))) # label(fact_959_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1503 (all F all B_1 all A_1 ((all X_1 (is_Pro1725146340le_alt(X_1) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_P1257947515le_alt(F,X_1)),hAPP_P1711233733t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f969456697l_bool(hAPP_f1857700889l_bool(member1549237916le_alt,F),pi_Pro610394757le_alt(A_1,B_1))))) # label(fact_264_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1504 (all A_12 all B_9 all A_11 all B_8 (is_Arr1861959080le_alt(B_9) & is_Arr1861959080le_alt(B_8) & is_Arr1861959080le_alt(A_11) & is_Arr1861959080le_alt(A_12) -> (hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_11),B_8) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_12),B_9) -> -(A_12 = A_11 -> B_9 != B_8)))) # label(fact_18_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1505 (all P all Q all R hAPP_A1785763630i_bool(hAPP_f580451669i_bool(hAPP_f712459161i_bool(cOMBC_1781321570l_bool,P),Q),R) = hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_105) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1506 (all F all B_1 all A_1 ((all X_1 (is_fun760276937t_bool(X_1) -> (hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A_1)) -> hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_f40547922le_alt(F,X_1)),hAPP_f996881846t_bool(B_1,X_1)))))) -> hBOOL(hAPP_f1976794890l_bool(hAPP_f1603005581l_bool(member1603119111le_alt,F),pi_fun553016520le_alt(A_1,B_1))))) # label(fact_185_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1507 (all Xs_1 all R_2 hBOOL(hAPP_f1634113933l_bool(hAPP_P1610428353l_bool(member1020705648le_alt,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Xs_1),Xs_1)),hAPP_f1865483825t_bool(listre760726333le_alt,transi1256616594le_alt(R_2))))) # label(fact_597_listrel__rtrancl__refl) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1508 (all N N != hAPP_nat_nat(suc,N)) # label(fact_1008_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1509 (all I_2 all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I_2),M))))) # label(fact_1094_less__add__Suc1) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1510 (all X_2 all F all A_1 all B_1 (hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A_1)) -> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B_1,X_2)))))) # label(fact_162_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1511 (all L_2 (hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin)) -> hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,L_2)),arrow_1721807329e_Prof)))) # label(fact_26_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 2.20/2.74 1512 (all Aa hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),top_to1576102282i_bool))) # label(fact_989_top__greatest) # label(axiom) # label(non_clause). [assumption]. 6.19/6.42 1513 (all B_1_1 all B_2_1 is_bool(hAPP_f1468796453l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____076) # label(axiom) # label(non_clause). [assumption]. 6.19/6.42 1514 (all F all Aa all Ba (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(produc231070560t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1327827171t_bool(F,hAPP_l391088160le_alt(hAPP_l1869074853le_alt(produc237774329le_alt,Aa),Ba))))) # label(fact_330_curryE) # label(axiom) # label(non_clause). [assumption]. 6.19/6.42 1515 (all P all Q (is_fun1236654035i_bool(P) -> P = hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___115) # label(axiom) # label(non_clause). [assumption]. 6.19/6.42 1516 (all F all Aa all Ba (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P606313927t_bool(hAPP_f791205069t_bool(produc2022255647t_bool,F),hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba))))) # label(fact_516_splitI) # label(axiom) # label(non_clause). [assumption]. 6.19/6.42 1517 -(all I (is_Arr43961803e_indi(I) -> (hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),c)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_1539419881_below,hAPP_A1677245848t_bool(p,I)),c),b))) <-> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_A1677245848t_bool(p,I)))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 6.19/6.42 6.19/6.42 ============================== end of process non-clausal formulas === 6.19/6.42 6.19/6.42 ============================== PROCESS INITIAL CLAUSES =============== 6.19/6.42 6.19/6.42 ============================== PREDICATE ELIMINATION ================= 6.19/6.42 6.19/6.42 ============================== end predicate elimination ============= 6.19/6.42 6.19/6.42 Auto_denials: (non-Horn, no changes). 