0.10/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.36 % Computer : n013.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % DateTime : Thu Jul 2 14:43:03 EDT 2020 0.14/0.36 % CPUTime : 1.61/2.02 ============================== Prover9 =============================== 1.61/2.02 Prover9 (32) version 2009-11A, November 2009. 1.61/2.02 Process 11861 was started by sandbox2 on n013.cluster.edu, 1.61/2.02 Thu Jul 2 14:43:05 2020 1.61/2.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_11702_n013.cluster.edu". 1.61/2.02 ============================== end of head =========================== 1.61/2.02 1.61/2.02 ============================== INPUT ================================= 1.61/2.02 1.61/2.02 % Reading from file /tmp/Prover9_11702_n013.cluster.edu 1.61/2.02 1.61/2.02 set(prolog_style_variables). 1.61/2.02 set(auto2). 1.61/2.02 % set(auto2) -> set(auto). 1.61/2.02 % set(auto) -> set(auto_inference). 1.61/2.02 % set(auto) -> set(auto_setup). 1.61/2.02 % set(auto_setup) -> set(predicate_elim). 1.61/2.02 % set(auto_setup) -> assign(eq_defs, unfold). 1.61/2.02 % set(auto) -> set(auto_limits). 1.61/2.02 % set(auto_limits) -> assign(max_weight, "100.000"). 1.61/2.02 % set(auto_limits) -> assign(sos_limit, 20000). 1.61/2.02 % set(auto) -> set(auto_denials). 1.61/2.02 % set(auto) -> set(auto_process). 1.61/2.02 % set(auto2) -> assign(new_constants, 1). 1.61/2.02 % set(auto2) -> assign(fold_denial_max, 3). 1.61/2.02 % set(auto2) -> assign(max_weight, "200.000"). 1.61/2.02 % set(auto2) -> assign(max_hours, 1). 1.61/2.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.61/2.02 % set(auto2) -> assign(max_seconds, 0). 1.61/2.02 % set(auto2) -> assign(max_minutes, 5). 1.61/2.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.61/2.02 % set(auto2) -> set(sort_initial_sos). 1.61/2.02 % set(auto2) -> assign(sos_limit, -1). 1.61/2.02 % set(auto2) -> assign(lrs_ticks, 3000). 1.61/2.02 % set(auto2) -> assign(max_megs, 400). 1.61/2.02 % set(auto2) -> assign(stats, some). 1.61/2.02 % set(auto2) -> clear(echo_input). 1.61/2.02 % set(auto2) -> set(quiet). 1.61/2.02 % set(auto2) -> clear(print_initial_clauses). 1.61/2.02 % set(auto2) -> clear(print_given). 1.61/2.02 assign(lrs_ticks,-1). 1.61/2.02 assign(sos_limit,10000). 1.61/2.02 assign(order,kbo). 1.61/2.02 set(lex_order_vars). 1.61/2.02 clear(print_given). 1.61/2.02 1.61/2.02 % formulas(sos). % not echoed (1012 formulas) 1.61/2.02 1.61/2.02 ============================== end of input ========================== 1.61/2.02 1.61/2.02 % From the command line: assign(max_seconds, 960). 1.61/2.02 1.61/2.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.61/2.02 1.61/2.02 % Formulas that are not ordinary clauses: 1.61/2.02 1 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,hAPP_f118515775l_bool(cOMBK_1028572856l_bool,B_1)))))) # label(fact_210_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 2 (all Fa all I_4 (hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_4)) <-> (all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof)) -> hAPP_A340536322t_bool(X_2,I_4) = hAPP_f1817389232t_bool(Fa,X_2)))))) # label(fact_81_dictator__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 3 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (hBOOL(hAPP_f1472889102l_bool(hAPP_l1197505987l_bool(member1245674225le_alt,X_2),set_li1879521523le_alt(Xs))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_1),Z)),R_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Z)),R_1)))))) -> (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) -> (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Ys_1),Zs_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Zs_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))))))) # label(fact_623_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 4 (all F all Aa all Ba (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))))) # label(fact_437_splitI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 5 (all B_1_1 all B_2_1 is_bool(hAPP_f640821677l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_030) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 6 (all Xs (Xs != nil_Ar1135217151le_alt -> (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) -> butlas123970891le_alt(Xs) = takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),last_A1066338328le_alt(Xs))),Xs)))) # label(fact_336_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 7 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))))) # label(fact_226_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 8 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_011) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 9 (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,M_1),suc(N_1))))) # label(fact_675_less__SucI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 10 (all Xs all Ys_1 all Zs_1 all Ts (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Ts) <-> (exists Us (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Us) = Xs & Ts = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),Ys_1) | Zs_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Us) & hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),Ts) = Ys_1)))) # label(fact_371_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 11 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),hAPP_f1741989420t_bool(B_1,X_1)))))) # label(fact_131_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 12 (all Ca all P_1 (is_Pro1004667236le_alt(P_1) -> (hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(Ca),P_1)) -> -(all X_2 all Y_1 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_1) -> (P_1 = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1) -> -hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(Ca,X_2),Y_1)))))))) # label(fact_445_splitE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 13 (all Xs (nil_Ar1135217151le_alt = Xs <-> hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs)))) # label(fact_281_eq__Nil__null) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 14 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B_1,X_1)))))) # label(fact_151_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 15 (all X_1 hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),top_to935749874l_bool))) # label(fact_327_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 16 (all F all Aa all Ba (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))))) # label(fact_286_curryE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 17 (all Nat_1 all Nat (suc(Nat) = suc(Nat_1) <-> Nat_1 = Nat)) # label(fact_656_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 18 (all X_1 all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Xs)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))))) # label(fact_536_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 19 (all P all Q (is_fun1651000642t_bool(P) -> hAPP_f1741989420t_bool(hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___117) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 20 (all X_1 hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),top_to818291475t_bool))) # label(fact_322_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 21 (all Xs_38 splice1369921490le_alt(Xs_38,nil_Ar1135217151le_alt) = Xs_38) # label(fact_118_splice__Nil2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 22 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),hAPP_f1741989420t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))))) # label(fact_163_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 23 (all B_1_1 is_Pro1004667236le_alt(last_P15572062le_alt(B_1_1))) # label(gsy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oal) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 24 (all Xs (nil_Pr1710246567le_alt != Xs -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hd_Pro53798164le_alt(Xs)),set_Pr1756729158le_alt(Xs))))) # label(fact_590_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 25 (all X_1 all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> rev_Ar955429983le_alt(tl_Arr314474198le_alt(dropWh1165804960le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),Xs))) = takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),rev_Ar955429983le_alt(Xs))))) # label(fact_497_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 26 (all Xs list_c1434691767le_alt(nil_Ar1135217151le_alt,hAPP_f904937452le_alt(hAPP_f239458941le_alt(cOMBB_521986850le_alt,hAPP_f268020663le_alt(cOMBC_168079159le_alt,append28105492le_alt)),hAPP_l1693669363le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,cons_A77766063le_alt),nil_Ar1135217151le_alt)),Xs) = rotate184372300le_alt(Xs)) # label(fact_404_rotate1__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 27 (all A_7 all B_5 all A_6 all B_4 (is_Arr723427730le_alt(B_5) & is_Arr723427730le_alt(B_4) & is_Arr723427730le_alt(A_6) & is_Arr723427730le_alt(A_7) -> (hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_6),B_4) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_7),B_5) -> -(A_7 = A_6 -> B_5 != B_4)))) # label(fact_18_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 28 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),hAPP_f1329247136t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))))) # label(fact_223_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 29 (all B_1_1 is_Arr859726945e_indi(hd_Arr1280875809e_indi(B_1_1))) # label(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 30 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 31 (all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> size_s2106320494le_alt(Xs) = size_s2106320494le_alt(Ys_1))) # label(fact_456_listrel__eq__len) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 32 (all Xs all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Xs)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> Xs = nil_Ar1135217151le_alt)) # label(fact_451_listrel__Nil1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 33 (all P all Q (is_fun_bool_bool(P) -> P = hAPP_f591334822l_bool(hAPP_f498119908l_bool(cOMBK_874213703t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_098) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 34 (all P_2 (is_Pro1004667236le_alt(P_2) -> -(all X_2 all Y_1 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_1) -> P_2 != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1))))) # label(fact_259_PairE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 35 (all X_1 all Xs (hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> rev_fu580432980t_bool(tl_fun1512606109t_bool(dropWh1122107731t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),Xs))) = takeWh1268567035t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),rev_fu580432980t_bool(Xs))))) # label(fact_501_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 36 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> M_1 = N_1))) # label(fact_669_le__antisym) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 37 (all Xs all Pa all X_1 ((-hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) & (hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> dropWh1165804960le_alt(Pa,Xs) = dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs))))) # label(fact_427_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.02 38 (all X_1 all Xs (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) & hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs)) <-> hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs))))) # label(fact_560_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 39 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),hAPP_b805997823l_bool(B_1,X_1)))))) # label(fact_145_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 40 (all P all Q all R hAPP_f446648900l_bool(hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,P),Q),R) = hAPP_f446648900l_bool(hAPP_f656614015l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 41 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),hAPP_f1681297285t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))))) # label(fact_227_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 42 (all Pa all Xs hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,takeWh1545314552le_alt(Pa,Xs)),dropWh1165804960le_alt(Pa,Xs)) = Xs) # label(fact_433_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 43 (all Aa all X_1 all Ba all Y_2 all R_1 (is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),X_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Ba),Y_2))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) & Ba = Aa | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),R_1))))) # label(fact_291_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 44 (all B_1_1 all B_2_1 is_bool(hAPP_f1291635206l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_043) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 45 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),hAPP_f591334822l_bool(B_1,X_1)))))) # label(fact_126_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 46 (all X_18 all Xs_36 -hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_18),Xs_36)))) # label(fact_282_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 47 (all B_1_1 all B_2_1 is_bool(hAPP_l479254477i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 48 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),hAPP_b763490121t_bool(B_1,X_1)))))) # label(fact_138_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 49 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> Xs = insert_bool(X_1,Xs))) # label(fact_551_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 50 (all P all Q all R hAPP_P2032392041l_bool(P,hAPP_l591780830le_alt(Q,R)) = hAPP_l1493471510l_bool(hAPP_f622637325l_bool(hAPP_f1224738111l_bool(cOMBB_1407335828le_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]. 1.61/2.03 51 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,hAPP_f206814660l_bool(cOMBK_472365180e_indi,B_1)))))) # label(fact_212_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 52 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> (-hBOOL(hAPP_f1733357041l_bool(Pa,X_1)) -> takeWh572506194t_bool(Pa,Xs) = takeWh572506194t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1))))) # label(fact_569_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 53 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))))) # label(fact_236_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 54 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))))) # label(fact_245_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 55 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B_1)))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B_1))))) # label(fact_114_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 56 (all B_1_1 is_Pro1004667236le_alt(hd_Pro804272676le_alt(B_1_1))) # label(gsy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 57 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),hAPP_P1533476044l_bool(B_1,X_2))))) -> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))))) # label(fact_180_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 58 (all Fa (hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa)) <-> (all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof)) -> (all Xa (is_fun1264457267t_bool(Xa) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof)) -> (all A all B (is_Arr723427730le_alt(B) & is_Arr723427730le_alt(A) -> ((all I (is_Arr859726945e_indi(I) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(Xa,I)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,Xa))))))))))))))) # label(fact_32_IIA__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 59 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))))) # label(fact_174_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 60 (all X_1 all N all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(hAPP_l342779967t_bool(hAPP_n2058955628t_bool(drop_f1849462169t_bool,N),Xs)))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))))) # label(fact_520_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 61 (all B_1_1 all B_2_1 is_fun20916972t_bool(hAPP_P651748559t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_085) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 62 (all U all X_1 all Y_2 all Aa all Ba all R_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),R_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,U),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),X_1))),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,U),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Ba),Y_2)))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))) # label(fact_395_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 63 (exists X_2 (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),top_to186242507t_bool)) & is_Arr723427730le_alt(X_2))) # label(fact_358_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 64 (all Xs (Xs != nil_fu247759878t_bool -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hd_fun780865267t_bool(Xs)),set_fu222164517t_bool(Xs))))) # label(fact_595_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 65 (all F all Aa all Ba (hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) -> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F,Aa),Ba)))) # label(fact_441_splitD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 66 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_012) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 67 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_687_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 68 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,hAPP_f1228246954t_bool(cOMBK_906927855t_bool,B_1)))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),B_1))))) # label(fact_96_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 69 (all X_1 all Xs (hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs)) & -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) <-> hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs))))) # label(fact_557_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 70 (all P all Q (is_fun292781289l_bool(P) -> P = hAPP_b651754310l_bool(hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 71 (all X all Y (Y != X -> (-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_660_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 72 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,hAPP_f1274922098i_bool(cOMBK_948333518t_bool,B_1)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),B_1))))) # label(fact_87_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 73 (all X_1 hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),top_to207207712i_bool))) # label(fact_316_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 74 (all B_1_1 is_fun1264457267t_bool(hd_fun780865267t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 75 (all B_1_1 all B_2_1 is_bool(hAPP_f1422872597l_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]. 1.61/2.03 76 (all X_1 all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> insert1969589781le_alt(X_1,Xs) = Xs)) # label(fact_548_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 77 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))))) # label(fact_153_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 78 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),hAPP_A1014090479t_bool(B_1,X_1))) -> -hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))))) # label(fact_47_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 79 (all X_1 all Xs ((hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> insert1731565726e_indi(X_1,Xs) = Xs) & (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs) = insert1731565726e_indi(X_1,Xs)))) # label(fact_607_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 80 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B_1)))))) # label(fact_215_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 81 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),hAPP_b1461182872l_bool(B_1,X_1))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))))) # label(fact_54_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 82 (all X_1 all Xs (hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> dropWh1122107731t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),rev_fu580432980t_bool(Xs)) = hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),rev_fu580432980t_bool(takeWh1268567035t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),Xs)))))) # label(fact_509_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 83 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Ys_1)))) | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Xs)))) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1))))))) # label(fact_583_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 84 (all X_1 all A_1 (hBOOL(hAPP_P1373277879t_bool(A_1,X_1)) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)))) # label(fact_266_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 85 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),hAPP_A1014090479t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))))) # label(fact_233_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 86 (all P all Q (is_fun20916972t_bool(P) -> P = hAPP_P651748559t_bool(hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_106) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 87 (all B_1_1 is_fun20916972t_bool(set_Pr2031705942le_alt(B_1_1))) # label(gsy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 88 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),hAPP_f431432850i_bool(B_1,X_1)))))) # label(fact_128_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 89 (all X_1 all Xs (hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs)) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> rev_Pr816629831le_alt(tl_Pro645285392le_alt(dropWh1957015750le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),Xs))) = takeWh768831342le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),rev_Pr816629831le_alt(Xs))))) # label(fact_498_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 90 (all B_1_1 is_fun48324065t_bool(hd_fun1289819809t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 91 (all Pa all M all N ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> ((N = M -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)))))) # label(fact_664_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 92 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))))) # label(fact_168_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 93 (all Xs all R_1 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Xs)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))) # label(fact_409_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 94 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_1_1) -> is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 95 (all B_1_1 all B_2_1 (is_fun292781289l_bool(B_2_1) -> is_fun292781289l_bool(hAPP_f1028172757l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_047) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 96 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,B_1)))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),B_1))))) # label(fact_109_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 97 (all M_1 all N_1 (N_1 = M_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_667_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 98 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),hAPP_P1116266031t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))))) # label(fact_218_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 99 (all B_1_1 all B_2_1 is_bool(hAPP_f620747982l_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]. 1.61/2.03 100 (all Xs_40 all X_22 Xs_40 != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_22),Xs_40)) # label(fact_43_not__Cons__self) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 101 (all X_1 all Xs (rev_Ar955429983le_alt(Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt) <-> Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt))) # label(fact_493_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 102 (all Xs all R_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),X_2)),R_1)))) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Xs)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))) # label(fact_311_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 103 (all B_1 all G all F all A_1 ((all W (is_Pro1004667236le_alt(W) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A_1)) -> (hBOOL(hAPP_P1813625415t_bool(G,W)) <-> hBOOL(hAPP_P1813625415t_bool(F,W)))))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))) <-> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A_1,B_1)))))) # label(fact_251_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 104 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_fun48324065t_bool(X_2) & is_fun48324065t_bool(Y_1) & is_fun48324065t_bool(Z) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs))) -> (hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,Y_1),Z)),R_1)) -> hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Xs),Ys_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1))) -> (hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Ys_1),Zs_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1))) -> hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Xs),Zs_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1))))))) # label(fact_627_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 105 (all Y_5 (nil_Ar1135217151le_alt != Y_5 -> -(all A all List (is_Arr723427730le_alt(A) -> Y_5 != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),List))))) # label(fact_79_list_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 106 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,B_1)))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),B_1))))) # label(fact_94_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 107 (all X_1 all Xs (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs) = insert1683711393le_alt(X_1,Xs))) # label(fact_620_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 108 (all B_1_1 all B_2_1 is_Pro1004667236le_alt(hAPP_P802532161le_alt(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_086) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 109 (all X_1 hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),top_to207207712i_bool))) # label(fact_324_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 110 (all Y_2 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) <-> (exists A exists X_2 (is_Arr723427730le_alt(A) & hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),X_2) = Y_2)))) # label(fact_309_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 111 (all P all Q (is_fun_bool_bool(P) -> P = hAPP_f721327224l_bool(hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_116) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 112 (all B_1_1 (is_fun292781289l_bool(B_1_1) -> is_fun292781289l_bool(collec1517527055t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 113 (all X_1 hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),top_to935749874l_bool))) # label(fact_319_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 114 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__024) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 115 (all X all Y (X = Y | -hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y)))) # label(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 116 (all B_1_1 all B_2_1 is_fun48324065t_bool(hAPP_P482525630t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_082) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 117 (all P all Q (is_fun20916972t_bool(P) -> P = hAPP_A1014090479t_bool(hAPP_f102394819t_bool(cOMBK_78615028le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_089) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 118 (all F all Aa all Ba (hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) <-> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba)))) # label(fact_287_curry__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 119 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),hAPP_A701636433l_bool(B_1,X_1))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))))) # label(fact_52_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 120 (all Xs_20 all Ys_6 (nil_Ar1135217151le_alt = Ys_6 -> last_A1066338328le_alt(Xs_20) = last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_20),Ys_6)))) # label(fact_391_last__appendL) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 121 (all X all Y hAPP_P2096362161le_alt(hAPP_P1891191097le_alt(if_Pro1659200999le_alt(fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 122 (all B_1_1 all B_2_1 is_bool(hAPP_l1936415565l_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]. 1.61/2.03 123 (exists X_2 hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),top_to818291475t_bool))) # label(fact_355_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 124 (all X_7 hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_7),X_7))) # label(fact_475_equal__refl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 125 (all Xs all Pa all X_1 ((hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),takeWh1545314552le_alt(Pa,Xs))) & (-hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = nil_Ar1135217151le_alt))) # label(fact_340_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 126 (all X_1 all N all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N),Xs)))) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))))) # label(fact_515_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 127 (all P all Q all R hAPP_l486475401le_alt(hAPP_f593033837le_alt(hAPP_f332249751le_alt(cOMBB_96247696le_alt,P),Q),R) = hAPP_f879032165le_alt(P,hAPP_l1148780281le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_128) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 128 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__027) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 129 (all B_1_1 all B_2_1 is_fun1264457267t_bool(hAPP_P1689126160t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_080) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 130 (all B_1_1 all B_2_1 is_bool(hAPP_f1134444118l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_029) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 131 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M)),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_697_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 132 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),hAPP_P1436281263t_bool(B_1,X_1)))))) # label(fact_122_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 133 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,hAPP_f1954218281l_bool(cOMBK_549130676le_alt,B_1)))))) # label(fact_208_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 134 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1264457267t_bool(hAPP_b821377302t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls_015) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 135 (all X_1 all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> ((all Y_1 (is_Arr723427730le_alt(Y_1) -> (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Xs) = Ys_1 -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_1)),R_1))))) -> -(all Zs (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Zs) = Ys_1 -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Zs)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))))))) # label(fact_420_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 136 (all X_1 all Xs (hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs))) <-> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) & hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs)))) # label(fact_558_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 137 (all X_9 all Xs_16 tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_9),Xs_16)) = Xs_16) # label(fact_452_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 138 (all X_1 (hBOOL(top_top_bool) <-> hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_1)))) # label(fact_333_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 139 (all X_19 all Xs_37 (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_37)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,insert1969589781le_alt(X_19,Xs_37))))) # label(fact_263_distinct__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 140 (all Ys_1 all Xs all Zs_1 (Zs_1 = Ys_1 <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Xs) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Xs))) # label(fact_369_append__same__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 141 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),hAPP_P1533476044l_bool(B_1,X_1))) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))))) # label(fact_60_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 142 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Xs)))) | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Ys_1)))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1))))))) # label(fact_588_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 143 (all B_1_1 (is_fun1651000642t_bool(B_1_1) -> is_fun1420103068l_bool(order_1844940151le_alt(B_1_1)))) # label(gsy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 144 (all P all Q (is_fun2015243113i_bool(P) -> hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___096) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 145 (all B_1_1 all B_2_1 is_bool(hAPP_f890578273l_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]. 1.61/2.03 146 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),B_1))))) # label(fact_101_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 147 (all X_1 hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),top_to1849101472l_bool))) # label(fact_321_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 148 (all X_1 all Xs all Y_2 all Ys_1 all R_1 (is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(X_1) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) & X_1 = Y_2 | size_s2106320494le_alt(Ys_1) = size_s2106320494le_alt(Xs) & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))))) # label(fact_424_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 149 (all P all Q all R hAPP_A1120018583t_bool(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_A1120018583t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 150 (all X_1 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),top_to1773227171t_bool))) # label(fact_318_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 151 (all Xs all X_1 all Ys_1 (is_Arr723427730le_alt(X_1) -> (Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt)) <-> Ys_1 != nil_Ar1135217151le_alt & last_A1066338328le_alt(Ys_1) = X_1 & butlas123970891le_alt(Ys_1) = Xs))) # label(fact_365_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 152 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f812095627l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___068) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 153 (all K all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K))))) # label(fact_668_le__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 154 (all P all Q (is_fun1420103068l_bool(P) -> hAPP_P467353593l_bool(hAPP_f905851705l_bool(cOMBK_740566962le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_109) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 155 (all X_1 all Pa all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(takeWh572506194t_bool(Pa,Xs)))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) & hBOOL(hAPP_f1733357041l_bool(Pa,X_1)))) # label(fact_528_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 156 (all P all Q all R hAPP_l1791846092le_alt(hAPP_f1291634731le_alt(hAPP_f1654251593le_alt(cOMBB_1675847172le_alt,P),Q),R) = hAPP_P1891191097le_alt(P,hAPP_l591780830le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_126) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 157 (all X_1 hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_1))) # label(fact_297_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 158 (all P all Q all R hAPP_l1748807729l_bool(hAPP_f1893731349l_bool(hAPP_f1418100887l_bool(cOMBB_1150645560le_alt,P),Q),R) = hAPP_f622637325l_bool(P,hAPP_l1148780281le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 159 (all Xs all Ys_1 list_c1434691767le_alt(tl_Arr314474198le_alt(Ys_1),hAPP_f921948995le_alt(cOMBK_1825575856le_alt,hAPP_l1390889510le_alt(hAPP_f268020663le_alt(cOMBC_168079159le_alt,append28105492le_alt),Ys_1)),Xs) = tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))) # label(fact_449_tl__append) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 160 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f591334822l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__025) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 161 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_1),Y_2)))) # label(fact_476_equal__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 162 (all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> Xs = insert1409495663t_bool(X_1,Xs))) # label(fact_553_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 163 (all X_1 all Xs all Y_2 all Ys_1 all R_1 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) -> (Y_2 = X_1 & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) & Xs = Ys_1 <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))))) # label(fact_412_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 164 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,hAPP_f1698272152t_bool(cOMBK_242036279t_bool,B_1)))))) # label(fact_188_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 165 (all N_1 suc(N_1) != N_1) # label(fact_655_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 166 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> (-hBOOL(hAPP_f1378099862l_bool(Pa,X_1)) -> takeWh1813199437t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)) = takeWh1813199437t_bool(Pa,Xs)))) # label(fact_570_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 167 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Xs)))) | hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Ys_1)))) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))))))) # label(fact_581_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 168 (all B_1_1 all B_2_1 is_bool(hAPP_f704486919l_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]. 1.61/2.03 169 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,hAPP_f342341961t_bool(cOMBK_980874600le_alt,B_1)))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),B_1))))) # label(fact_83_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 170 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,B_1)))))) # label(fact_187_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 171 (all X_1 all A_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) <-> hBOOL(hAPP_f446648900l_bool(A_1,X_1)))) # label(fact_271_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 172 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),hAPP_f783549695i_bool(B_1,X_1)))))) # label(fact_132_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 173 (all Ys_1 all Pa all Xs ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs))) -> hBOOL(hAPP_f446648900l_bool(Pa,X_2))))) -> dropWh1122107731t_bool(Pa,Ys_1) = dropWh1122107731t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)))) # label(fact_635_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 174 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun48324065t_bool(hAPP_A88621982t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_004) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 175 (all B_1_1 is_Arr723427730le_alt(last_A1066338328le_alt(B_1_1))) # label(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 176 (all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> Xs = insert531176721le_alt(X_1,Xs))) # label(fact_549_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 177 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_1_1) -> is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 178 (all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> size_s2106320494le_alt(Ys_1) = size_s2106320494le_alt(Xs))) # label(fact_432_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 179 (all B_1_1 (is_fun20916972t_bool(B_1_1) -> is_fun866579754t_bool(in_rel1361124802le_alt(B_1_1)))) # label(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 180 (all Xs all Ys_1 all X_1 all Y_2 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) -> (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))))) # label(fact_448_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 181 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),hAPP_f783549695i_bool(B_1,X_1))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))))) # label(fact_74_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 182 (all F all Aa all Ba (hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) -> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba)))) # label(fact_277_curryI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 183 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> (-hBOOL(hAPP_A416869060i_bool(Pa,X_1)) -> takeWh1088896635e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = takeWh1088896635e_indi(Pa,Xs)))) # label(fact_566_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 184 (all Y_2 all X_1 all Xs (is_fun20916972t_bool(X_1) & is_fun20916972t_bool(Y_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Y_2),set_fu444796538t_bool(hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs)))) -> Y_2 = X_1 | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Y_2),set_fu444796538t_bool(Xs)))))) # label(fact_545_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 185 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_fun701126715l_bool(hAPP_f1901083135l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__026) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 186 (all P all Q all R hAPP_l2066632447t_bool(hAPP_f1895633847t_bool(hAPP_f1997384703t_bool(cOMBC_1696964078t_bool,P),Q),R) = hAPP_f4315714t_bool(hAPP_l2144750563t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_111) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 187 (all X_1 all A_1 (hBOOL(hAPP_A416869060i_bool(A_1,X_1)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)))) # label(fact_265_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 188 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun1651000642t_bool(hAPP_f1068593625t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___064) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 189 (all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) <-> (exists Ys exists Zs Xs = hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Ys),hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Zs))))) # label(fact_649_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 190 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (suc(M_1) != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1))))) # label(fact_674_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 191 (all Pa all X_1 all Xs hAPP_P2096362161le_alt(produc1250814607le_alt(hAPP_f794134621le_alt(hAPP_f2122335314le_alt(cOMBS_1569784209le_alt,hAPP_f310101886le_alt(hAPP_f1558754397le_alt(cOMBB_1988247237le_alt,cOMBS_1626428525le_alt),hAPP_f1504748473le_alt(hAPP_f1949171529le_alt(cOMBB_215060470le_alt,hAPP_f1654251593le_alt(cOMBB_1675847172le_alt,if_Pro1659200999le_alt(hAPP_A1120018583t_bool(Pa,X_1)))),hAPP_f670565125le_alt(hAPP_f1124725731le_alt(cOMBB_1236261828le_alt,produc2031778509le_alt),hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1))))),hAPP_f670565125le_alt(hAPP_f351228915le_alt(cOMBC_72147604le_alt,hAPP_f593033837le_alt(hAPP_f332249751le_alt(cOMBB_96247696le_alt,cOMBB_1303549321le_alt),produc2031778509le_alt)),hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1)))),partit1336600824le_alt(Pa,Xs)) = partit1336600824le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs))) # label(fact_426_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 192 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_Pro1004667236le_alt(hAPP_A503573454le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__prod_I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 193 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) & hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)))) # label(fact_559_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 194 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___062) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 195 (all B_1_1 all B_2_1 is_bool(hAPP_l300482276t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 196 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,hAPP_f905851705l_bool(cOMBK_740566962le_alt,B_1)))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),B_1))))) # label(fact_107_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 197 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),B_1)))) -> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,hAPP_f1197671953l_bool(cOMBK_165199855le_alt,B_1)))))) # label(fact_213_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 198 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),hAPP_f3167870t_bool(B_1,X_1)))))) # label(fact_123_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 199 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___070) # label(axiom) # label(non_clause). [assumption]. 