6.19/6.42 6.19/6.42 Term ordering decisions: 6.19/6.42 Function symbol KB weights: member1441201108le_alt=1. produc1400112471le_alt=1. member1020705648le_alt=1. produc237774329le_alt=1. cons_A1216297413le_alt=1. nil_Ar126264853le_alt=1. append1166636842le_alt=1. member496995196t_bool=1. member760917689t_bool=1. ord_less_eq_nat=1. member520425275t_bool=1. member1071917752le_alt=1. ord_less_nat=1. suc=1. zero_zero_nat=1. member1493247163e_indi=1. member_bool=1. member_nat=1. member1208501972le_alt=1. produc26555607le_alt=1. cons_l650111674le_alt=1. listre904073838le_alt=1. produc2022255647t_bool=1. arrow_1681063817le_Lin=1. arrow_1721807329e_Prof=1. lexord1945649794le_alt=1. listre760726333le_alt=1. size_s1873794948le_alt=1. fNot=1. rev_Ar2093961333le_alt=1. listre635569361le_alt=1. distin1223878664le_alt=1. member2144312714le_alt=1. produc1593382163le_alt=1. lexord484930493le_alt=1. listre638180162le_alt=1. append153154761e_indi=1. append1995644103t_bool=1. append308931554le_alt=1. append381950793t_bool=1. append923785710t_bool=1. append_bool=1. arrow_1539419881_below=1. butlas1262502241le_alt=1. f=1. nil_li1922300522le_alt=1. top_top_bool=1. lexord1102905201e_indi=1. lexord1728804490le_alt=1. lexord2016448367t_bool=1. lexord46855665t_bool=1. lexord485014854t_bool=1. lexord_bool=1. member1058364180t_bool=1. member1385125268le_alt=1. member1457870584t_bool=1. member1461267796e_indi=1. member307575252t_bool=1. member813910868t_bool=1. produc1067887767t_bool=1. produc1256910039t_bool=1. produc1867223169t_bool=1. produc347570391e_indi=1. produc556103063le_alt=1. produc966439767t_bool=1. append1181015317le_alt=1. append1415857790le_alt=1. append_nat=1. top_to1853035173l_bool=1. member2066943042le_alt=1. produc1326092875le_alt=1. arrow_1654180089le_IIA=1. top_to1576102282i_bool=1. top_to1714702858l_bool=1. top_to2076077793t_bool=1. top_to522745736l_bool=1. produc748227559le_alt=1. top_to565915683t_bool=1. cons_bool=1. cons_A104257774e_indi=1. cons_P893004579le_alt=1. cons_P993230855le_alt=1. cons_f1416466313t_bool=1. cons_f14678382t_bool=1. cons_f1803648492t_bool=1. cons_nat=1. ord_le1004900979t_bool=1. b=1. cOMBK_2038534567t_bool=1. drop_A186780501le_alt=1. ord_le1069525464l_bool=1. fTrue=1. ord_le2009287770l_bool=1. ord_le2085964885l_bool=1. ord_le249613274i_bool=1. tl_Arr1453005548le_alt=1. a=1. lex_Ar255587961le_alt=1. lexord1965430054le_alt=1. lexord_nat=1. member1036419453e_indi=1. member1055039380t_bool=1. member1258861596ol_nat=1. member1366121996le_alt=1. member1463820796le_alt=1. member1501249940le_alt=1. member1535903113le_alt=1. member1549237916le_alt=1. member1567747746le_alt=1. member1603119111le_alt=1. member1620122743le_alt=1. member1636995890le_alt=1. member1846971697ol_nat=1. member1870621557le_alt=1. member1881985050ol_nat=1. member1986685623t_bool=1. member2056165217t_bool=1. member2061588323l_bool=1. member234128621e_indi=1. member26406738le_alt=1. member357566570t_bool=1. member383660628t_bool=1. member392258873t_bool=1. member478669795t_bool=1. member547554753lt_nat=1. member797673069le_alt=1. member832622164e_indi=1. member855864530t_bool=1. member880664588l_bool=1. member905797074e_indi=1. member910422074st_nat=1. member989885409l_bool=1. ord_le893483153t_bool=1. produc1810286871le_alt=1. produc1869962435st_nat=1. arrow_107136085le_alt=1. arrow_610963188ctator=1. ord_le340789135t_bool=1. arrow_1587283740nimity=1. ord_min_nat=1. rotate1322903650le_alt=1. cOMBB_2104979073le_alt=1. equal_499625528le_alt=1. lex_li678151430le_alt=1. member107042095t_bool=1. member1139774916t_bool=1. member1329875721t_bool=1. member1494731740t_bool=1. member2043543687t_bool=1. member24871799le_alt=1. member290075938le_alt=1. member379339614t_bool=1. p=1. produc1527919682t_bool=1. produc1995698397l_bool=1. produc315582749t_bool=1. produc51145731t_bool=1. produc89849422i_bool=1. c=1. fequal1160105444le_alt=1. one_one_nat=1. ord_le1568362934t_bool=1. ord_le742797417l_bool=1. cOMBB_1769989562e_indi=1. cOMBC_1353880399t_bool=1. cOMBC_898791271t_bool=1. cOMBK_657557929e_indi=1. fFalse=1. null_A361035805le_alt=1. produc1102988737t_bool=1. top_to1647826457l_bool=1. cOMBC_1628726426t_bool=1. cOMBK_1076156777e_indi=1. cOMBK_246631416le_alt=1. distin1358019435e_indi=1. distin1553582624le_alt=1. distin1691228364t_bool=1. distin1991771627t_bool=1. distin22312297t_bool=1. distin856461956le_alt=1. distinct_bool=1. distinct_nat=1. fequal1196706959e_indi=1. fequal1258273448t_bool=1. fequal1596628751t_bool=1. fequal454353832le_alt=1. fequal673514820le_alt=1. fequal785189517t_bool=1. fequal_bool=1. fequal_nat=1. insert960637483le_alt=1. size_s1310206929le_alt=1. bool=1. butlas1157436197t_bool=1. butlas1456493703le_alt=1. butlas1472553170t_bool=1. butlas1888624491le_alt=1. butlas309371216t_bool=1. butlas995342418e_indi=1. butlast_bool=1. butlast_nat=1. cOMBB_1141363506e_indi=1. cOMBB_1459698610t_bool=1. cOMBB_1604919143le_alt=1. cOMBB_310009925t_bool=1. cOMBB_433601099le_alt=1. cOMBB_871930928t_bool=1. cOMBB_bool_bool_bool=1. cOMBB_bool_bool_nat=1. cOMBC_1136104858l_bool=1. cOMBC_1428934564i_bool=1. cOMBC_1455277858l_bool=1. cOMBC_1470522126t_bool=1. cOMBC_1576836772l_bool=1. cOMBC_1745481870l_bool=1. cOMBC_1781321570l_bool=1. cOMBC_188453282l_bool=1. cOMBC_2105056416l_bool=1. cOMBC_226598744l_bool=1. cOMBC_564645218l_bool=1. cOMBC_574836706l_bool=1. cOMBC_607108822t_bool=1. cOMBC_62805014l_bool=1. cOMBC_864945570l_bool=1. cOMBC_bool_bool_bool=1. cOMBC_nat_nat_bool=1. cOMBK_1021277149l_bool=1. cOMBK_1305974367l_bool=1. cOMBK_1369841150le_alt=1. cOMBK_1389630288e_indi=1. cOMBK_1411148035t_bool=1. cOMBK_1550261278le_alt=1. cOMBK_1626211664t_bool=1. cOMBK_1632198563le_alt=1. cOMBK_1638246986le_alt=1. cOMBK_1693871704t_bool=1. cOMBK_1773325549t_bool=1. cOMBK_1778599651le_alt=1. cOMBK_1786248882t_bool=1. cOMBK_1914291077t_bool=1. cOMBK_1915602921le_alt=1. cOMBK_208474378t_bool=1. cOMBK_2117707615t_bool=1. cOMBK_2130565512t_bool=1. cOMBK_215999438e_indi=1. cOMBK_370033373t_bool=1. cOMBK_480812327t_bool=1. cOMBK_488408421t_bool=1. cOMBK_545135096l_bool=1. cOMBK_607931107t_bool=1. cOMBK_673344138le_alt=1. cOMBK_684046286t_bool=1. cOMBK_69806648l_bool=1. cOMBK_8746725le_alt=1. cOMBK_964928722t_bool=1. ord_less_eq_bool=1. produc1170920579l_bool=1. produc2091914181t_bool=1. produc2129949100l_bool=1. produc998313258l_bool=1. take_A1601602045le_alt=1. top_top_fun_nat_bool=1. cOMBB_1171600517le_alt=1. cOMBK_1193272835le_alt=1. cOMBK_1786282629le_alt=1. cOMBK_1901607710le_alt=1. cOMBK_2131602312ol_nat=1. cOMBK_39620975ol_nat=1. cOMBK_532713098ol_nat=1. cOMBK_751995742le_alt=1. cOMBK_856666543ol_nat=1. fequal796301787le_alt=1. insert1665396998t_bool=1. insert178756925le_alt=1. insert1946138248t_bool=1. insert202184175t_bool=1. insert256706849le_alt=1. insert915800584e_indi=1. insert_bool=1. insert_nat=1. p_1=1. rev_Ar2090626622e_indi=1. rev_Pr295966039le_alt=1. rev_Pr464210035le_alt=1. rev_bool=1. rev_fu1041356345t_bool=1. rev_fu1629171390t_bool=1. rev_fu1957290812t_bool=1. rev_nat=1. size_size_nat=1. top_to772840767t_bool=1. arrow_1271263838e_indi=1. cOMBB_1058319106le_alt=1. cOMBB_1818168801le_alt=1. cOMBB_2052911494le_alt=1. cOMBB_2112722489le_alt=1. cOMBB_283473102le_alt=1. cOMBB_353715312le_alt=1. cOMBB_576205818le_alt=1. cOMBB_747702273le_alt=1. cOMBB_84213429le_alt=1. cOMBB_903467948lt_nat=1. cOMBB_nat_nat_nat=1. cOMBC_1058495865le_alt=1. cOMBC_1330649024le_alt=1. cOMBC_1511969967le_alt=1. cOMBC_1635684702l_bool=1. cOMBC_1740746827l_bool=1. cOMBC_364043868t_bool=1. cOMBC_672290030t_bool=1. member1065824984t_bool=1. member232255508at_nat=1. member345815512e_indi=1. member624253174l_bool=1. member636962260t_bool=1. member739461844t_bool=1. nat_size=1. produc1096087521t_bool=1. produc1208780001e_indi=1. produc1246214911l_bool=1. produc32696407t_bool=1. produc586224093t_bool=1. product_Pair_nat_nat=1. cOMBB_1193902096le_alt=1. cOMBB_1450165017le_alt=1. cOMBB_164218871le_alt=1. cOMBB_2017209238le_alt=1. cOMBB_2048157563le_alt=1. cOMBB_500037706le_alt=1. cOMBB_723746886le_alt=1. cOMBB_881934114le_alt=1. cOMBC_1697899890le_alt=1. cOMBC_1919297930le_alt=1. cOMBC_nat_nat_nat=1. cOMBI_nat=1. cOMBK_1626390631t_bool=1. cOMBK_1646462604le_alt=1. cOMBK_1656150864t_bool=1. cOMBK_1696648346le_alt=1. cOMBK_272667621t_bool=1. cOMBK_306730240le_alt=1. cOMBK_575487463e_indi=1. cOMBK_bool_nat=1. cOMBS_1294827559le_alt=1. cOMBS_1399042523le_alt=1. nil_Ar1968865438e_indi=1. nil_Pr1357826771le_alt=1. nil_Pr2088511415le_alt=1. nil_bool=1. nil_fu1891063196t_bool=1. nil_fu507235289t_bool=1. nil_fu81264926t_bool=1. nil_nat=1. drop_A1037593438e_indi=1. drop_P13505143le_alt=1. drop_P283022739le_alt=1. drop_bool=1. drop_f1080688732t_bool=1. drop_f176122846t_bool=1. drop_f642150681t_bool=1. drop_nat=1. member1013148679le_alt=1. produc1817385812t_bool=1. produc49943708le_alt=1. take_A1967759030e_indi=1. take_P1280951759le_alt=1. take_P580715755le_alt=1. take_bool=1. take_f1428279094t_bool=1. take_f1669843892t_bool=1. take_f1937952705t_bool=1. take_nat=1. tl_Arr1614430599e_indi=1. tl_Pro12277920le_alt=1. tl_Pro292865596le_alt=1. tl_bool=1. tl_fun2071351216t_bool=1. tl_fun38025093t_bool=1. tl_fun413860871t_bool=1. tl_nat=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. hAPP_l726444215le_alt=1. hAPP_f592646513l_bool=1. hAPP_nat_nat=1. hAPP_nat_bool=1. hAPP_P229966473l_bool=1. hAPP_A702847159le_alt=1. hAPP_f1634113933l_bool=1. hAPP_A1505516597le_alt=1. hAPP_P1610428353l_bool=1. hAPP_l1869074853le_alt=1. hAPP_l391088160le_alt=1. hAPP_n1699378549t_bool=1. hAPP_A408086601le_alt=1. hAPP_f1749234559l_bool=1. hAPP_f777333846l_bool=1. hAPP_l568342716le_alt=1. hAPP_f566237389l_bool=1. hAPP_f461621971l_bool=1. hAPP_A862370221t_bool=1. hAPP_f1865483825t_bool=1. hAPP_f250445784l_bool=1. hAPP_f2013399995l_bool=1. hAPP_l1386638586t_bool=1. hAPP_f1253375959l_bool=1. hAPP_A297543629l_bool=1. hAPP_f1599966040l_bool=1. hAPP_f387058535l_bool=1. hAPP_f54304608l_bool=1. hAPP_A1602262231l_bool=1. hAPP_b1787118453l_bool=1. hAPP_n215258509l_bool=1. hAPP_P606313927t_bool=1. hAPP_l1891879573le_alt=1. hAPP_f1757554033l_bool=1. hAPP_P753566857l_bool=1. hAPP_f1662382841t_bool=1. hAPP_l1508829665le_alt=1. hAPP_l190821901le_alt=1. hAPP_l1189022293t_bool=1. hAPP_l1075146559t_bool=1. hAPP_l1660244757t_bool=1. hAPP_l1766111573le_alt=1. hAPP_l210315413t_bool=1. hAPP_l54953109e_indi=1. hAPP_A1664620203t_bool=1. hAPP_l656323104le_alt=1. hAPP_l1493873