1.61/2.03 200 (all Aa all X_1 all Ba all Y_2 all R_1 (Aa = Ba & hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_1),Y_2)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) | hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)),R_1)) <-> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Aa),X_1)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Ba),Y_2))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))))) # label(fact_290_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 201 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))))) # label(fact_222_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 202 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),hAPP_P651748559t_bool(B_1,X_2))))) -> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))))) # label(fact_235_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 203 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),hAPP_f1741989420t_bool(B_1,X_1))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))))) # label(fact_73_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 204 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,hAPP_f684471657t_bool(cOMBK_509674590t_bool,B_1)))))) # label(fact_194_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 205 (all Ys_16 all Us_2 all Xs_29 all Xs1_1 all Zs_4 (Zs_4 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_29),Xs1_1) -> (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs1_1),Us_2) = Ys_16 -> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_29),Ys_16) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_4),Us_2)))) # label(fact_368_append__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 206 (all B_1_1 all B_2_1 is_bool(hAPP_f1720639399l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 207 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),hAPP_A1745457982l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))))) # label(fact_171_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 208 (all X_1 all Xs (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> insert531176721le_alt(X_1,Xs) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs))) # label(fact_614_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 209 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_1_1) -> is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 210 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_fun1651000642t_bool(hAPP_f3167870t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__023) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 211 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),hAPP_f3167870t_bool(B_1,X_1))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))))) # label(fact_65_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 212 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),hAPP_b763490121t_bool(B_1,X_1))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))))) # label(fact_50_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 213 (all Pa ((all X1 hBOOL(hAPP_P1373277879t_bool(Pa,X1))) <-> (all A all B hBOOL(hAPP_P1373277879t_bool(Pa,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B)))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 214 (all Xs all Ys_1 (nil_Ar1135217151le_alt = Xs & Ys_1 = nil_Ar1135217151le_alt <-> nil_Ar1135217151le_alt = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))) # label(fact_376_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 215 (all Xs (hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs)) <-> Xs = nil_Ar1135217151le_alt)) # label(fact_280_List_Onull__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 216 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun701126715l_bool(hAPP_A1745457982l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_003) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 217 (all A_1 top_to935749874l_bool = pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool))) # label(fact_304_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 218 (all Ys_3 all Xs_10 (nil_Ar1135217151le_alt != Xs_10 -> hd_Arr1814706386le_alt(Xs_10) = hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_10),Ys_3)))) # label(fact_471_hd__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 219 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),hAPP_f1329247136t_bool(B_1,X_1)))))) # label(fact_125_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 220 (all B_1_1 all B_2_1 is_bool(hAPP_l4338847l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 221 (all I (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_A340536322t_bool(p_1,I))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_A340536322t_bool(p,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 222 (all Aa all Ba all L_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_1)) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_1))))) # label(fact_29_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 223 (all Ys_12 Ys_12 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,nil_Ar1135217151le_alt),Ys_12)) # label(fact_375_append__Nil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 224 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,hAPP_f342341961t_bool(cOMBK_980874600le_alt,B_1)))))) # label(fact_185_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 225 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun1264457267t_bool(hAPP_f590186314t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___067) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 226 (all A1 all A2 all R_1 (A2 = nil_Ar1135217151le_alt & nil_Ar1135217151le_alt = A1 | (exists X_2 exists Y_1 exists Xs_9 exists Ys (is_Arr723427730le_alt(X_2) & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1)) & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs_9),Ys)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) & A2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys) & hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9) = A1 & is_Arr723427730le_alt(Y_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A1),A2)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))))) # label(fact_466_listrel_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 227 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_Arr723427730le_alt(hAPP_f1273877800le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_036) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 228 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),hAPP_b805997823l_bool(B_1,X_1))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))))) # label(fact_57_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 229 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))))) # label(fact_183_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 230 (all B_1 all F all G all A_1 ((all W (is_fun1264457267t_bool(W) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A_1)) -> hAPP_f1817389232t_bool(G,W) = hAPP_f1817389232t_bool(F,W)))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))) <-> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A_1,B_1)))))) # label(fact_252_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 231 (all Ys_1 all Pa all Xs ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs))) -> hBOOL(hAPP_f1733357041l_bool(Pa,X_2))))) -> takeWh572506194t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)) = hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),takeWh572506194t_bool(Pa,Ys_1)))) # label(fact_644_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 232 (all X all Y (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(fequal318101288t_bool,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 233 (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,suc(M_1)),suc(N_1))))) # label(fact_653_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 234 (all Ys_5 all Xs_14 (nil_Ar1135217151le_alt != Xs_14 -> tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_14),Ys_5)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,tl_Arr314474198le_alt(Xs_14)),Ys_5))) # label(fact_457_tl__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 235 (all X_1 (hBOOL(top_top_bool) <-> hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_1)))) # label(fact_334_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 236 (exists X_2 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)) & is_fun20916972t_bool(X_2))) # label(fact_361_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 237 (all X all Y (is_Pro1004667236le_alt(X) & is_Pro1004667236le_alt(Y) -> -hBOOL(hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(fequal1881358376le_alt,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 238 (all X_1 hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),top_to186242507t_bool))) # label(fact_317_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 239 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_2_1) -> is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_035) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 240 (all As (As != nil_Ar1135217151le_alt -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,last_A1066338328le_alt(As)),set_Ar426477344le_alt(As))))) # label(fact_572_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 241 (all P all Q all R hAPP_l372964747le_alt(hAPP_l1390889510le_alt(P,R),Q) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(hAPP_f268020663le_alt(cOMBC_168079159le_alt,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 242 (all Ca all P_1 (hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(Ca),P_1)) -> -(all X_2 all Y_1 (P_1 = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1) -> -hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(Ca,X_2),Y_1)))))) # label(fact_444_splitE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 243 (all X_1 all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> insert1731565726e_indi(X_1,Xs) = Xs)) # label(fact_550_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 244 (all P all Q (is_fun20916972t_bool(P) -> hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_092) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 245 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> (-hBOOL(hAPP_P1373277879t_bool(Pa,X_1)) -> takeWh768831342le_alt(Pa,Xs) = takeWh768831342le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1))))) # label(fact_565_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 246 (all B_1_1 all B_2_1 is_bool(hAPP_f1094272486l_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]. 1.61/2.04 247 (all P all Q all R hAPP_bool_bool(P,hAPP_A416869060i_bool(Q,R)) = hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order___088) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 248 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_689_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 249 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> (-hBOOL(hAPP_bool_bool(Pa,X_1)) -> hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,dropWhile_bool(Pa,Xs)),Ys_1) = dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1))))) # label(fact_600_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 250 (all X_1 hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),top_to846262053l_bool))) # label(fact_328_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 251 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),hAPP_f431432850i_bool(B_1,X_1))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))))) # label(fact_70_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 252 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_fun20916972t_bool(hAPP_P1999019327t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__079) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 253 (all P all Q (is_fun292781289l_bool(P) -> P = hAPP_A990651116l_bool(hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_118) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 254 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,B_1)))))) # label(fact_196_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 255 (all P all Q all R hAPP_l1148780281le_alt(hAPP_f670565125le_alt(hAPP_f1124725731le_alt(cOMBB_1236261828le_alt,P),Q),R) = hAPP_l1148780281le_alt(P,hAPP_l372964747le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_113) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 256 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_bool(X_2) & is_bool(Y_1) & is_bool(Z) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs))) -> (hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,Y_1),Z)),R_1)) -> hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Ys_1)),hAPP_f1114274611l_bool(lexord_bool,R_1))) -> (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_1))) -> hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_1))))))) # label(fact_626_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 257 (all P all Q all R hAPP_l486097526le_alt(hAPP_f310101886le_alt(hAPP_f1558754397le_alt(cOMBB_1988247237le_alt,P),Q),R) = hAPP_f1928725626le_alt(P,hAPP_l436896263le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_130) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 258 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),hAPP_P467353593l_bool(B_1,X_1))) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))))) # label(fact_56_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 259 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,hAPP_f590186314t_bool(cOMBK_776703103e_indi,B_1)))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),B_1))))) # label(fact_99_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 260 (all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> Xs = insert22093680t_bool(X_1,Xs))) # label(fact_554_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 261 (all L_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_1)),arrow_583275979e_Prof)))) # label(fact_26_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 262 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B_1,X_1))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))))) # label(fact_78_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 263 (all B_1_1 all B_2_1 is_bool(hAPP_f1508705733l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 264 -(all C (is_Arr723427730le_alt(C) -> -hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,a),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,b),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_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]. 1.61/2.04 265 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B_1)))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),B_1))))) # label(fact_91_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 266 (all P all Q (is_fun1651000642t_bool(P) -> hAPP_P1116266031t_bool(hAPP_f342341961t_bool(cOMBK_980874600le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 267 (all I_3 all X_6 hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_6),replic1360561849le_alt(I_3,X_6)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(I_3,X_6)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_6),nil_Ar1135217151le_alt))) # label(fact_480_replicate__append__same) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 268 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),hAPP_A955165183l_bool(B_1,X_1)))))) # label(fact_147_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 269 (all X_1 all Xs (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> insert1731565726e_indi(X_1,Xs) = hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs))) # label(fact_615_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 270 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,hAPP_f684471657t_bool(cOMBK_509674590t_bool,B_1)))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),B_1))))) # label(fact_92_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 271 (all P all Q (is_bool(P) -> P = hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 272 (all B_1_1 all B_2_1 is_bool(hAPP_f2140553640l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 273 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> (-hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> takeWh1545314552le_alt(Pa,Xs) = takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))))) # label(fact_564_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 274 (all P all Q (is_fun20916972t_bool(P) -> hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 275 (all Xs_22 all Ys_8 ((Ys_8 = nil_Ar1135217151le_alt -> last_A1066338328le_alt(Xs_22) = last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_22),Ys_8))) & (nil_Ar1135217151le_alt != Ys_8 -> last_A1066338328le_alt(Ys_8) = last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_22),Ys_8))))) # label(fact_389_last__append) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 276 (all N_4 hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_4),nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt) # label(fact_484_drop__Nil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 277 (all Xs (Xs != nil_fu1714546777t_bool -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hd_fun1937506860t_bool(Xs)),set_fu444796538t_bool(Xs))))) # label(fact_594_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 278 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),hAPP_f591334822l_bool(B_1,X_1))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))))) # label(fact_68_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 279 (all B_1_1 all B_2_1 is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_053) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 280 (all X all Y (suc(Y) = suc(X) -> X = Y)) # label(fact_657_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 281 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> N != M & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_692_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 282 (all P all Q all R hAPP_A433435097l_bool(hAPP_f1656652505l_bool(hAPP_f1585690341l_bool(cOMBB_711698847le_alt,P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 283 (all Ys_1 all Pa all Xs ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs))) -> hBOOL(hAPP_P1373277879t_bool(Pa,X_2)))) -> dropWh1957015750le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = dropWh1957015750le_alt(Pa,Ys_1))) # label(fact_632_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 284 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),hAPP_A990651116l_bool(B_1,X_1)))))) # label(fact_146_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 285 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun292781289l_bool(hAPP_A990651116l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_005) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 286 (all B_1_1 all B_2_1 (is_fun1651000642t_bool(B_1_1) & is_Arr723427730le_alt(B_2_1) -> is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 287 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun701126715l_bool(hAPP_b1461182872l_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]. 1.61/2.04 288 (all N all X_1 all Xs hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = nat_ca247420624le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs),hAPP_l1244209582le_alt(hAPP_f1660378693le_alt(cOMBC_1158490499le_alt,drop_A1195732799le_alt),Xs),N)) # label(fact_513_drop__Cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 289 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))))) # label(fact_156_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 290 (all Ys_1 all Xs (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = Ys_1 <-> Xs = nil_Ar1135217151le_alt)) # label(fact_379_self__append__conv2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 291 (all P all Q (is_bool(P) -> hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 292 (all P_a all Pa all A_2 all B_3 all Aa all Ba (is_Arr723427730le_alt(A_2) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(B_3) -> (Ba != Aa -> (A_2 != B_3 -> (B_3 != Aa -> (Ba != A_2 -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_a),arrow_583275979e_Prof)) -> ((all I (is_Arr859726945e_indi(I) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_A340536322t_bool(P_a,I))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_f1817389232t_bool(f,P_a))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))))))))))))) # label(fact_24__C2_C) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 293 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),hAPP_P957402556i_bool(B_1,X_1)))))) # label(fact_121_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 294 (all X_1 all N all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(hAPP_l850073941le_alt(hAPP_n2100915976le_alt(drop_P1440509687le_alt,N),Xs)))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))))) # label(fact_522_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 295 (all B_1_1 all B_2_1 is_bool(hAPP_f1021828400l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_052) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 296 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),hAPP_f812095627l_bool(B_1,X_1))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))))) # label(fact_72_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 297 (all B_1_1 (is_fun20916972t_bool(B_1_1) -> is_fun866579754t_bool(produc616221118t_bool(B_1_1)))) # label(gsy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oal) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 298 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,B_1)))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),B_1))))) # label(fact_102_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 299 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),hAPP_P1116266031t_bool(B_1,X_1))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))))) # label(fact_62_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 300 (all B_1_1 is_fun701126715l_bool(set_fu222164517t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 301 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_fun1264457267t_bool(Y_1) & is_fun1264457267t_bool(Z) & is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs))) -> (hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,Y_1),Z)),R_1)) -> hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Xs),Ys_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1))) -> (hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Ys_1),Zs_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1))) -> hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Xs),Zs_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1))))))) # label(fact_629_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 302 (all P_2 -(all X_2 all Y_1 hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1) != P_2)) # label(fact_258_PairE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 303 (all B_1_1 all B_2_1 (is_fun1651000642t_bool(B_2_1) -> is_bool(hAPP_f87553445l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 304 (all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) <-> (exists Ys exists Zs Xs = hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Ys),hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Zs))))) # label(fact_648_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 305 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,hAPP_f1768325679l_bool(cOMBK_391161927l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),B_1))))) # label(fact_105_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 306 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_fun20916972t_bool(X_2) & is_fun20916972t_bool(Z) & is_fun20916972t_bool(Y_1) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs))) -> (hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,Y_1),Z)),R_1)) -> hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Xs),Ys_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1))) -> (hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Ys_1),Zs_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1))) -> hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Xs),Zs_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1))))))) # label(fact_628_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 307 (all Xs_8 (Xs_8 != nil_Ar1135217151le_alt -> last_A1066338328le_alt(rev_Ar955429983le_alt(Xs_8)) = hd_Arr1814706386le_alt(Xs_8))) # label(fact_478_last__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 308 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_658_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 309 (all Pa all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,takeWh1545314552le_alt(Pa,Xs))))) # label(fact_339_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 310 (all B_1_1 all B_2_1 is_bool(hAPP_f412569108l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 311 (all Ca all P_1 (is_Pro1004667236le_alt(P_1) -> ((all A all B (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) -> (P_1 = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B) -> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(Ca,A),B))))) -> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(Ca),P_1))))) # label(fact_443_splitI2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 312 (all B_1_1 all B_2_1 is_bool(hAPP_f740740988l_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]. 1.61/2.04 313 (all B_1_1 all B_2_1 is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_033) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 314 (all B_1_1 all B_2_1 is_bool(hAPP_f1518247545l_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]. 1.61/2.04 315 (all X all Y (X != Y | hBOOL(hAPP_f446648900l_bool(hAPP_f656614015l_bool(fequal547890341t_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____w) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 316 (all Xs all X_1 all Ys_1 all Y_2 all R_1 (is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(X_1) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt))),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt)))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) <-> Ys_1 = Xs & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) | Y_2 = X_1 & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))))) # label(fact_403_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 317 (all Ys_1 all Pa all Xs ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs))) -> hBOOL(hAPP_P1813625415t_bool(Pa,X_2))))) -> hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),takeWh808795006le_alt(Pa,Ys_1)) = takeWh808795006le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)))) # label(fact_646_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 318 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),hAPP_P1533476044l_bool(B_1,X_1)))))) # label(fact_148_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 319 (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_eq_nat,M_1),N_1)))) # label(fact_690_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 320 (all Xs all X_1 all Ys_1 all Y_2 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) -> (X_1 = Y_2 & Ys_1 = Xs <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt))))) # label(fact_386_append1__eq__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 321 (all X all Y (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 322 (all N_5 all Xs_5 hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_5),butlas123970891le_alt(Xs_5)) = butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_5),Xs_5))) # label(fact_483_drop__butlast) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 323 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))))) # label(fact_164_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 324 (all F1 all Aa all Ba (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F1,Aa),Ba)) -> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F1),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))))) # label(fact_438_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 325 (all Ys_1 all Xs all Us_1 all Vs_1 all X_1 all Y_2 all R_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) -> (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Vs_1)) = Xs -> (Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Vs_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))))))) # label(fact_415_listrel1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 326 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_2_1) -> is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 327 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),B_1))))) -> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,B_1)))))) # label(fact_197_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 328 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),hAPP_P467353593l_bool(B_1,X_2))))) -> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))))) # label(fact_242_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 329 (all X_1 all Xs (hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs)) & -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) <-> hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs))))) # label(fact_561_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 330 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),hAPP_A433435097l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))))) # label(fact_241_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 331 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),suc(N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_670_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 332 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,hAPP_f118515775l_bool(cOMBK_1028572856l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),B_1))))) # label(fact_108_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 333 (all B_1_1 is_fun1651000642t_bool(set_Ar426477344le_alt(B_1_1))) # label(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 334 (all X_1 all Xs (hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> takeWh572506194t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),rev_fu101184185t_bool(Xs)) = rev_fu101184185t_bool(tl_fun1131179056t_bool(dropWh193383674t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),Xs)))))) # label(fact_502_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 335 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) & is_fun2015243113i_bool(B_1_1) -> is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 336 (all B_1_1 is_fun20916972t_bool(hd_fun1937506860t_bool(B_1_1))) # label(gsy_c_List_Ohd_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 337 (all X_1 all Xs all Ys_1 all Zs_1 (Ys_1 = nil_Ar1135217151le_alt & hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) = Zs_1 | (exists Ys_10 (Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_10),Zs_1) & Ys_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_10))) <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Zs_1) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs))) # label(fact_385_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 338 (all Ws (-hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Ws)) -> (exists Xs_9 exists Ys exists Zs exists Y_1 (is_Arr723427730le_alt(Y_1) & Ws = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_9),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)),Zs)))))))) # label(fact_446_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 339 (all P all Q (is_fun1651000642t_bool(P) -> P = hAPP_f1068593625t_bool(hAPP_f391873743t_bool(cOMBK_339579368t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___094) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 340 (all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Xs)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))))) # label(fact_533_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 341 (all X_1 all Xs (hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> dropWh193383674t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),rev_fu101184185t_bool(Xs)) = hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),rev_fu101184185t_bool(takeWh572506194t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),Xs)))))) # label(fact_510_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 342 (all F (is_fun866579754t_bool(F) -> produc616221118t_bool(produc278404511t_bool(F)) = F)) # label(fact_431_curry__split) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 343 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_661_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 344 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),hAPP_f1329247136t_bool(B_1,X_1))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))))) # label(fact_67_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 345 (all X_1 all Xs (hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> rev_Pr1722970583le_alt(tl_Pro1439282464le_alt(dropWh1186971862le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),Xs))) = takeWh808795006le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),rev_Pr1722970583le_alt(Xs))))) # label(fact_504_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.04 346 (all Xs (nil_Ar1135217151le_alt = Xs <-> rev_Ar955429983le_alt(Xs) = nil_Ar1135217151le_alt)) # label(fact_488_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 347 (all X_1 all Xs (hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs))) <-> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) & hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs)))) # label(fact_562_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 348 (all B_1_1 all B_2_1 is_fun1420103068l_bool(hAPP_P467353593l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_084) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 349 (exists X_2 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)) & is_Pro1004667236le_alt(X_2))) # label(fact_359_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 350 (all Xs_30 (nil_Ar1135217151le_alt != Xs_30 -> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,butlas123970891le_alt(Xs_30)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,last_A1066338328le_alt(Xs_30)),nil_Ar1135217151le_alt)) = Xs_30)) # label(fact_364_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 351 (all Pa ((exists A exists B (is_Arr723427730le_alt(A) & hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B))) & is_Arr723427730le_alt(B))) <-> (exists X1 (is_Pro1004667236le_alt(X1) & hBOOL(hAPP_P1813625415t_bool(Pa,X1)))))) # label(fact_261_split__paired__Ex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 352 (all Xs_15 (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_15)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,tl_Arr314474198le_alt(Xs_15))))) # label(fact_454_distinct__tl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 353 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),hAPP_P1436281263t_bool(B_1,X_1))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))))) # label(fact_64_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 354 (all P all Q all R hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(P,R),Q) = hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 355 (all B_1_1 all B_2_1 is_bool(hAPP_f270557859l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_054) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 356 (all X all Y (is_fun1264457267t_bool(X) & is_fun1264457267t_bool(Y) -> Y = X | -hBOOL(hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(fequal1289369847t_bool,X),Y)))) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 357 (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_eq_nat,suc(M_1)),N_1)))) # label(fact_695_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 358 (all Y_2 all X_1 all Xs (is_fun48324065t_bool(X_1) & is_fun48324065t_bool(Y_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Y_2),set_fu1433968595t_bool(hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Y_2),set_fu1433968595t_bool(Xs))) | Y_2 = X_1))) # label(fact_544_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 359 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (N = M <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M)))))) # label(fact_677_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 360 (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]. 1.61/2.05 361 (all X_14 all Xs_31 (is_Arr723427730le_alt(X_14) -> (nil_Ar1135217151le_alt != Xs_31 -> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_14),Xs_31)) = last_A1066338328le_alt(Xs_31)) & (Xs_31 = nil_Ar1135217151le_alt -> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_14),Xs_31)) = X_14))) # label(fact_308_last_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 362 (all F (is_fun20916972t_bool(F) -> produc278404511t_bool(produc616221118t_bool(F)) = F)) # label(fact_430_split__curry) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 363 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),hAPP_P651748559t_bool(B_1,X_2))))) -> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))))) # label(fact_169_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 364 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) & is_fun866579754t_bool(B_1_1) -> is_fun1651000642t_bool(hAPP_A1781286015t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 365 (all X_1 all Xs ((-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> insert1969589781le_alt(X_1,Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) & (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> insert1969589781le_alt(X_1,Xs) = Xs))) # label(fact_605_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 366 (all X_1 all Pa all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(takeWhile_bool(Pa,Xs)))) -> hBOOL(hAPP_bool_bool(Pa,X_1)) & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))))) # label(fact_526_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 367 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,hAPP_f102394819t_bool(cOMBK_78615028le_alt,B_1)))))) # label(fact_200_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 368 (all B_1_1 (is_fun1420103068l_bool(B_1_1) -> is_fun1420103068l_bool(collec612883262t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 369 (all Y_2 all Ys_1 all Xs all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1)),Xs)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) -> -(all Y_1 all Ys (Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Ys) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_2),Y_1)),R_1)) -> -hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Ys_1),Ys)),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))))))) # label(fact_460_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 370 (all B_1_1 all B_2_1 is_bool(hAPP_l548550096t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 371 (all Pa (is_fun1651000642t_bool(Pa) -> Pa = collec591097828le_alt(Pa))) # label(fact_272_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 372 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,B_1)))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),B_1))))) # label(fact_112_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 373 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,hAPP_f102394819t_bool(cOMBK_78615028le_alt,B_1)))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),B_1))))) # label(fact_98_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 374 (all X_1 all L_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_163947511_mkbot(L_1),X_1)),arrow_912654623le_Lin)))) # label(fact_27_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 375 (all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rev_Ar955429983le_alt(Xs))) <-> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)))) # label(fact_491_distinct__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 376 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,hAPP_f303195352t_bool(cOMBK_1264040257t_bool,B_1)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),B_1))))) # label(fact_88_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 377 (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]. 1.61/2.05 378 (all Xs (Xs != nil_Ar637146932e_indi -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hd_Arr1280875809e_indi(Xs)),set_Ar1035526739e_indi(Xs))))) # label(fact_591_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 379 (all F all Aa all Ba (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))))) # label(fact_284_curryD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 380 (all P all Q all R hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R)) = hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 381 (all X all Y (hBOOL(hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(fequal1881358376le_alt,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 382 (all P all Q all R hAPP_bool_bool(hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 383 (all As (As != nil_Ar637146932e_indi -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,last_A560832347e_indi(As)),set_Ar1035526739e_indi(As))))) # label(fact_574_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 384 (all As (nil_fu1714546777t_bool != As -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,last_f1172522866t_bool(As)),set_fu444796538t_bool(As))))) # label(fact_577_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 385 (all X_1 (hBOOL(top_top_bool) <-> hBOOL(hAPP_A1120018583t_bool(top_to186242507t_bool,X_1)))) # label(fact_335_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 386 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__021) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 387 (all A_1 (is_fun1651000642t_bool(A_1) -> ((all X_2 (is_Arr723427730le_alt(X_2) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)))) -> top_to186242507t_bool = A_1))) # label(fact_350_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 388 (all X all Y (is_Arr859726945e_indi(X) & is_Arr859726945e_indi(Y) -> X = Y | -hBOOL(hAPP_A416869060i_bool(hAPP_A1609075839i_bool(fequal2012472101e_indi,X),Y)))) # label(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 389 (all B_1_1 (is_fun1651000642t_bool(B_1_1) -> is_fun1651000642t_bool(collec591097828le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 390 (all A_5 all B_2 (is_Arr723427730le_alt(B_2) & is_Arr723427730le_alt(A_5) -> (A_5 != B_2 -> (exists C (is_Arr723427730le_alt(C) & hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_5),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B_2),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_alt)))))))))) # label(fact_31_third__alt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 391 (all P all Q (is_fun292781289l_bool(P) -> hAPP_A955165183l_bool(hAPP_f206814660l_bool(cOMBK_472365180e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_120) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 392 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun292781289l_bool(hAPP_b651754310l_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]. 1.61/2.05 393 (all X_1 hBOOL(hAPP_A1120018583t_bool(top_to186242507t_bool,X_1))) # label(fact_300_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 394 (all X_1 all N all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N),Xs)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))))) # label(fact_518_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 395 (all X_1 all Xs (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs) = insert1409495663t_bool(X_1,Xs))) # label(fact_618_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 396 (all X_1 all Y_2 all L_1 all Z_1 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Z_1) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_312654597_mktop(L_1),Z_1))) <-> Z_1 != X_1 & (Z_1 = Y_2 -> X_1 != Y_2) & (Y_2 != Z_1 -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 397 (all X_1 all N all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(hAPP_l1149974805t_bool(hAPP_n587545160t_bool(drop_f1274868084t_bool,N),Xs)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))))) # label(fact_519_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 398 (all Xs_13 (nil_Ar1135217151le_alt != Xs_13 -> rotate184372300le_alt(Xs_13) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,tl_Arr314474198le_alt(Xs_13)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,hd_Arr1814706386le_alt(Xs_13)),nil_Ar1135217151le_alt)))) # label(fact_464_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 399 (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]. 1.61/2.05 400 (all P all Q P = hAPP_P1436281263t_bool(hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 401 (all Y_2 all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,Y_2),set_Pr1756729158le_alt(hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,Y_2),set_Pr1756729158le_alt(Xs))) | X_1 = Y_2)) # label(fact_541_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 402 (all P all Q all R hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(P,R),Q) = hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 403 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))))) # label(fact_160_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 404 (all A_1 (is_fun701126715l_bool(A_1) -> ((all X_2 (is_fun1264457267t_bool(X_2) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)))) -> top_to935749874l_bool = A_1))) # label(fact_352_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 405 (all V_1 all Va hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,V_1),Va) = splice1369921490le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,V_1),Va),nil_Ar1135217151le_alt)) # label(fact_115_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 406 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),hAPP_A1745457982l_bool(B_1,X_1))) -> -hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))))) # label(fact_51_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 407 (all X_1 all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) & -hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) <-> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs))))) # label(fact_556_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 408 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> (-hBOOL(hAPP_f446648900l_bool(Pa,X_1)) -> dropWh1122107731t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)) = hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,dropWh1122107731t_bool(Pa,Xs)),Ys_1)))) # label(fact_601_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 409 (exists X_2 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)) & is_fun1264457267t_bool(X_2))) # label(fact_360_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 410 (all X_2 all Xa all Xb (hBOOL(hAPP_P1813625415t_bool(X_2,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Xa),Xb))) <-> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(X_2),Xa),Xb)))) # label(fact_276_curry__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 411 (all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> Xs = insert1683711393le_alt(X_1,Xs))) # label(fact_555_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 412 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> (-hBOOL(hAPP_f1733357041l_bool(Pa,X_1)) -> hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,dropWh193383674t_bool(Pa,Xs)),Ys_1) = dropWh193383674t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1))))) # label(fact_602_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 413 (all X_1 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),top_to1773227171t_bool))) # label(fact_326_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 414 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))))) # label(fact_224_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 415 (all P all Q (is_fun_bool_bool(P) -> hAPP_f812095627l_bool(hAPP_f2062029545l_bool(cOMBK_753699544t_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]. 