365le_alt=1. hAPP_l248265089st_nat=1. hAPP_l1747810175t_bool=1. hAPP_f312250286l_bool=1. hAPP_A568203993t_bool=1. hAPP_f791205069t_bool=1. hAPP_A1677245848t_bool=1. hAPP_f412050202t_bool=1. hAPP_bool_bool=1. hAPP_P1327827171t_bool=1. hAPP_l1872264749lt_nat=1. hAPP_A1785763630i_bool=1. pi_fun150026276t_bool=1. hAPP_f965095724l_bool=1. pi_Pro666468413t_bool=1. hAPP_f108029607l_bool=1. hAPP_A832564074le_alt=1. hAPP_P1336117749l_bool=1. hAPP_P1524963591le_alt=1. hAPP_P665560703le_alt=1. pi_Arr990697634t_bool=1. hAPP_f863359027l_bool=1. hAPP_l1892800522le_alt=1. hAPP_l1947611924t_bool=1. hAPP_l265951104t_bool=1. hAPP_l367315107e_indi=1. hAPP_l583487011t_bool=1. hAPP_l776124325t_bool=1. hAPP_f1111021425l_bool=1. hAPP_f117508401l_bool=1. hAPP_f1382465777l_bool=1. hAPP_f1478750961l_bool=1. hAPP_f2076022549l_bool=1. hAPP_f263022001l_bool=1. hAPP_P1068600713l_bool=1. hAPP_P1136391889l_bool=1. hAPP_P1215479305l_bool=1. hAPP_P1320270217l_bool=1. hAPP_P1870454025l_bool=1. hAPP_P215277193l_bool=1. hAPP_f1114274611l_bool=1. hAPP_f1446256145l_bool=1. hAPP_f1802593209l_bool=1. hAPP_f1823567903t_bool=1. hAPP_f2045380501l_bool=1. hAPP_f554166545i_bool=1. hAPP_l1146224941t_bool=1. hAPP_l1152370491le_alt=1. hAPP_l1242990405t_bool=1. hAPP_l1347264831t_bool=1. hAPP_l1349316624t_bool=1. hAPP_l1646733722le_alt=1. hAPP_l1806296521t_bool=1. hAPP_l2052497089e_indi=1. hAPP_l218095399t_bool=1. hAPP_l29767369e_indi=1. hAPP_l546743617t_bool=1. hAPP_l869099372t_bool=1. hAPP_n280362926st_nat=1. hAPP_b994696797t_bool=1. hAPP_f536389215l_bool=1. hAPP_l1570526551le_alt=1. hAPP_l1686876398le_alt=1. hAPP_l710375585st_nat=1. hAPP_A974963564e_indi=1. hAPP_P1057207891le_alt=1. hAPP_P1580093797l_bool=1. hAPP_P2141504567le_alt=1. hAPP_P47603675le_alt=1. hAPP_P734992695le_alt=1. hAPP_f1812326636t_bool=1. hAPP_f613335309t_bool=1. hAPP_f726713198t_bool=1. hAPP_A1941004017t_bool=1. hAPP_f344580165t_bool=1. hAPP_n2139729636le_alt=1. hAPP_P1861769507t_bool=1. hAPP_f1552576127i_bool=1. arrow_230821333_above=1. hAPP_P1056860425le_alt=1. hAPP_f1078809103le_alt=1. hAPP_P1711233733t_bool=1. hAPP_P1875867302i_bool=1. hAPP_P324742453l_bool=1. hAPP_n49391885le_alt=1. hAPP_A1805174428t_bool=1. hAPP_P2082381915t_bool=1. hAPP_P2136891882t_bool=1. hAPP_b1703662281t_bool=1. hAPP_b589554111l_bool=1. hAPP_f1146952189l_bool=1. hAPP_f1924755118l_bool=1. hAPP_f10461143l_bool=1. hAPP_f1252760917l_bool=1. hAPP_f1271753300l_bool=1. hAPP_f1276380911l_bool=1. hAPP_f1306865520l_bool=1. hAPP_f1351174655l_bool=1. hAPP_f1424540178l_bool=1. hAPP_f1525366679l_bool=1. hAPP_f1534526009l_bool=1. hAPP_f1581553471l_bool=1. hAPP_f16559284l_bool=1. hAPP_f167218729l_bool=1. hAPP_f1725204053l_bool=1. hAPP_f1732944975l_bool=1. hAPP_f1790426673l_bool=1. hAPP_f1837019376l_bool=1. hAPP_f1919691607l_bool=1. hAPP_f196630486l_bool=1. hAPP_f1976794890l_bool=1. hAPP_f2014742713t_bool=1. hAPP_f2017347493l_bool=1. hAPP_f2042909150l_bool=1. hAPP_f236193164l_bool=1. hAPP_f384959233l_bool=1. hAPP_f43523585l_bool=1. hAPP_f560831258l_bool=1. hAPP_f570668343l_bool=1. hAPP_f597137892l_bool=1. hAPP_f599145828l_bool=1. hAPP_f651410150l_bool=1. hAPP_f68732431l_bool=1. hAPP_f785974231l_bool=1. hAPP_f817604743l_bool=1. hAPP_f859154022l_bool=1. hAPP_f899439636l_bool=1. hAPP_f969456697l_bool=1. hAPP_P1303953929l_bool=1. hAPP_P1736545109l_bool=1. hAPP_f1073701219l_bool=1. hAPP_f1153917531l_bool=1. hAPP_f1175923213l_bool=1. hAPP_f1212866771l_bool=1. hAPP_f1254328783l_bool=1. hAPP_f1339774669l_bool=1. hAPP_f1345320373l_bool=1. hAPP_f137298509l_bool=1. hAPP_f1556434125l_bool=1. hAPP_f1603005581l_bool=1. hAPP_f1666015481l_bool=1. hAPP_f1721660479l_bool=1. hAPP_f1857700889l_bool=1. hAPP_f1868812933l_bool=1. hAPP_f2069145881l_bool=1. hAPP_f2103233871l_bool=1. hAPP_f2111526677l_bool=1. hAPP_f2116028941l_bool=1. hAPP_f2127575245l_bool=1. hAPP_f2142494605l_bool=1. hAPP_f29979067t_bool=1. hAPP_f40035149l_bool=1. hAPP_f407092109l_bool=1. hAPP_f452990795l_bool=1. hAPP_f471467367t_bool=1. hAPP_f586020557l_bool=1. hAPP_f652666381l_bool=1. hAPP_f666018637l_bool=1. hAPP_f671616325l_bool=1. hAPP_f721935245l_bool=1. hAPP_f742962061l_bool=1. hAPP_f937842381l_bool=1. hAPP_f976491405l_bool=1. hAPP_l1148138287st_nat=1. hAPP_l139141107le_alt=1. hAPP_l318352527st_nat=1. hAPP_l993078710le_alt=1. hAPP_n588788980t_bool=1. hAPP_nat_fun_nat_nat=1. pi_Arr1199386158le_alt=1. pi_Arr1306565967t_bool=1. pi_Arr1600668070t_bool=1. pi_Arr1936979349t_bool=1. pi_Arr2020412179t_bool=1. pi_Arr44017448t_bool=1. pi_Arr55294401le_alt=1. pi_Pro1270767662e_indi=1. pi_Pro2035602019le_alt=1. pi_Pro264071722lt_nat=1. pi_Pro610394757le_alt=1. pi_boo1117000868t_bool=1. pi_boo115158845le_alt=1. pi_boo175444770t_bool=1. pi_boo538701011t_bool=1. pi_fun1002945429e_indi=1. pi_fun1575168891l_bool=1. pi_fun1597968236ol_nat=1. pi_fun1792636103le_alt=1. pi_fun2080023171ol_nat=1. pi_fun380945313le_alt=1. pi_fun462417760le_alt=1. pi_fun52649508l_bool=1. pi_fun553016520le_alt=1. pi_fun684211550le_alt=1. pi_fun753830419e_indi=1. pi_fun770049925