1.61/2.05 416 (all P all Q all R hAPP_A416869060i_bool(hAPP_A1609075839i_bool(P,R),Q) = hAPP_A416869060i_bool(hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 417 (all X_1 hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),top_to186242507t_bool))) # label(fact_325_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 418 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))))) # label(fact_240_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 419 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))))) # label(fact_535_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 420 (all X_1 all Pa all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(takeWh768831342le_alt(Pa,Xs)))) -> hBOOL(hAPP_P1373277879t_bool(Pa,X_1)) & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))))) # label(fact_524_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 421 (all Aa all Ba all A_2 all B_3 (is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(A_2) & is_Arr723427730le_alt(B_3) & is_Arr723427730le_alt(Ba) -> (hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3) <-> A_2 = Aa & B_3 = Ba))) # label(fact_16_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 422 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_Arr859726945e_indi(Y_1) & is_Arr859726945e_indi(Z) & is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs))) -> (hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,Y_1),Z)),R_1)) -> hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Xs),Ys_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1))) -> (hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Ys_1),Zs_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1))) -> hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Xs),Zs_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1))))))) # label(fact_625_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 423 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))))) # label(fact_248_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 424 (all B_1_1 all B_2_1 is_bool(hAPP_f2139503478l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____059) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 425 (all A_1 ((all X_2 hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))) -> top_to818291475t_bool = A_1)) # label(fact_347_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 426 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_671_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 427 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))))) # label(fact_166_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 428 (all As (nil_fu1180010164t_bool != As -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,last_f584510683t_bool(As)),set_fu1433968595t_bool(As))))) # label(fact_576_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 429 (all X_1 all A_1 (hBOOL(hAPP_f1378099862l_bool(A_1,X_1)) <-> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)))) # label(fact_269_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 430 (all X_1 all R_1 all Y_2 ((exists B exists Z Y_2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B),Z)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),Y_2))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))) # label(fact_397_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 431 (all B_1_1 (is_fun701126715l_bool(B_1_1) -> is_fun701126715l_bool(collec1567922785t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 432 (all Pa (is_fun2015243113i_bool(Pa) -> Pa = collec279390863e_indi(Pa))) # label(fact_273_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 433 (all Ys_17 Ys_17 = splice1369921490le_alt(nil_Ar1135217151le_alt,Ys_17)) # label(fact_117_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 434 (all Xs all R_1 ((all X_2 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),X_2)),R_1))) -> -hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Xs)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))))) # label(fact_310_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 435 (all Pa all Xs (dropWh1165804960le_alt(Pa,Xs) != nil_Ar1135217151le_alt -> -hBOOL(hAPP_A1120018583t_bool(Pa,hd_Arr1814706386le_alt(dropWh1165804960le_alt(Pa,Xs)))))) # label(fact_472_hd__dropWhile) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 436 (all X_1 all Y_2 all L_1 all Aa all Ba (is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(X_1) -> (Ba != Aa -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> ((X_1 != Ba -> (Ba = Y_2 -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Aa)),L_1)) | Aa = X_1) & (Y_2 != Ba -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)))) & (X_1 = Ba -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_1))) & X_1 != Y_2 <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_1046586475_above(L_1,Aa),Ba)))))))) # label(fact_35_in__above) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 437 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,B_1)))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),B_1))))) # label(fact_97_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 438 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> (-hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,dropWh1165804960le_alt(Pa,Xs)),Ys_1)))) # label(fact_597_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 439 (all A_1 (is_fun292781289l_bool(A_1) -> ((all X_2 (is_fun48324065t_bool(X_2) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)))) -> top_to1849101472l_bool = A_1))) # label(fact_354_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 440 (all R_1 all A1 all A2 (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),A1),A2)) <-> (exists X_2 exists Y_1 exists Xs_9 exists Ys (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9) = A1 & A2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys) & hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_2),Y_1)) & hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs_9),Ys)) & is_Arr723427730le_alt(Y_1) & is_Arr723427730le_alt(X_2))) | A2 = nil_Ar1135217151le_alt & A1 = nil_Ar1135217151le_alt)) # label(fact_473_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 441 (all Ys_1 all Pa all Xs ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs))) -> hBOOL(hAPP_P1373277879t_bool(Pa,X_2)))) -> hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),takeWh768831342le_alt(Pa,Ys_1)) = takeWh768831342le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)))) # label(fact_640_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 442 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))))) # label(fact_158_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 443 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs))) -> (hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,Y_1),Z)),R_1)) -> hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,X_2),Z)),R_1)))))) -> (hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Xs),Ys_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1))) -> (hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Ys_1),Zs_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1))) -> hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Xs),Zs_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1))))))) # label(fact_624_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 444 (all A1 all A2 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,A1),A2)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) <-> A1 = nil_li7342420le_alt & nil_li7342420le_alt = A2 | (exists X_2 exists Y_1 exists Xs_9 exists Ys (hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Ys) = A2 & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1)) & hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs_9),Ys)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) & A1 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Xs_9))))) # label(fact_465_listrel_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 445 (all X_1 all Y_2 (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_1),Y_2)) <-> Y_2 = X_1)) # label(fact_301_equal__list__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 446 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),hAPP_P467353593l_bool(B_1,X_2))))) -> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))))) # label(fact_176_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 447 (all X_20 hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_20),nil_Ar1135217151le_alt) = insert1969589781le_alt(X_20,nil_Ar1135217151le_alt)) # label(fact_262_insert__Nil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 448 (all B_1 all F all G all A_1 ((all W (is_Arr859726945e_indi(W) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A_1)) -> hAPP_A340536322t_bool(G,W) = hAPP_A340536322t_bool(F,W)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A_1,B_1))) <-> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1)))))) # label(fact_253_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 449 (all Pa all Xs ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))) -> hBOOL(hAPP_A1120018583t_bool(Pa,X_2))))) <-> nil_Ar1135217151le_alt = dropWh1165804960le_alt(Pa,Xs))) # label(fact_580_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 450 (all P all Q (is_fun1420103068l_bool(P) -> P = hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_112) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 451 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,B_1)))))) # label(fact_199_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 452 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N_1)),N_1))) # label(fact_681_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 453 (all P all Q all R hAPP_bool_bool(P,hAPP_P1813625415t_bool(Q,R)) = hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_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]. 1.61/2.05 454 (all X_1 all Xs (hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> rev_Ar758908116e_indi(tl_Arr282712093e_indi(dropWh1417102291e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),Xs))) = takeWh1088896635e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),rev_Ar758908116e_indi(Xs))))) # label(fact_499_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 455 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),hAPP_f1068593625t_bool(B_1,X_1)))))) # label(fact_127_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 456 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,B_1)))))) # label(fact_203_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 457 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),hAPP_A990651116l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))))) # label(fact_244_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 458 (all Y_2 all X_1 all Xs (is_Pro1004667236le_alt(X_1) & is_Pro1004667236le_alt(Y_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Y_2),set_Pr2031705942le_alt(hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs)))) -> Y_2 = X_1 | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Y_2),set_Pr2031705942le_alt(Xs)))))) # label(fact_547_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 459 (all Ys_1 all Pa all Xs ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs))) -> hBOOL(hAPP_f1733357041l_bool(Pa,X_2))))) -> dropWh193383674t_bool(Pa,Ys_1) = dropWh193383674t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)))) # label(fact_636_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 460 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),hAPP_A433435097l_bool(B_1,X_1)))))) # label(fact_143_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 461 (all Aa all Ba (is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(Aa) -> (Ba != Aa -> (exists X_2 (is_fun20916972t_bool(X_2) & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),arrow_912654623le_Lin)) & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_2))))))) # label(fact_34_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 462 (all X all Y (hBOOL(hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(fequal1289369847t_bool,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 463 (all A_1 pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool) # label(fact_302_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 464 (all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> -(all X_2 all Xs_9 (is_Arr723427730le_alt(X_2) -> (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9) = Xs -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs_9),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))))))))) # label(fact_459_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 465 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | N = M <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_691_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 466 (all Xs_25 Xs_25 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_25),nil_Ar1135217151le_alt)) # label(fact_377_append__Nil2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 467 (all P all Q all R hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,P),Q),R) = hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 468 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),hAPP_A990651116l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))))) # label(fact_178_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 469 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),hAPP_f812095627l_bool(B_1,X_1)))))) # label(fact_130_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 470 (all Xs_26 all Zs_2 all X_12 all Xs1 all Ys_13 (Ys_13 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_12),Xs1) -> (Xs_26 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs1),Zs_2) -> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_13),Zs_2) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_12),Xs_26)))) # label(fact_374_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 471 (all X_1 all Xs all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) -> ((all Y_1 (hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Xs) = Ys_1 -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_1)),R_1)))) -> -(all Zs (Ys_1 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Zs) -> -hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Zs)),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))))))) # label(fact_419_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 472 (all X_1 all Xs ((hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> Xs = insert_bool(X_1,Xs)) & (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) = insert_bool(X_1,Xs)))) # label(fact_608_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 473 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,hAPP_f1197671953l_bool(cOMBK_165199855le_alt,B_1)))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),B_1))))) # label(fact_111_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 474 (all B_1_1 all B_2_1 is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_032) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 475 (all B_1_1 all B_2_1 is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_055) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 476 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),hAPP_A433435097l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))))) # label(fact_175_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 477 (all F all Aa all Ba (hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) -> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba)))) # label(fact_278_curryI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 478 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,B_1)))))) # label(fact_211_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 479 (all X_1 all Xs (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> insert_bool(X_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) # label(fact_616_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 480 (all As (nil_fu247759878t_bool != As -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,last_f1921219373t_bool(As)),set_fu222164517t_bool(As))))) # label(fact_578_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 481 (all Ys_1 all Pa all Xs ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs))) -> hBOOL(hAPP_bool_bool(Pa,X_2))))) -> dropWhile_bool(Pa,Ys_1) = dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)))) # label(fact_634_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 482 (all X_1 all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> insert897399838t_bool(X_1,Xs) = Xs)) # label(fact_552_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 483 (all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Xs)))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))))) # label(fact_538_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 484 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))))) # label(fact_184_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 485 (all X_1 all Xs (hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),rev_Ar758908116e_indi(takeWh1088896635e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),Xs))) = dropWh1417102291e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),rev_Ar758908116e_indi(Xs))))) # label(fact_507_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 486 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_663_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 487 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> (-hBOOL(hAPP_P1813625415t_bool(Pa,X_1)) -> takeWh808795006le_alt(Pa,Xs) = takeWh808795006le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1))))) # label(fact_571_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 488 (all X_1 all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> dropWh1165804960le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),rev_Ar955429983le_alt(Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),rev_Ar955429983le_alt(takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),Xs)))))) # label(fact_505_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 489 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),hAPP_f1068593625t_bool(B_1,X_1))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))))) # label(fact_69_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 490 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,B_1)))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),B_1))))) # label(fact_85_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 491 (all B_1_1 all B_2_1 is_bool(hAPP_f2129568089l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_031) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 492 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),hAPP_f1329247136t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))))) # label(fact_157_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 493 (all A_1 (is_fun20916972t_bool(A_1) -> ((all X_2 (is_Pro1004667236le_alt(X_2) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)))) -> top_to1773227171t_bool = A_1))) # label(fact_351_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 494 (all P all Q hAPP_f1114489970t_bool(hAPP_f1228246954t_bool(cOMBK_906927855t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___124) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 495 (all P all Q all R hAPP_bool_bool(P,hAPP_f1733357041l_bool(Q,R)) = hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,P),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]. 1.61/2.05 496 (all Y_2 all X_1 all Xs (is_Arr859726945e_indi(X_1) & is_Arr859726945e_indi(Y_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),set_Ar1035526739e_indi(hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs)))) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),set_Ar1035526739e_indi(Xs))) | Y_2 = X_1))) # label(fact_542_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 497 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))))) # label(fact_179_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 498 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))))) # label(fact_250_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 499 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),hAPP_A340536322t_bool(B_1,X_1))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))))) # label(fact_48_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 500 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_Arr723427730le_alt(hAPP_P870295781le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 501 (all Xs all Pa (hBOOL(hAPP_l300482276t_bool(Pa,nil_Ar1135217151le_alt)) -> ((all X_2 all Xs_9 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_l300482276t_bool(Pa,Xs_9)) -> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_9),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),nil_Ar1135217151le_alt))))))) -> hBOOL(hAPP_l300482276t_bool(Pa,Xs))))) # label(fact_400_rev__induct) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 502 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_Arr723427730le_alt(hAPP_f459545019le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 503 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B_1)))))) # label(fact_216_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.05 504 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),hAPP_P2049543454l_bool(B_1,X_1))) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))))) # label(fact_53_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 505 (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,N),suc(M))) <-> N = M))) # label(fact_694_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 506 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M))) <-> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_680_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 507 (all P all Q all R hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 508 (all R_1 all X_2 all Xa (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_2),Xa)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) <-> hBOOL(hAPP_l784127213t_bool(hAPP_l508185643t_bool(listre1064220282le_alt(hAPP_f1895633847t_bool(hAPP_f1997384703t_bool(cOMBC_1696964078t_bool,hAPP_f1837837439t_bool(hAPP_f1503353479t_bool(cOMBB_1326560562le_alt,cOMBC_1827582133l_bool),hAPP_f1893731349l_bool(hAPP_f1418100887l_bool(cOMBB_1150645560le_alt,hAPP_f1224738111l_bool(cOMBB_1407335828le_alt,member1373125444le_alt)),produc2031778509le_alt))),R_1)),X_2),Xa)))) # label(fact_463_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 509 (all Xs_35 (Xs_35 != nil_Ar1135217151le_alt -> (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_35)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,butlas123970891le_alt(Xs_35)))))) # label(fact_292_distinct__butlast) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 510 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),hAPP_f721327224l_bool(B_1,X_1))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))))) # label(fact_76_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 511 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_1_1) & is_fun20916972t_bool(B_2_1) -> is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___063) # label(hypothesis) # label(non_clause). [assumption]. 1.61/2.06 512 (all Xs all Ys_1 all X_1 all Y_2 all R_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))))) # label(fact_447_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 513 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),hAPP_A701636433l_bool(B_1,X_1)))))) # label(fact_140_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 514 (all Xs all X_1 all Y_2 all R_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Xs))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))))) # label(fact_413_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 515 (all B_1_1 all B_2_1 is_bool(hAPP_f937100551l_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]. 1.61/2.06 516 (all X_1 all Xs (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) & hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs)) <-> hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs))))) # label(fact_563_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 517 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),hAPP_f1681297285t_bool(B_1,X_1))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))))) # label(fact_71_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 518 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> M_1 != N_1)) # label(fact_662_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 519 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_040) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 520 (all B_1_1 all B_2_1 is_bool(hAPP_f1342253361l_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]. 