ol_nat=1. pi_fun823343522l_bool=1. pi_fun896360044e_indi=1. pi_fun90241866le_alt=1. hAPP_P139894920l_bool=1. hAPP_P1606644490l_bool=1. hAPP_P1905961381l_bool=1. hAPP_f111185985l_bool=1. hAPP_f146009813l_bool=1. hAPP_f1765205l_bool=1. hAPP_f310455147l_bool=1. hAPP_f515126293t_bool=1. hAPP_f580451669i_bool=1. hAPP_f825175477t_bool=1. hAPP_f961197973l_bool=1. hAPP_f1468796453l_bool=1. hAPP_f1508559628l_bool=1. hAPP_f1642286869t_bool=1. hAPP_f2115479956l_bool=1. hAPP_f2835579l_bool=1. hAPP_f307807922l_bool=1. hAPP_f354239713l_bool=1. hAPP_f799496074l_bool=1. hAPP_f800510211t_bool=1. hAPP_f903371257l_bool=1. hAPP_A313542399i_bool=1. hAPP_P1267694911t_bool=1. hAPP_f105614477l_bool=1. hAPP_f1229756829l_bool=1. hAPP_f1425186181i_bool=1. hAPP_f1502595491l_bool=1. hAPP_f1546082457l_bool=1. hAPP_f1577179519l_bool=1. hAPP_f1577576703l_bool=1. hAPP_f1708325453t_bool=1. hAPP_f1783389935t_bool=1. hAPP_f1867424333l_bool=1. hAPP_f1984771213t_bool=1. hAPP_f27970449t_bool=1. hAPP_f491986957l_bool=1. hAPP_f720124009l_bool=1. hAPP_f975710927l_bool=1. hAPP_f984565261l_bool=1. pi_Pro1636653258t_bool=1. pi_Pro492447587le_alt=1. pi_Pro531915080t_bool=1. pi_Pro623007021t_bool=1. pi_nat1317494091t_bool=1. pi_nat1370421354t_bool=1. pi_nat249006182le_alt=1. pi_nat955432909t_bool=1. hAPP_A187815023l_bool=1. hAPP_P163071551t_bool=1. hAPP_b1048178734l_bool=1. hAPP_b1812770943l_bool=1. hAPP_b517355696l_bool=1. hAPP_f103356543l_bool=1. hAPP_f1663053423t_bool=1. hAPP_f612708895l_bool=1. fun=1. hAPP_A1159885342t_bool=1. hAPP_A1906441908t_bool=1. hAPP_A2102641565t_bool=1. hAPP_A479848479t_bool=1. hAPP_A638717112le_alt=1. hAPP_P1257947515le_alt=1. hAPP_P1599728724t_bool=1. hAPP_P1699981037le_alt=1. hAPP_P19446482t_bool=1. hAPP_P710098616e_indi=1. hAPP_b1376601646t_bool=1. hAPP_b317196972t_bool=1. hAPP_b55004359le_alt=1. hAPP_f1054274129le_alt=1. hAPP_f1331183759t_bool=1. hAPP_f1582908258e_indi=1. hAPP_f1659309744l_bool=1. hAPP_f1693298207e_indi=1. hAPP_f1800079444le_alt=1. hAPP_f1808153265t_bool=1. hAPP_f210227915t_bool=1. hAPP_f248867553t_bool=1. hAPP_f329301088t_bool=1. hAPP_f666924118le_alt=1. hAPP_f758198165t_bool=1. hAPP_f836059805e_indi=1. hAPP_l1795316048t_bool=1. hAPP_l2034560823i_bool=1. hAPP_l2060223415l_bool=1. hAPP_l54057324t_bool=1. hAPP_l89806901l_bool=1. hAPP_l982832318l_bool=1. hAPP_list_bool_bool=1. hAPP_list_nat_bool=1. hAPP_n1875670159le_alt=1. hAPP_n1965810497t_bool=1. hAPP_n291670979t_bool=1. hAPP_n324757596le_alt=1. hAPP_A1112981887l_bool=1. hAPP_A1928120382l_bool=1. hAPP_A1952883197l_bool=1. hAPP_A366518464l_bool=1. hAPP_A60074736l_bool=1. hAPP_P1095651821le_alt=1. hAPP_P339823136lt_nat=1. hAPP_f1277514478l_bool=1. hAPP_f1416261241ol_nat=1. hAPP_f1418366331ol_nat=1. hAPP_f1619707799le_alt=1. hAPP_f1624277646l_bool=1. hAPP_f1790240989le_alt=1. hAPP_f1948454017i_bool=1. hAPP_f2068374643l_bool=1. hAPP_f210572555l_bool=1. hAPP_f228695594t_bool=1. hAPP_f239852716t_bool=1. hAPP_f244157820i_bool=1. hAPP_f40547922le_alt=1. hAPP_f53317332le_alt=1. hAPP_f816335862ol_nat=1. hAPP_f839832464l_bool=1. hAPP_l1071513828lt_nat=1. hAPP_n1674354836l_bool=1. hAPP_n2095207769l_bool=1. hAPP_n295497947l_bool=1. hAPP_f1172769267l_bool=1. hAPP_f1250179763i_bool=1. hAPP_f1297597679t_bool=1. hAPP_f1348208725i_bool=1. hAPP_f135580393t_bool=1. hAPP_f1362748656t_bool=1. hAPP_f1368393520i_bool=1. hAPP_f1382209403t_bool=1. hAPP_f14382104t_bool=1. hAPP_f1438487600t_bool=1. hAPP_f1460506473l_bool=1. hAPP_f152453811l_bool=1. hAPP_f1556356969l_bool=1. hAPP_f1593910865t_bool=1. hAPP_f1609079369t_bool=1. hAPP_f1622901481t_bool=1. hAPP_f1628730575t_bool=1. hAPP_f1686853802l_bool=1. hAPP_f1688301673l_bool=1. hAPP_f1722879237t_bool=1. hAPP_f1739666797l_bool=1. hAPP_f1809347209t_bool=1. hAPP_f1874082285l_bool=1. hAPP_f1897201897l_bool=1. hAPP_f1956380189l_bool=1. hAPP_f1982584345l_bool=1. hAPP_f1996228283l_bool=1. hAPP_f2018922499l_bool=1. hAPP_f2069340078l_bool=1. hAPP_f2122673039l_bool=1. hAPP_f2129183278i_bool=1. hAPP_f2136780329i_bool=1. hAPP_f2139078121t_bool=1. hAPP_f214899148l_bool=1. hAPP_f229349961t_bool=1. hAPP_f256804927l_bool=1. hAPP_f340261009t_bool=1. hAPP_f356431923l_bool=1. hAPP_f372103450t_bool=1. hAPP_f393984045t_bool=1. hAPP_f420098683t_bool=1. hAPP_f49469479t_bool=1. hAPP_f495827653l_bool=1. hAPP_f5761716t_bool=1. hAPP_f585152361i_bool=1. hAPP_f589776703l_bool=1. hAPP_f600409331t_bool=1. hAPP_f62793075t_bool=1. hAPP_f712459161i_bool=1. hAPP_f746617550l_bool=1. hAPP_f779223135l_bool=1. hAPP_f786857743l_bool=1. hAPP_f81007726t_bool=1. hAPP_f823172443l_bool=1. hAPP_f856106132t_bool=1. hAPP_f862836377l_bool=1. hAPP_f86548619l_bool=1. hAPP_f880868799t_bool=1. hAPP_f894608603t_bool=1. hAPP_f898562478t_bool=1. hAPP_f906821569t_bool=1. hAPP_f932544453t_bool=1. hAPP_f996881846t_bool=1. product_prod=1. hAPP_A2091627584i_bool=1. hAPP_A210478249t_bool=1. hAPP_A822657487l_bool=1. hAPP_f1067427061l_bool=1. hAPP_f1098788115l_bool=1. hAPP_f11902820l_bool=1. hAPP_f1328016200t_bool=1. hAPP_f1514103381le_alt=1. hAPP_f1617919085t_bool=1. hAPP_f1783828715t_bool=1. hAPP_f1806001137l_bool=1. hAPP_f1879785608l_bool=1. hAPP_f336430449l_bool=1. hAPP_f57507985t_bool=1. hAPP_f584002568l_bool=1. hAPP_f681285561l_bool=1. hAPP_f695414965l_bool=1. hAPP_f746471349le_alt=1. hAPP_f879361201l_bool=1. hAPP_f927478261l_bool=1. hAPP_f952375653l_bool=1. hAPP_l1284365004t_bool=1. hAPP_l1328583473l_bool=1. hAPP_l1542188220l_bool=1. hAPP_l1661879987l_bool=1. list_c380068407le_alt=1. partit327648526le_alt=1. hAPP_A101171597t_bool=1. hAPP_A1266156941e_indi=1. hAPP_A1345295975l_bool=1. hAPP_A1350932668e_indi=1. hAPP_A1470764750t_bool=1. hAPP_A1862272720t_bool=1. hAPP_A1965262040i_bool=1. hAPP_A490104565t_bool=1. hAPP_P1039044241l_bool=1. hAPP_P1251024649l_bool=1. hAPP_P1563303057l_bool=1. hAPP_P1971325577l_bool=1. hAPP_P738148045l_bool=1. hAPP_P80514697l_bool=1. hAPP_P864444517le_alt=1. hAPP_b1115999851l_bool=1. hAPP_b1337486384i_bool=1. hAPP_b2048821609l_bool=1. hAPP_b30302907t_bool=1. hAPP_f1013417831le_alt=1. hAPP_f1056253543l_bool=1. hAPP_f1065005691t_bool=1. hAPP_f1133021325t_bool=1. hAPP_f1152779391t_bool=1. hAPP_f1267389329t_bool=1. hAPP_f1294513379le_alt=1. hAPP_f1318121625le_alt=1. hAPP_f1324249913t_bool=1. hAPP_f1457563459t_bool=1. hAPP_f1544433597t_bool=1. hAPP_f156764033l_bool=1. hAPP_f1585078997at_nat=1. hAPP_f1688983057l_bool=1. hAPP_f1792349771le_alt=1. hAPP_f1886133174t_bool=1. hAPP_f1914919701at_nat=1. hAPP_f1925192252t_bool=1. hAPP_f1953650287l_bool=1. hAPP_f2058969401t_bool=1. hAPP_f2068969285le_alt=1. hAPP_f231379647t_bool=1. hAPP_f311173987t_bool=1. hAPP_f370419053l_bool=1. hAPP_f402821245le_alt=1. hAPP_f541777673t_bool=1. hAPP_f548810715le_alt=1. hAPP_f634775919le_alt=1. hAPP_f66177535t_bool=1. hAPP_f778758417l_bool=1. hAPP_f991870303t_bool=1. hAPP_l1352613953l_bool=1. hAPP_l1538437917t_bool=1. hAPP_l1824974724l_bool=1. hAPP_l377001987t_bool=1. hAPP_l382792410le_alt=1. hAPP_l395992834l_bool=1. hAPP_n1289843868at_nat=1. hAPP_n1865633855at_nat=1. nat_ca14895078le_alt=1. nat_case_nat=1. hAPP_A1043896845le_alt=1. hAPP_A1553574765l_bool=1. hAPP_A1625428400t_bool=1. hAPP_A572596845t_bool=1. hAPP_A621939144t_bool=1. hAPP_b1013836512t_bool=1. hAPP_f1291559232le_alt=1. hAPP_f1349184697le_alt=1. hAPP_f1460305297t_bool=1. hAPP_f1532338415le_alt=1. hAPP_f1539445765l_bool=1. hAPP_f1564521144le_alt=1. hAPP_f1608056749le_alt=1. hAPP_f1707011108l_bool=1. hAPP_f170721165l_bool=1. hAPP_f1728064559t_bool=1. hAPP_f1777336662le_alt=1. hAPP_f1933751673le_alt=1. hAPP_f1939049849le_alt=1. hAPP_f1956511609le_alt=1. hAPP_f2001490223le_alt=1. hAPP_f216801278le_alt=1. hAPP_f318645548t_bool=1. hAPP_f416620757at_nat=1. hAPP_f469186021le_alt=1. hAPP_f500394983le_alt=1. hAPP_f628327744le_alt=1. hAPP_f653880381t_bool=1. hAPP_f657005563le_alt=1. hAPP_f724700817t_bool=1. hAPP_f749699165le_alt=1. hAPP_f939319677le_alt=1. hAPP_l1288188215t_bool=1. hAPP_l1406283231le_alt=1. hAPP_l1437188439t_bool=1. hAPP_l1629075165l_bool=1. hAPP_l1701840224le_alt=1. hAPP_l489874441le_alt=1. hAPP_l578398296l_bool=1. hAPP_l618618165le_alt=1. hAPP_l693571982le_alt=1. hAPP_n1117890248e_indi=1. hAPP_n1200821448t_bool=1. hAPP_n1429822280t_bool=1. hAPP_n19406600le_alt=1. hAPP_n2038854252t_bool=1. hAPP_n2132365064le_alt=1. hAPP_n479129736t_bool=1. lexn_A1157915829le_alt=1. nat_case_bool=1. hAPP_l1107171823l_bool=1. produc1449729469le_alt=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f18=1. f19=1. f21=1. f22=1. f24=1. f25=1. f26=1. f27=1. f44=1. f45=1. f46=1. f49=1. f50=1. f52=1. f53=1. f67=1. f68=1. f70=1. f71=1. f76=1. f77=1. f78=1. f79=1. f81=1. f88=1. f89=1. f90=1. f95=1. f96=1. f105=1. f106=1. f107=1. f108=1. f109=1. f111=1. f112=1. f119=1. f129=1. f130=1. f141=1. f142=1. f149=1. f150=1. f157=1. f158=1. f159=1. f164=1. f165=1. f167=1. f168=1. f173=1. f174=1. f176=1. f177=1. f185=1. f186=1. f187=1. f192=1. f193=1. f194=1. f195=1. f208=1. f209=1. f214=1. f215=1. f216=1. f217=1. f218=1. f230=1. f237=1. f238=1. f239=1. f240=1. f248=1. f249=1. f250=1. f251=1. f253=1. f254=1. f255=1. f256=1. f258=1. f259=1. f260=1. f281=1. f282=1. f288=1. f292=1. f296=1. f297=1. f298=1. f299=1. f311=1. f318=1. f319=1. f320=1. f321=1. f339=1. f340=1. f343=1. f344=1. f345=1. f346=1. f354=1. f355=1. f356=1. f357=1. f361=1. f362=1. f363=1. f364=1. f368=1. f369=1. f371=1. f372=1. f388=1. f394=1. f395=1. f403=1. f404=1. f418=1. f425=1. f426=1. f428=1. f429=1. f436=1. f442=1. f448=1. f449=1. f450=1. f451=1. f455=1. f470=1. f471=1. f474=1. f475=1. f480=1. f481=1. f482=1. f483=1. f484=1. f485=1. f486=1. f487=1. f491=1. f492=1. f497=1. f498=1. f500=1. f501=1. f502=1. f505=1. f513=1. f514=1. f518=1. f519=1. f536=1. f537=1. f540=1. f541=1. f546=1. f547=1. f553=1. f554=1. f558=1. f559=1. f560=1. f561=1. plus_plus_nat=1. minus_minus_nat=1. set_Ar1565008694le_alt=1. transi1256616594le_alt=1. transi992120749le_alt=1. set_bool=1. set_Ar219761597e_indi=1. set_Pr604701398le_alt=1. set_fu1384968698t_bool=1. set_fu1865467835t_bool=1. set_fu335223357t_bool=1. set_Pr1404309362le_alt=1. set_nat