1.61/2.06 521 (all F all Aa all Ba (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))))) # label(fact_436_splitI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 522 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),hAPP_P1436281263t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))))) # label(fact_154_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 523 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),hAPP_f1068593625t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))))) # label(fact_225_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 524 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),hAPP_P651748559t_bool(B_1,X_1)))))) # label(fact_137_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 525 (all F all Aa all Ba (hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) -> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F,Aa),Ba)))) # label(fact_440_splitD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 526 (all R_2 all X_1 all Y_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_2)) <-> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(in_rel264468792le_alt(R_2),X_1),Y_2)))) # label(fact_19_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 527 (all P all Q (is_bool(P) -> hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 528 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Ys_1)))) | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Xs)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1))))))) # label(fact_585_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 529 (all P (is_bool(P) -> P = fFalse | fTrue = P)) # label(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 530 (all Ys_1 all Pa all Xs ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs))) -> hBOOL(hAPP_bool_bool(Pa,X_2))))) -> hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),takeWhile_bool(Pa,Ys_1)) = takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)))) # label(fact_642_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 531 (all Xs all Y_2 all Ys_1 (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1) = rev_Ar955429983le_alt(Xs) <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Ys_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt)) = Xs)) # label(fact_496_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 532 (all I_2 all Xs_4 (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_4)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,I_2),Xs_4))))) # label(fact_485_distinct__drop) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 533 (all P all Q all R hAPP_A1849759038le_alt(hAPP_l1693669363le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,P),Q),R) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_090) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 534 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B_1,X_1))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))))) # label(fact_77_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 535 (all X_1 hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_1))) # label(fact_295_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 536 (all P all Q all R hAPP_bool_bool(P,hAPP_f1378099862l_bool(Q,R)) = hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Arrow__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 537 (all Ys_4 all Xs_11 ((nil_Ar1135217151le_alt = Xs_11 -> hd_Arr1814706386le_alt(Ys_4) = hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_11),Ys_4))) & (nil_Ar1135217151le_alt != Xs_11 -> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_11),Ys_4)) = hd_Arr1814706386le_alt(Xs_11)))) # label(fact_470_hd__append) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 538 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__076) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 539 (all X all Y (hBOOL(hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(fequal1025934616le_alt,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 540 (all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) -> -(all X_2 all Xs_9 (Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Xs_9) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_2)),R_1)) -> -hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs_9),Ys_1)),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))))))) # label(fact_458_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 541 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),hAPP_f1681297285t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))))) # label(fact_161_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 542 (all B_1_1 all B_2_1 is_fun292781289l_bool(hAPP_P1533476044l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_083) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 543 (all X_1 all A_1 (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) <-> hBOOL(hAPP_A1120018583t_bool(A_1,X_1)))) # label(fact_264_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 544 (all Ys_1 all Pa all Xs ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs))) -> hBOOL(hAPP_f1378099862l_bool(Pa,X_2))))) -> dropWh2056378277t_bool(Pa,Ys_1) = dropWh2056378277t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)))) # label(fact_637_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 545 (all Us_1 all Vs_1 all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) & Vs_1 = Us_1 | Xs = Ys_1 & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Us_1),Vs_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Us_1)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Vs_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))))) # label(fact_410_append__listrel1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 546 (all X_1 all Y_2 all L_1 all Aa all Ba (is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(X_1) -> (Aa != Ba -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> ((Y_2 = Aa -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Ba)),L_1))) & (Y_2 != Aa -> (X_1 != Aa -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1))) & (X_1 = Aa -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_1)) | Ba = Y_2)) & Y_2 != X_1 <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,L_1),Aa),Ba)))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 547 (all X_1 all Pa all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(takeWh1545314552le_alt(Pa,Xs)))) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) & hBOOL(hAPP_A1120018583t_bool(Pa,X_1)))) # label(fact_523_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 548 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))))) # label(fact_181_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 549 (all B_1_1 all B_2_1 is_bool(hAPP_f404365000l_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]. 1.61/2.06 550 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__078) # label(hypothesis) # label(non_clause). [assumption]. 1.61/2.06 551 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_fun_bool_bool(hAPP_f721327224l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_041) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 552 (all Y_2 all X_1 all Xs (is_fun1264457267t_bool(X_1) & is_fun1264457267t_bool(Y_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Y_2),set_fu222164517t_bool(hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs)))) -> X_1 = Y_2 | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Y_2),set_fu222164517t_bool(Xs)))))) # label(fact_546_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 553 (all B_1_1 all B_2_1 (is_fun866579754t_bool(B_2_1) -> is_fun866579754t_bool(hAPP_f271508829t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc___018) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 554 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))))) # label(fact_162_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 555 (all Y_3 (is_Pro1004667236le_alt(Y_3) -> -(all A all B (is_Arr723427730le_alt(B) & is_Arr723427730le_alt(A) -> hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B) != Y_3)))) # label(fact_257_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 556 (all Y_2 all Ys_1 all Xs all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)),Xs)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> -(all Y_1 all Ys (is_Arr723427730le_alt(Y_1) -> (Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),Y_1)),R_1)) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Ys_1),Ys)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))))))))) # label(fact_461_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 557 (all X_1 all Xs (hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> dropWh2056378277t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),rev_fu313987494t_bool(Xs)) = hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),rev_fu313987494t_bool(takeWh1813199437t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),Xs)))))) # label(fact_511_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 558 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,B_1)))))) # label(fact_214_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 559 (all Xs all L all Pa all X_1 (-hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) -> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),L))) = takeWh1545314552le_alt(Pa,Xs))) # label(fact_387_takeWhile__tail) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 560 (all M all N (M != N <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_659_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 561 (all X_1 all Pa all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(takeWh1813199437t_bool(Pa,Xs)))) -> hBOOL(hAPP_f1378099862l_bool(Pa,X_1)) & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))))) # label(fact_529_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 562 (all X_1 all Y_2 all R_1 ((all A all B (A = B | hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,B),A)),R_1)) | hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B)),R_1)))) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_1),Y_2)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) | hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Y_2),X_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) | X_1 = Y_2)) # label(fact_312_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 563 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),hAPP_P957402556i_bool(B_1,X_1))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))))) # label(fact_63_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 564 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_037) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 565 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),hAPP_b651754310l_bool(B_1,X_1)))))) # label(fact_149_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 566 (all X_1 (hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_1)) <-> hBOOL(top_top_bool))) # label(fact_332_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 567 (all Xs all Ys_1 all R_1 all N (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),lexn_A19384479le_alt(R_1,N))) -> N = size_s2106320494le_alt(Xs) & N = size_s2106320494le_alt(Ys_1))) # label(fact_435_lexn__length) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 568 (all Xs (Xs != nil_Pr1368032311le_alt -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hd_Pro804272676le_alt(Xs)),set_Pr2031705942le_alt(Xs))))) # label(fact_596_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 569 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,hAPP_f1228246954t_bool(cOMBK_906927855t_bool,B_1)))))) # label(fact_198_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 570 (all B_1_1 (is_fun20916972t_bool(B_1_1) -> is_fun20916972t_bool(collec1376511890le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 571 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> (-hBOOL(hAPP_bool_bool(Pa,X_1)) -> takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = takeWhile_bool(Pa,Xs)))) # label(fact_567_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 572 (all L_1 all X_1 all Y_2 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) -> (X_1 != Y_2 -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_1046586475_above(L_1,X_1),Y_2)),arrow_912654623le_Lin)))))) # label(fact_44_above__Lin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 573 (all P all Q (is_fun701126715l_bool(P) -> P = hAPP_P2049543454l_bool(hAPP_f978113205l_bool(cOMBK_1549622337le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_114) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 574 (all Xs (hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs)) <-> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,Xs),nil_Ar1135217151le_alt)))) # label(fact_288_equal__Nil__null) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 575 (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,suc(M)),suc(N))))) # label(fact_678_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 576 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) & is_fun1264457267t_bool(B_1_1) -> is_fun20916972t_bool(hAPP_A340536322t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_013) # label(hypothesis) # label(non_clause). [assumption]. 1.61/2.06 577 (all Xs all X_1 (Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt) <-> rev_Ar955429983le_alt(Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt))) # label(fact_492_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 578 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),B_1)))) -> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,B_1)))))) # label(fact_202_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 579 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),hAPP_P2049543454l_bool(B_1,X_2))))) -> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))))) # label(fact_173_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 580 (all P all Q all R hAPP_l372964747le_alt(hAPP_n344665784le_alt(P,R),Q) = hAPP_n2108195705le_alt(hAPP_l1244209582le_alt(hAPP_f1660378693le_alt(cOMBC_1158490499le_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]. 1.61/2.06 581 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_Pro1004667236le_alt(hAPP_A1561816353le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__prod_It) # label(hypothesis) # label(non_clause). [assumption]. 1.61/2.06 582 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,hAPP_f1768325679l_bool(cOMBK_391161927l_bool,B_1)))))) # label(fact_207_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 583 (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]. 1.61/2.06 584 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),hAPP_f1681297285t_bool(B_1,X_1)))))) # label(fact_129_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 585 (all Y_2 all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(Xs))) | (hBOOL(Y_2) <-> hBOOL(X_1)))) # label(fact_543_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 586 (all Pa (is_fun1420103068l_bool(Pa) -> Pa = collec612883262t_bool(Pa))) # label(fact_274_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 587 (all Pa all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) -> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,dropWh1165804960le_alt(Pa,Xs))))) # label(fact_429_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 588 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,hAPP_f978113205l_bool(cOMBK_1549622337le_alt,B_1)))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),B_1))))) # label(fact_104_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 589 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,B_1)))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),B_1))))) # label(fact_103_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 590 (all Xs all Ys_1 (Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) <-> Xs = nil_Ar1135217151le_alt)) # label(fact_382_append__self__conv2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 591 (all R_2 all X_1 all Y_2 (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(in_rel1361124802le_alt(R_2),X_1),Y_2)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_2)))) # label(fact_20_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 592 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,B_1)))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),B_1))))) # label(fact_100_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 593 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),hAPP_A433435097l_bool(B_1,X_1))) -> -hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))))) # label(fact_55_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 594 (all X_1 all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Xs)))) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))))) # label(fact_534_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 595 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),hAPP_f3167870t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))))) # label(fact_221_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 596 (all X_1 hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),top_to818291475t_bool))) # label(fact_314_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 597 (all P all Q all R hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_093) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 598 (all Ys_1 all Pa all Xs ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs))) -> hBOOL(hAPP_P1813625415t_bool(Pa,X_2))))) -> dropWh1186971862le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)) = dropWh1186971862le_alt(Pa,Ys_1))) # label(fact_638_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 599 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),hAPP_P1116266031t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))))) # label(fact_152_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 600 (all P all Q all R hAPP_l436896263le_alt(hAPP_f1504748473le_alt(hAPP_f1949171529le_alt(cOMBB_215060470le_alt,P),Q),R) = hAPP_f1291634731le_alt(P,hAPP_l1148780281le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_129) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 601 (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]. 1.61/2.06 602 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Ys_1)))) | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Xs)))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1))))))) # label(fact_587_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 603 (all B_1_1 is_fun292781289l_bool(set_fu1433968595t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqm) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 604 (all X_1 all U all V all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,X_1),U)),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,X_1),V))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) -> ((all A -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),A)),R_1))) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,U),V)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))))) # label(fact_398_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 605 (all N_2 all X_4 all Xs_2 hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_2,X_4)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_4),Xs_2)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_4),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_2,X_4)),Xs_2))) # label(fact_494_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 606 (all X_1 all Pa all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(takeWh1088896635e_indi(Pa,Xs)))) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) & hBOOL(hAPP_A416869060i_bool(Pa,X_1)))) # label(fact_525_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 607 (all B_1_1 all B_2_1 is_bool(hAPP_l784127213t_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]. 1.61/2.06 608 (all Xs_3 all Ys_2 rev_Ar955429983le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_3),Ys_2)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Ys_2)),rev_Ar955429983le_alt(Xs_3))) # label(fact_486_rev__append) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 609 (all X_23 all Xs_41 hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_23),Xs_41) != Xs_41) # label(fact_42_not__Cons__self2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 610 (all P all Q (is_fun701126715l_bool(P) -> hAPP_b1461182872l_bool(hAPP_f1768325679l_bool(cOMBK_391161927l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 611 (all P all Q (is_fun701126715l_bool(P) -> hAPP_A701636433l_bool(hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_105) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 612 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,hAPP_f3439105i_bool(cOMBK_520250367le_alt,B_1)))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),B_1))))) # label(fact_84_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 613 (all X_1 all N all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(hAPP_l1557274901e_indi(hAPP_n568645704e_indi(drop_A1853358580e_indi,N),Xs)))) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))))) # label(fact_517_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 614 (all Xs_21 all Ys_7 (nil_Ar1135217151le_alt != Ys_7 -> last_A1066338328le_alt(Ys_7) = last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_21),Ys_7)))) # label(fact_390_last__appendR) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 615 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),hAPP_P1533476044l_bool(B_1,X_2))))) -> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))))) # label(fact_246_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 616 (all X_1 all Xs (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> insert22093680t_bool(X_1,Xs) = hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs))) # label(fact_619_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 617 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_b805997823l_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]. 1.61/2.06 618 (all B_1_1 all B_2_1 is_bool(hAPP_l1684828478l_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]. 1.61/2.06 619 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_1_1) & is_fun1264457267t_bool(B_2_1) -> is_fun20916972t_bool(hAPP_f1817389232t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__028) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 620 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),B_1)))) -> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,hAPP_f905851705l_bool(cOMBK_740566962le_alt,B_1)))))) # label(fact_209_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 621 (all X_3 all Xs_1 rev_Ar955429983le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_3),Xs_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Xs_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_3),nil_Ar1135217151le_alt))) # label(fact_495_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 622 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_fun1651000642t_bool(hAPP_f1741989420t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_039) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 623 (all A_4 all List_4 nil_Ar1135217151le_alt != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_4),List_4)) # label(fact_37_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 624 (all X_1 all U all V all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),U)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),V))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) -> ((all A (is_Arr723427730le_alt(A) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),A)),R_1)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,U),V)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))))) # label(fact_399_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 625 (all P all Q (is_fun701126715l_bool(P) -> hAPP_A1745457982l_bool(hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_103) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 626 (all B_1_1 all B_2_1 is_bool(hAPP_f288803825l_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]. 1.61/2.06 627 (all B_1_1 all B_2_1 is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_050) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 628 (all R_1 all X_2 all Xa (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) <-> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(hAPP_f1682340965t_bool(cOMBB_333235735le_alt,cOMBC_943734388l_bool),hAPP_f1747206697l_bool(hAPP_f274832101l_bool(cOMBB_885534287le_alt,hAPP_f1585690341l_bool(cOMBB_711698847le_alt,member720722004le_alt)),produc1456060119le_alt))),R_1)),X_2),Xa)))) # label(fact_462_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 629 (all P_a all Pa all A_2 all B_3 all Aa all Ba (is_Arr723427730le_alt(A_2) & is_Arr723427730le_alt(B_3) & is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(Aa) -> (Ba != Aa -> (A_2 != B_3 -> (Aa != B_3 -> (A_2 != Ba -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_a),arrow_583275979e_Prof)) -> ((all I (is_Arr859726945e_indi(I) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_A340536322t_bool(P_a,I)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_f1817389232t_bool(f,P_a))))))))))))) # label(fact_23__C1_C) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 630 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,hAPP_f206814660l_bool(cOMBK_472365180e_indi,B_1)))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),B_1))))) # label(fact_110_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 631 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),hAPP_P2049543454l_bool(B_1,X_2))))) -> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))))) # label(fact_239_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 632 (all B_1_1 is_Arr723427730le_alt(hd_Arr1814706386le_alt(B_1_1))) # label(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 633 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B_1,X_1))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))))) # label(fact_46_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 634 (all B_1_1 is_fun48324065t_bool(last_f584510683t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 635 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,B_1)))))) # label(fact_204_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 636 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> (-hBOOL(hAPP_P1373277879t_bool(Pa,X_1)) -> dropWh1957015750le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,dropWh1957015750le_alt(Pa,Xs)),Ys_1)))) # label(fact_598_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 637 (all X_1 all Xs (-hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) -> hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) = insert1969589781le_alt(X_1,Xs))) # label(fact_613_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 638 (all N_3 all X_5 all K_1 hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(K_1,X_5)),replic1360561849le_alt(N_3,X_5)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_3,X_5)),replic1360561849le_alt(K_1,X_5))) # label(fact_490_append__replicate__commute) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 639 (all Xs_24 all Ys_11 (Xs_24 = Ys_11 -> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,nil_Ar1135217151le_alt),Ys_11) = Xs_24)) # label(fact_383_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 640 (all Xs_17 (Xs_17 != nil_Ar1135217151le_alt -> -(all Ys all Y_1 (is_Arr723427730le_alt(Y_1) -> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)) != Xs_17)))) # label(fact_401_rev__cases) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 641 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),hAPP_f1570138413i_bool(B_1,X_1)))))) # label(fact_124_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 642 (all Xs (Xs != nil_fu1180010164t_bool -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hd_fun1289819809t_bool(Xs)),set_fu1433968595t_bool(Xs))))) # label(fact_593_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 643 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_2_1) -> is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_056) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 644 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_2_1) -> is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_034) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 645 (all P all Q all R hAPP_f1427069397le_alt(hAPP_l486097526le_alt(P,R),hAPP_l1148780281le_alt(Q,R)) = hAPP_l1148780281le_alt(hAPP_f794134621le_alt(hAPP_f2122335314le_alt(cOMBS_1569784209le_alt,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_125) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 646 (all B_1_1 all B_2_1 is_bool(hAPP_f437011961l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_058) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 647 (exists A exists B exists C (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) & hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_alt))))) & is_Arr723427730le_alt(C))) # label(fact_39_alt3) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 648 (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_651_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 649 (all P all Q (is_bool(P) -> hAPP_A1120018583t_bool(hAPP_b287951269t_bool(cOMBK_507931254le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 650 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),hAPP_f1068593625t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))))) # label(fact_159_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 651 (all Pa ((exists A exists B hBOOL(hAPP_P1373277879t_bool(Pa,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B)))) <-> (exists X1 hBOOL(hAPP_P1373277879t_bool(Pa,X1))))) # label(fact_260_split__paired__Ex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 652 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))))) # label(fact_230_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 653 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_b2116075462i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls_014) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 654 (all As (As != nil_Pr1368032311le_alt -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,last_P15572062le_alt(As)),set_Pr2031705942le_alt(As))))) # label(fact_579_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 655 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),hAPP_f1114489970t_bool(B_1,X_1)))))) # label(fact_133_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 656 (all X_1 all N all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(hAPP_l182884309le_alt(hAPP_n323901960le_alt(drop_P635442535le_alt,N),Xs)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))))) # label(fact_516_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 657 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) -> (-hBOOL(hAPP_A416869060i_bool(Pa,X_1)) -> hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,dropWh1417102291e_indi(Pa,Xs)),Ys_1) = dropWh1417102291e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1))))) # label(fact_599_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 658 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))))) # label(fact_234_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 659 (all B_1_1 is_fun2015243113i_bool(set_Ar1035526739e_indi(B_1_1))) # label(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 660 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 661 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__019) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 662 (all B_1_1 is_fun20916972t_bool(last_f1172522866t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsun) # label(axiom) # label(non_clause). [assumption]. 1.61/2.06 663 (all X_21 all Xs_39 all Y_4 all Ys_18 splice1369921490le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_21),Xs_39),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_4),Ys_18)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_21),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_4),splice1369921490le_alt(Xs_39,Ys_18)))) # label(fact_116_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 664 (all X all Y (-hBOOL(hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(fequal1025934616le_alt,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 665 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),hAPP_A1745457982l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))))) # label(fact_237_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 666 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B_1,X_1)))))) # label(fact_150_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 667 (all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) -> ((all X_2 (Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Ys_1) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_2)),R_1)))) -> -(all Zs (Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Zs) -> -hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Zs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))))))) # label(fact_421_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 668 (all X_1 hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),top_to846262053l_bool))) # label(fact_320_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 669 (all P all Q all R hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f446648900l_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]. 1.61/2.07 670 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,hAPP_f1698272152t_bool(cOMBK_242036279t_bool,B_1)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),B_1))))) # label(fact_86_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 671 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,hAPP_f2062029545l_bool(cOMBK_753699544t_bool,B_1)))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),B_1))))) # label(fact_93_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 672 (all P all Q all R hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q) = hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_101) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 673 (all X_1 all Y_2 all L_1 all Z_1 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Z_1) & is_Arr723427730le_alt(Y_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_163947511_mkbot(L_1),Z_1))) <-> (X_1 = Z_1 -> Y_2 != X_1) & (Z_1 != X_1 -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1))) & Y_2 != Z_1))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 674 (all Xs ((exists Y_1 exists Ys (Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys) & is_Arr723427730le_alt(Y_1))) <-> nil_Ar1135217151le_alt != Xs)) # label(fact_80_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 675 (all Y_2 all X_1 all Xs (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,Y_2),set_Ar426477344le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)))) -> X_1 = Y_2 | hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,Y_2),set_Ar426477344le_alt(Xs)))))) # label(fact_540_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 676 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),B_1))))) -> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,hAPP_f3439105i_bool(cOMBK_520250367le_alt,B_1)))))) # label(fact_186_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 677 (all X_1 hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_1))) # label(fact_299_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 678 (all B_1_1 all B_2_1 is_bool(hAPP_f1488127117l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____060) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 679 (all Xs all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) -> Xs = nil_Ar1135217151le_alt)) # label(fact_450_listrel__Nil2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 680 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun20916972t_bool(hAPP_b763490121t_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]. 1.61/2.07 681 (all A_1 (is_fun2015243113i_bool(A_1) -> ((all X_2 (is_Arr859726945e_indi(X_2) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)))) -> top_to207207712i_bool = A_1))) # label(fact_349_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 682 (all Pa all Xs (Xs != nil_Ar1135217151le_alt -> ((all X_2 (is_Arr723427730le_alt(X_2) -> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),nil_Ar1135217151le_alt))))) -> ((all X_2 all Xs_9 (is_Arr723427730le_alt(X_2) -> (nil_Ar1135217151le_alt != Xs_9 -> (hBOOL(hAPP_l300482276t_bool(Pa,Xs_9)) -> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9))))))) -> hBOOL(hAPP_l300482276t_bool(Pa,Xs)))))) # label(fact_275_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 683 (all P all Q P = hAPP_f1329247136t_bool(hAPP_f303195352t_bool(cOMBK_1264040257t_bool,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___115) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 684 (all Pa nil_Ar1135217151le_alt = dropWh1165804960le_alt(Pa,nil_Ar1135217151le_alt)) # label(fact_428_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 685 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),hAPP_A1745457982l_bool(B_1,X_1)))))) # label(fact_139_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 686 (all Ys_1 all Pa all Xs ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))) -> hBOOL(hAPP_A1120018583t_bool(Pa,X_2))))) -> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),takeWh1545314552le_alt(Pa,Ys_1)))) # label(fact_639_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 687 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),hAPP_P651748559t_bool(B_1,X_1))) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))))) # label(fact_49_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 688 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),hAPP_P467353593l_bool(B_1,X_1)))))) # label(fact_144_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 689 (all X_1 hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_1))) # label(fact_296_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 690 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))))) # label(fact_170_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 691 (all X_1 all N all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(hAPP_l1130749077t_bool(hAPP_n2099236808t_bool(drop_f1584869062t_bool,N),Xs)))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))))) # label(fact_521_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 692 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun1264457267t_bool(hAPP_A630236912t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_002) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 693 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),hAPP_P2049543454l_bool(B_1,X_1)))))) # label(fact_141_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 694 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))))) # label(fact_696_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 695 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun48324065t_bool(hAPP_b327863236t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_016) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 696 (all X_1 (hBOOL(top_top_bool) <-> hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_1)))) # label(fact_330_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 697 (all N_1 N_1 != suc(N_1)) # label(fact_654_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 698 (all Xs all R_1 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1)))) # label(fact_366_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 699 (all Xs (nil_bool != Xs -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hd_bool(Xs)),set_bool(Xs))))) # label(fact_592_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 700 (all X_1 all A_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) <-> hBOOL(hAPP_f1733357041l_bool(A_1,X_1)))) # label(fact_270_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 701 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) & is_fun292781289l_bool(B_1_1) -> is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_038) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 702 (all S_1 all R_2 (is_fun20916972t_bool(R_2) & is_fun20916972t_bool(S_1) -> (R_2 = S_1 <-> (all X_2 all Xa (is_Arr723427730le_alt(Xa) & is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Xa)),R_2)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Xa)),S_1)))))))) # label(fact_255_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 703 (all B_1_1 all B_2_1 is_bool(hAPP_f511649569l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___071) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 704 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) & is_fun701126715l_bool(B_1_1) -> is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__022) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 705 (all X_8 all Xs_12 (is_Arr723427730le_alt(X_8) -> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_8),Xs_12)) = X_8)) # label(fact_467_hd_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 706 (all Ys_1 all Pa all Xs ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs))) -> hBOOL(hAPP_A416869060i_bool(Pa,X_2))))) -> dropWh1417102291e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = dropWh1417102291e_indi(Pa,Ys_1))) # label(fact_633_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 707 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,hAPP_f590186314t_bool(cOMBK_776703103e_indi,B_1)))))) # label(fact_201_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 708 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_006) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 709 (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]. 1.61/2.07 710 (all F all B_1 all A_1 ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),hAPP_A1014090479t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))))) # label(fact_167_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 711 (all B_1_1 all B_2_1 is_bool(hAPP_f2053170815l_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]. 1.61/2.07 712 (all Ys_1 all Pa all Xs ((all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))) -> hBOOL(hAPP_A1120018583t_bool(Pa,X_2))))) -> dropWh1165804960le_alt(Pa,Ys_1) = dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)))) # label(fact_631_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 713 (all B_1_1 all B_2_1 (is_fun1651000642t_bool(B_2_1) -> is_fun1651000642t_bool(hAPP_f246757773t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc___017) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 714 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B_1)))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B_1))))) # label(fact_82_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 715 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))))) # label(fact_247_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 716 (all F all Aa all Ba (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))))) # label(fact_285_curryE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 717 (all X_1 hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_1))) # label(fact_298_top1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 718 (all X_1 hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),top_to1849101472l_bool))) # label(fact_329_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 719 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_057) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 720 (all X_15 all Xs_32 ((Xs_32 = nil_Ar1135217151le_alt -> nil_Ar1135217151le_alt = butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),Xs_32))) & (nil_Ar1135217151le_alt != Xs_32 -> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),Xs_32)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),butlas123970891le_alt(Xs_32))))) # label(fact_307_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 721 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_693_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 722 (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]. 1.61/2.07 723 (all X_1 all L_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_312654597_mktop(L_1),X_1)),arrow_912654623le_Lin)))) # label(fact_28_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 724 (all X_1 all A_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) <-> hBOOL(hAPP_P1813625415t_bool(A_1,X_1)))) # label(fact_268_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 725 (all A_1 pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool) # label(fact_303_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 726 (all X_1 all Xs ((hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> insert897399838t_bool(X_1,Xs) = Xs) & (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs) = insert897399838t_bool(X_1,Xs)))) # label(fact_609_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 727 (all X_1 all Xs (hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),rev_Pr1722970583le_alt(takeWh808795006le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),Xs))) = dropWh1186971862le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),rev_Pr1722970583le_alt(Xs))))) # label(fact_512_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 728 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),hAPP_A1014090479t_bool(B_1,X_1)))))) # label(fact_135_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 729 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_1) & is_Arr723427730le_alt(Z) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_1),Z)),R_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Ys_1),Zs_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Zs_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))))) # label(fact_622_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 730 (all Xs (Xs = nil_Ar1135217151le_alt <-> nil_Ar1135217151le_alt = rev_Ar955429983le_alt(Xs))) # label(fact_487_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 731 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,hAPP_f303195352t_bool(cOMBK_1264040257t_bool,B_1)))))) # label(fact_190_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 732 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),hAPP_A955165183l_bool(B_1,X_1))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))))) # label(fact_59_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 733 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))))) # label(fact_177_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 734 (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]. 1.61/2.07 735 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),B_1))))) -> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,hAPP_f1274922098i_bool(cOMBK_948333518t_bool,B_1)))))) # label(fact_189_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 736 (all B_1_1 is_Arr859726945e_indi(last_A560832347e_indi(B_1_1))) # label(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 737 (all B_1_1 is_fun1420103068l_bool(set_fu444796538t_bool(B_1_1))) # label(gsy_c_List_Oset_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 738 (all P all Q all R hAPP_A1660609715le_alt(hAPP_f904937452le_alt(hAPP_f239458941le_alt(cOMBB_521986850le_alt,P),Q),R) = hAPP_l1390889510le_alt(P,hAPP_A1849759038le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 739 (all P all Q all R hAPP_A643475905l_bool(hAPP_f1747206697l_bool(hAPP_f274832101l_bool(cOMBB_885534287le_alt,P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 740 (all Xs_23 all Ys_9 ((nil_Ar1135217151le_alt != Ys_9 -> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),Ys_9)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),butlas123970891le_alt(Ys_9))) & (nil_Ar1135217151le_alt = Ys_9 -> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),Ys_9)) = butlas123970891le_alt(Xs_23)))) # label(fact_388_butlast__append) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 741 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_Pro1004667236le_alt(hAPP_b1482008903le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 742 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun1264457267t_bool(hAPP_A739031709t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_008) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 743 (all X_1 all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))))) # label(fact_407_listrel1I2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 744 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun48324065t_bool(hAPP_A1433148491t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_010) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 745 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),hAPP_f1114489970t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))))) # label(fact_231_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 746 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,hAPP_f498119908l_bool(cOMBK_874213703t_bool,B_1)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),B_1))))) # label(fact_89_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 747 (all X all Y (is_Arr723427730le_alt(Y) & is_Arr723427730le_alt(X) -> -hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(fequal21574094le_alt,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 748 (all X all Y (is_bool(Y) & is_bool(X) -> -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 749 (all P all Q all R hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q) = hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_099) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 750 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun866579754t_bool(hAPP_f1840820673t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___065) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 751 (all Pa hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),nil_Ar1135217151le_alt) = partit1336600824le_alt(Pa,nil_Ar1135217151le_alt)) # label(fact_337_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 752 (all B_1_1 all B_2_1 is_bool(hAPP_f1140617841l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_072) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 753 (exists X_2 (is_Arr859726945e_indi(X_2) & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)))) # label(fact_357_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 754 (all B_1_1 all B_2_1 is_bool(hAPP_P1373277879t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 755 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),suc(N))) <-> N = M | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_679_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 756 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Ys_1)))) | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Xs)))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1))))))) # label(fact_586_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 