=1. takeWh536362254le_alt=1. dropWh156852662le_alt=1. last_A57386030le_alt=1. transi580536954le_alt=1. listre53232751le_alt=1. takeWh1309019107t_bool=1. takeWh1512678354t_bool=1. takeWh1529274110le_alt=1. takeWh169821797t_bool=1. takeWh273131493e_indi=1. takeWhile_bool=1. dropWh1133555834t_bool=1. dropWh1552197947t_bool=1. dropWh1907450966le_alt=1. dropWh23362493t_bool=1. dropWh601337149e_indi=1. dropWhile_bool=1. takeWh416411546le_alt=1. takeWhile_nat=1. list_u1050032253le_alt=1. dropWh1604595954le_alt=1. dropWhile_nat=1. hd_Arr805754088le_alt=1. transi54034710le_alt=1. replic351609551le_alt=1. produc212588606t_bool=1. fconj=1. arrow_1495666017_mkbot=1. arrow_1644373103_mktop=1. splice360969192le_alt=1. collec1553055422t_bool=1. collec1611109369e_indi=1. collec1729629178le_alt=1. if_Pro1306781203le_alt=1. in_rel1305177154le_alt=1. produc231070560t_bool=1. collec1063742455t_bool=1. collec2096990994le_alt=1. collec418781817t_bool=1. collect_nat=1. hd_Arr465110667e_indi=1. hd_Pro1524751780le_alt=1. hd_bool=1. hd_fun191074571t_bool=1. hd_fun276684937t_bool=1. hd_fun730195372t_bool=1. in_rel617948260le_alt=1. last_A1892550853e_indi=1. last_P736051166le_alt=1. last_bool=1. last_f1417039043t_bool=1. last_f1633249093t_bool=1. last_f2112695026t_bool=1. listre831694736le_alt=1. maps_A461338881le_alt=1. order_835987853le_alt=1. produc335266950le_alt=1. transi94963304le_alt=1. hd_Pro1848862016le_alt=1. hd_nat=1. last_P723779706le_alt=1. last_nat=1. set_li1646995977le_alt=1. undefi1445431868t_bool=1. undefi1481304379t_bool=1. undefi2070130874t_bool=1. undefi237088188e_indi=1. undefi462180727le_alt=1. undefi95778005le_alt=1. undefined_bool=1. f16=1. f17=1. f20=1. f30=1. f35=1. f56=1. f69=1. f83=1. f84=1. f85=1. f116=1. f117=1. f156=1. f180=1. f181=1. f202=1. f203=1. f204=1. f278=1. f279=1. f280=1. f284=1. f285=1. f286=1. f287=1. f301=1. f302=1. f303=1. f304=1. f313=1. f314=1. f315=1. f316=1. f335=1. f336=1. f338=1. f365=1. f376=1. f377=1. f378=1. f384=1. f385=1. f386=1. f387=1. f391=1. f392=1. f405=1. f406=1. f407=1. f447=1. f515=1. f516=1. f539=1. f1=1. f2=1. f3=1. f4=1. f14=1. f15=1. f23=1. f31=1. f33=1. f36=1. f37=1. f38=1. f39=1. f40=1. f43=1. f47=1. f48=1. f51=1. f54=1. f55=1. f59=1. f60=1. f61=1. f63=1. f64=1. f65=1. f72=1. f73=1. f80=1. f82=1. f86=1. f87=1. f91=1. f92=1. f97=1. f99=1. f100=1. f110=1. f113=1. f118=1. f120=1. f121=1. f122=1. f123=1. f128=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f139=1. f140=1. f143=1. f144=1. f146=1. f147=1. f148=1. f151=1. f152=1. f153=1. f154=1. f160=1. f161=1. f162=1. f163=1. f166=1. f169=1. f170=1. f171=1. f172=1. f175=1. f178=1. f179=1. f182=1. f183=1. f188=1. f196=1. f197=1. f200=1. f211=1. f212=1. f213=1. f225=1. f226=1. f229=1. f231=1. f232=1. f233=1. f235=1. f236=1. f242=1. f247=1. f252=1. f257=1. f261=1. f262=1. f263=1. f264=1. f265=1. f266=1. f271=1. f272=1. f273=1. f274=1. f275=1. f276=1. f277=1. f300=1. f305=1. f306=1. f307=1. f308=1. f309=1. f310=1. f312=1. f322=1. f323=1. f324=1. f325=1. f326=1. f327=1. f328=1. f329=1. f330=1. f333=1. f334=1. f337=1. f341=1. f342=1. f349=1. f353=1. f360=1. f370=1. f373=1. f374=1. f375=1. f380=1. f381=1. f382=1. f383=1. f393=1. f399=1. f400=1. f402=1. f408=1. f409=1. f410=1. f411=1. f412=1. f413=1. f414=1. f415=1. f416=1. f417=1. f420=1. f421=1. f427=1. f430=1. f431=1. f432=1. f433=1. f434=1. f435=1. f437=1. f439=1. f440=1. f441=1. f443=1. f453=1. f454=1. f456=1. f457=1. f458=1. f459=1. f460=1. f464=1. f465=1. f466=1. f467=1. f468=1. f469=1. f472=1. f473=1. f479=1. f488=1. f489=1. f490=1. f493=1. f494=1. f495=1. f496=1. f503=1. f504=1. f506=1. f507=1. f508=1. f509=1. f510=1. f512=1. f517=1. f520=1. f521=1. f523=1. f527=1. f528=1. f529=1. f530=1. f531=1. f532=1. f533=1. f534=1. f535=1. f538=1. f542=1. f543=1. f544=1. f545=1. f548=1. f549=1. f550=1. f551=1. f552=1. f557=1. f563=1. f564=1. f565=1. f566=1. f567=1. f12=1. f13=1. f28=1. f29=1. f34=1. f41=1. f42=1. f57=1. f58=1. f62=1. f66=1. f74=1. f75=1. f93=1. f94=1. f98=1. f101=1. f102=1. f103=1. f104=1. f114=1. f115=1. f131=1. f138=1. f145=1. f155=1. f184=1. f189=1. f190=1. f191=1. f198=1. f199=1. f201=1. f205=1. f206=1. f207=1. f210=1. f219=1. f220=1. f227=1. f228=1. f234=1. f289=1. f290=1. f291=1. f293=1. f294=1. f295=1. f317=1. f347=1. f348=1. f350=1. f351=1. f352=1. f366=1. f367=1. f379=1. f389=1. f390=1. f396=1. f397=1. f398=1. f401=1. f422=1. f423=1. f424=1. f438=1. f444=1. f445=1. f446=1. f452=1. f461=1. f462=1. f463=1. f476=1. f477=1. f478=1. f499=1. f511=1. f522=1. f524=1. f525=1. f526=1. f555=1. f556=1. f562=1. f241=1. f283=1. f331=1. f332=1. f358=1. f359=1. f32=1. f124=1. f125=1. f126=1. f127=1. f221=1. f222=1. f223=1. f224=1. f243=1. f244=1. f245=1. f246=1. f267=1. f268=1. f269=1. f270=1. f419=1. 24.85/25.04 24.85/25.04 ============================== end of process initial clauses ======== 24.85/25.04 24.85/25.04 ============================== CLAUSES FOR SEARCH ==================== 24.85/25.04 24.85/25.04 ============================== end of clauses for search ============= 24.85/25.04 24.85/25.04 ============================== SEARCH ================================ 24.85/25.04 24.85/25.04 % Starting search at 4.02 seconds. 24.85/25.04 24.85/25.04 Low Water (keep): wt=116.000, iters=3427 24.85/25.04 24.85/25.04 Low Water (keep): wt=90.000, iters=3365 24.85/25.04 24.85/25.04 Low Water (keep): wt=85.000, iters=3604 24.85/25.04 24.85/25.04 Low Water (keep): wt=70.000, iters=4946 24.85/25.04 24.85/25.04 Low Water (keep): wt=64.000, iters=3945 24.85/25.04 24.85/25.04 ============================== STATISTICS ============================ 24.85/25.04 24.85/25.04 Given=390. Generated=28033. Kept=8134. proofs=0. 24.85/25.04 Usable=390. Sos=7065. Demods=179. Limbo=15, Disabled=3360. Hints=0. 24.85/25.04 Kept_by_rule=0, Deleted_by_rule=0. 24.85/25.04 Forward_subsumed=19815. Back_subsumed=633. 24.85/25.04 Sos_limit_deleted=84. Sos_displaced=0. Sos_removed=0. 24.85/25.04 New_demodulators=182 (1 lex), Back_demodulated=25. Back_unit_deleted=5. 24.85/25.04 Demod_attempts=1159942. Demod_rewrites=1567. 24.85/25.04 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 24.85/25.04 Nonunit_fsub_feature_tests=66371. Nonunit_bsub_feature_tests=39418. 24.85/25.04 Megabytes=419.43. 24.85/25.04 User_CPU=22.56, System_CPU=0.13, Wall_clock=23. 24.85/25.04 24.85/25.04 Megs malloced by palloc(): 400. 24.85/25.04 type (bytes each) gets frees in use bytes 24.85/25.04 chunk ( 104) 63279 63279 0 0.0 K 24.85/25.04 string_buf ( 8) 52824 52824 0 0.0 K 24.85/25.04 token ( 20) 143912 143912 0 0.0 K 24.85/25.04 pterm ( 16) 82728 82728 0 0.0 K 24.85/25.04 hashtab ( 8) 1517 1517 0 0.0 K 24.85/25.04 hashnode ( 8) 6222 6222 0 0.0 K 24.85/25.04 term ( 20) 2025245 1681892 343353 6706.1 K 24.85/25.04 term arg arrays: 1738.1 K 24.85/25.04 attribute ( 12) 14871 418 14453 169.4 K 24.85/25.04 ilist ( 8) 205838594 205810146 28448 222.2 K 24.85/25.04 plist ( 8) 112432 77688 34744 271.4 K 24.85/25.04 i2list ( 12) 198973 198973 0 0.0 K 24.85/25.04 just ( 12) 50138 33419 16719 195.9 K 24.85/25.04 parajust ( 16) 108 72 36 0.6 K 24.85/25.04 instancejust ( 8) 0 0 0 0.0 K 24.85/25.04 ivyjust ( 24) 0 0 0 0.0 K 24.85/25.04 formula ( 28) 66190 43544 22646 619.2 K 24.85/25.04 formula arg arrays: 76.6 K 24.85/25.04 topform ( 52) 32247 19899 12348 627.0 K 24.85/25.04 clist_pos ( 20) 22880 11871 11009 215.0 K 24.85/25.04 clist ( 16) 8 1 7 0.1 K 24.85/25.04 context ( 808) 477089 477088 1 0.8 K 24.85/25.04 trail ( 12) 2178030 2178030 0 0.0 K 24.85/25.04 ac_match_pos (70044) 0 0 0 0.0 K 24.85/25.04 ac_match_free_vars_pos (20020) 24.85/25.04 0 0 0 0.0 K 24.85/25.04 btm_state ( 60) 0 0 0 0.0 K 24.85/25.04 btu_state ( 60) 0 0 0 0.0 K 24.85/25.04 ac_position (285432) 0 0 0 0.0 K 24.85/25.04 fpa_trie ( 20) 78363 646 77717 1517.9 K 24.85/25.04 fpa_state ( 28) 13345 13345 0 0.0 K 24.85/25.04 fpa_index ( 12) 10 0 10 0.1 K 24.85/25.04 fpa_chunk ( 20) 83705 33033 50672 989.7 K 24.85/25.04 fpa_list ( 16) 31207 0 31207 487.6 K 24.85/25.04 fpa_list chunks: 3093.9 K 24.85/25.04 discrim ( 12) 3740 67 3673 43.0 K 24.85/25.04 discrim_pos ( 16) 2622 2622 0 0.0 K 24.85/25.04 flat2 ( 32) 983589 983589 0 0.0 K 24.85/25.04 flat ( 48) 0 0 0 0.0 K 24.85/25.04 flatterm ( 32) 1914178 1914178 0 0.0 K 24.85/25.04 mindex ( 28) 13 0 13 0.4 K 24.85/25.04 mindex_pos ( 56) 301484 301484 0 0.0 K 24.85/25.04 lindex ( 12) 5 0 5 0.1 K 24.85/25.04 clash ( 40) 0 0 0 0.0 K 24.85/25.04 di_tree ( 12) 36544015 3129654 33414361 391574.5 K 24.85/25.04 avl_node ( 20) 13486 1649 11837 231.2 K 24.85/25.04 24.85/25.04 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 24.85/25.04 List 1, length 7, 0.0 K 24.85/25.04 List 4, length 3, 0.0 K 24.85/25.04 List 5, length 8, 0.2 K 24.85/25.04 List 7, length 25, 0.7 K 24.85/25.04 List 8, length 25, 0.8 K 24.85/25.04 List 9, length 2, 0.1 K 24.85/25.04 List 10, length 2, 0.1 K 24.85/25.04 List 11, length 1, 0.0 K 24.85/25.04 List 12, length 2, 0.1 K 24.85/25.04 List 14, length 4, 0.2 K 24.85/25.04 List 15, length 2, 0.1 K 24.85/25.04 List 16, length 4, 0.2 K 24.85/25.04 List 21, length 2, 0.2 K 24.85/25.04 List 23, length 2, 0.2 K 24.85/25.04 List 26, length 143, 14.5 K 24.85/25.04 List 32, length 132, 16.5 K 24.85/25.04 List 202, length 3, 2.4 K 24.85/25.04 24.85/25.04 ============================== SELECTOR REPORT ======================= 24.85/25.04 Sos_deleted=84, Sos_displaced=0, Sos_size=7065 24.85/25.04 SELECTOR PART PRIORITY ORDER SIZE SELECTED 24.85/25.04 I 2147483647 high age 2293 390 24.85/25.04 H 1 high weight 0 0 24.85/25.04 A 1 low age 4772 0 24.85/25.04 F 4 low weight 2 0 24.85/25.04 T 4 low weight 4770 0 24.85/25.04 ============================== end of selector report ================ 24.85/25.04 24.85/25.04 ============================== end of statistics ===================== 24.85/25.04 24.85/25.04 Exiting with failure. 24.85/25.04 24.85/25.04 Process 25699 exit (max_megs) Tue Jul 13 16:51:13 2021 24.85/25.04 Prover9 interrupted 24.85/25.04 EOF