757 (all F all B_1 all A_1 ((all X_2 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),B_1)))) -> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,hAPP_f978113205l_bool(cOMBK_1549622337le_alt,B_1)))))) # label(fact_206_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 758 (all B_1_1 all B_2_1 is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_045) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 759 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> M_1 = N_1))) # label(fact_672_less__SucE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 760 (all As (As != nil_bool -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,last_bool(As)),set_bool(As))))) # label(fact_575_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 761 (all Xs all X_1 all Ys_1 all Y_2 all R_1 (X_1 = Y_2 & hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) | Xs = Ys_1 & hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) <-> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),nil_li7342420le_alt))),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Ys_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),nil_li7342420le_alt)))),hAPP_f664322981t_bool(listre868094907le_alt,R_1))))) # label(fact_402_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 762 (all X_13 all Xs_27 all Ys_14 hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_13),Xs_27)),Ys_14) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_13),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_27),Ys_14))) # label(fact_373_append__Cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 763 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),hAPP_A340536322t_bool(B_1,X_1)))))) # label(fact_136_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 764 (all B_1_1 all B_2_1 is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_044) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 765 (all F all Aa all Ba (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))))) # label(fact_283_curryD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 766 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> M_1 = suc(N_1)))) # label(fact_686_le__SucE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 767 (all Ca all P_1 ((all A all B (P_1 = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B) -> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(Ca,A),B)))) -> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(Ca),P_1)))) # label(fact_442_splitI2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 768 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))))) # label(fact_172_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 769 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),hAPP_f1114489970t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))))) # label(fact_165_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 770 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))))) # label(fact_249_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 771 (all P all Q all R hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_108) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 772 (all P all Q all R hAPP_l591780830le_alt(hAPP_f1216999144le_alt(hAPP_f879032165le_alt(cOMBB_1303549321le_alt,P),Q),R) = hAPP_l591780830le_alt(P,hAPP_l372964747le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_107) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 773 (all X all Y (X != Y | hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(fequal21574094le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 774 (all X_1 all Y_2 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) & size_s2106320494le_alt(Y_2) = size_s2106320494le_alt(X_1))) # label(fact_434_lexord__lex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 775 (all P all Q (is_fun2015243113i_bool(P) -> P = hAPP_f783549695i_bool(hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___119) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 776 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),B_1))))) -> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,hAPP_f391873743t_bool(cOMBK_339579368t_bool,B_1)))))) # label(fact_192_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 777 (all X all Y (X != Y | hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 778 (all F1 all Aa all Ba (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F1,Aa),Ba)) -> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F1),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))))) # label(fact_439_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 779 (all A_3 all List_3 hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_3),List_3) != nil_Ar1135217151le_alt) # label(fact_38_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 780 (all P all Q (is_fun2015243113i_bool(P) -> hAPP_f1570138413i_bool(hAPP_f1274922098i_bool(cOMBK_948333518t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___104) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 781 (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]. 1.61/2.07 782 (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),suc(N))))) # label(fact_698_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 783 (all Ys_1 all Pa all Xs ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs))) -> hBOOL(hAPP_f1378099862l_bool(Pa,X_2))))) -> hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),takeWh1813199437t_bool(Pa,Ys_1)) = takeWh1813199437t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)))) # label(fact_645_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 784 (all P all Q P = hAPP_A1660609715le_alt(hAPP_f921948995le_alt(cOMBK_1825575856le_alt,P),Q)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 785 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))))) # label(fact_228_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 786 (all X_1 all Xs ((hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> Xs = insert531176721le_alt(X_1,Xs)) & (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> insert531176721le_alt(X_1,Xs) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs)))) # label(fact_606_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 787 (all M all N (M = suc(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),suc(N))))) # label(fact_683_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 788 (all Pa all Xs (takeWh1545314552le_alt(Pa,Xs) = Xs <-> (all X_2 (is_Arr723427730le_alt(X_2) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))) -> hBOOL(hAPP_A1120018583t_bool(Pa,X_2))))))) # label(fact_531_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 789 (all X all Y (is_fun48324065t_bool(X) & is_fun48324065t_bool(Y) -> -hBOOL(hAPP_f446648900l_bool(hAPP_f656614015l_bool(fequal547890341t_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____w) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 790 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),hAPP_f721327224l_bool(B_1,X_1)))))) # label(fact_134_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 791 (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]. 1.61/2.07 792 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,B_1)))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),B_1))))) # label(fact_95_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 793 (all Xs (hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) <-> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rotate184372300le_alt(Xs))))) # label(fact_406_distinct1__rotate) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 794 (all X_16 all Xs_33 (Xs_33 != nil_Ar1135217151le_alt -> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_16),Xs_33)) = last_A1066338328le_alt(Xs_33))) # label(fact_294_last__ConsR) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 795 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,hAPP_f1954218281l_bool(cOMBK_549130676le_alt,B_1)))) -> (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),B_1))))) # label(fact_106_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 796 (all B_1_1 (is_fun2015243113i_bool(B_1_1) -> is_fun2015243113i_bool(collec279390863e_indi(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 797 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun2015243113i_bool(hAPP_A1609075839i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 798 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),hAPP_P1436281263t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))))) # label(fact_220_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 799 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B_1)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B_1))))) # label(fact_113_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 800 (all Xs all R_1 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))) # label(fact_408_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 801 (all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> ((all X_2 (is_Arr723427730le_alt(X_2) -> (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Ys_1) = Xs -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1))))) -> -(all Zs (Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Zs) -> -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Zs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))))))) # label(fact_422_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 802 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B_1,X_1)))))) # label(fact_119_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 803 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),hAPP_f1570138413i_bool(B_1,X_1))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))))) # label(fact_66_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 804 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,B_1)))))) # label(fact_205_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 805 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___069) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 806 (all Pa nil_Ar1135217151le_alt = takeWh1545314552le_alt(Pa,nil_Ar1135217151le_alt)) # label(fact_338_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 807 (all X_1 all Xs ((hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> Xs = insert22093680t_bool(X_1,Xs)) & (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs) = insert22093680t_bool(X_1,Xs)))) # label(fact_611_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 808 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> 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_1)),rev_bool(Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),rev_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_1)),Xs)))))) # label(fact_508_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 809 (all X_1 all Xs ((-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs) = insert1683711393le_alt(X_1,Xs)) & (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> Xs = insert1683711393le_alt(X_1,Xs)))) # label(fact_612_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 810 (all Xs rev_Ar955429983le_alt(Xs) = foldl_107212092le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,cons_A77766063le_alt),nil_Ar1135217151le_alt,Xs)) # label(fact_514_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 811 (all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Xs)))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))))) # label(fact_539_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 812 (all Pa all Xs all Yes all No (hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Yes),No) = partit1336600824le_alt(Pa,Xs) -> (all X_2 (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Yes))) -> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)))) & (all X_2 (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(No))) -> -hBOOL(hAPP_A1120018583t_bool(Pa,X_2)))))) # label(fact_621_partition__P) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 813 (all P all Q all R hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,P),Q),R) = hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 814 (all Aa all Ba all A_2 all B_3 (hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_2),B_3) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba) <-> Ba = B_3 & A_2 = Aa)) # label(fact_15_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 815 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B_1,X_2)))))) -> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))))) # label(fact_219_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 816 (all Xs (Xs != nil_Ar1135217151le_alt -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hd_Arr1814706386le_alt(Xs)),set_Ar426477344le_alt(Xs))))) # label(fact_589_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 817 (all B_1_1 all B_2_1 (is_fun48324065t_bool(B_2_1) -> is_fun292781289l_bool(hAPP_f656614015l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_042) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 818 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) -> (-hBOOL(hAPP_P1813625415t_bool(Pa,X_1)) -> hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,dropWh1186971862le_alt(Pa,Xs)),Ys_1) = dropWh1186971862le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1))))) # label(fact_604_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 819 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__073) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 820 (all Xs_7 (nil_Ar1135217151le_alt != Xs_7 -> last_A1066338328le_alt(Xs_7) = hd_Arr1814706386le_alt(rev_Ar955429983le_alt(Xs_7)))) # label(fact_479_hd__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 821 (all P all Q (is_fun1420103068l_bool(P) -> P = hAPP_A433435097l_bool(hAPP_f1954218281l_bool(cOMBK_549130676le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_095) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 822 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> (-hBOOL(hAPP_f1378099862l_bool(Pa,X_1)) -> hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,dropWh2056378277t_bool(Pa,Xs)),Ys_1) = dropWh2056378277t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1))))) # label(fact_603_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 823 (all X all Y (hBOOL(hAPP_A416869060i_bool(hAPP_A1609075839i_bool(fequal2012472101e_indi,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_T) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 824 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))))) # label(fact_238_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 825 (all Y_3 -(all A all B Y_3 != hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B))) # label(fact_256_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 826 (all P all Q all R hAPP_P2096362161le_alt(hAPP_l1791846092le_alt(P,R),hAPP_l591780830le_alt(Q,R)) = hAPP_l591780830le_alt(hAPP_f1427069397le_alt(hAPP_f1928725626le_alt(cOMBS_1626428525le_alt,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 827 (all R_1 hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))) # label(fact_455_listrel_ONil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 828 (all Pa all Xs ((exists X_2 (hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) & hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs))))) -> -(all Ys all X_2 (is_Arr723427730le_alt(X_2) -> ((exists Zs hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Zs)) = Xs) -> -hBOOL(hAPP_A1120018583t_bool(Pa,X_2))))))) # label(fact_647_split__list__propE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 829 (all X_1 all A_1 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) <-> hBOOL(hAPP_bool_bool(A_1,X_1)))) # label(fact_267_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.07 830 (all Ys_1 all Zs_1 all X_1 all Xs (Ys_1 = nil_Ar1135217151le_alt & Zs_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) | (exists Ys_10 (Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_10),Zs_1) & hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_10) = Ys_1)) <-> hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Zs_1))) # label(fact_384_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 831 (all P all Q (is_fun2015243113i_bool(P) -> P = hAPP_P957402556i_bool(hAPP_f3439105i_bool(cOMBK_520250367le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___091) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 832 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,hAPP_f391873743t_bool(cOMBK_339579368t_bool,B_1)))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),B_1))))) # label(fact_90_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 833 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_007) # label(hypothesis) # label(non_clause). [assumption]. 1.61/2.08 834 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)))) # label(fact_666_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 835 (all N_1 all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(M_1))) -> M_1 = N_1))) # label(fact_676_less__antisym) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 836 (all X_1 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool))) # label(fact_323_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 837 (all Xs all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) -> -(all X_2 all Y_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1)) -> (all Us all Vs (hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Vs)) = Xs -> hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Vs)) != Ys_1)))))) # label(fact_417_listrel1E) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 838 (all I_4 all Fa (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) -> ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof)) -> (all A all B (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) -> (A != B -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I_4))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2)))))))))) -> hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_4))))) # label(fact_45_dictatorI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 839 (all Ys_1 all R_1 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Ys_1)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1)))) # label(fact_367_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 840 (all X_1 all Xs (hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs)) -> (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) -> dropWh1957015750le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),rev_Pr816629831le_alt(Xs)) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),rev_Pr816629831le_alt(takeWh768831342le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),Xs)))))) # label(fact_506_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 841 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(N_1)))) # label(fact_652_lessI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 842 (all Xs_28 all Ys_15 all Zs_3 hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_28),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_15),Zs_3)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_28),Ys_15)),Zs_3)) # label(fact_372_append__assoc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 843 (all X_1 all Y_2 all L_1 (is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(X_1) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> (Y_2 != X_1 -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_1)),L_1))))))) # label(fact_30_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 844 (all X_1 all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) <-> (exists Ys exists Zs Xs = hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Ys),hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Zs))))) # label(fact_650_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 845 (all N_6 all Xs_6 hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_6),butlas123970891le_alt(Xs_6)) = butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_6),Xs_6))) # label(fact_482_butlast__drop) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 846 (all X_1 all Y_2 all R_1 ((all A all B (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),R_1)) | A = B | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,B),A)),R_1)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_2),X_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) | X_1 = Y_2 | hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))) # label(fact_313_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 847 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),hAPP_f1741989420t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))))) # label(fact_229_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 848 (all B_1_1 all B_2_1 is_bool(hAPP_f742658307l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_049) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 849 (all P all Q (is_bool(P) -> P = hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 850 (all X_1 all Xs (hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Xs)))) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))))) # label(fact_532_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 851 (all P all Q (is_fun292781289l_bool(P) -> P = hAPP_P1533476044l_bool(hAPP_f1197671953l_bool(cOMBK_165199855le_alt,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_123) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 852 (all P all Q (is_fun1651000642t_bool(P) -> P = hAPP_f3167870t_bool(hAPP_f1698272152t_bool(cOMBK_242036279t_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___102) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 853 (all K all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(I_1)),K))))) # label(fact_673_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 854 (all X all Y hAPP_P2096362161le_alt(hAPP_P1891191097le_alt(if_Pro1659200999le_alt(fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 855 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))) -> (-hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),hAPP_f1114489970t_bool(B_1,X_1))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))))) # label(fact_75_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 856 (all X_1 all R_1 -hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))) # label(fact_306_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 857 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1651000642t_bool(hAPP_b287951269t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 858 (all Xs all Ys_1 (nil_Ar1135217151le_alt = Ys_1 <-> Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))) # label(fact_381_append__self__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 859 (all P all Q all R hAPP_f921250311t_bool(P,hAPP_l1748807729l_bool(Q,R)) = hAPP_l2144750563t_bool(hAPP_f1837837439t_bool(hAPP_f1503353479t_bool(cOMBB_1326560562le_alt,P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_127) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 860 (all P all Q (is_fun1420103068l_bool(P) -> P = hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_097) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 861 (all B_1_1 all B_2_1 is_bool(hAPP_f505027144l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_048) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 862 (all R_1 hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),nil_Ar1135217151le_alt),nil_Ar1135217151le_alt))) # label(fact_469_listrelp_ONil) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 863 (all Xs all Ys_1 all Zs_1 (Zs_1 = Ys_1 <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Zs_1))) # label(fact_370_same__append__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 864 (all Fa (hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa)) <-> (all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof)) -> (all A all B (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) -> ((all I (is_Arr859726945e_indi(I) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I))))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2))))))))))) # label(fact_33_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 865 (all B_1_1 all B_2_1 is_fun701126715l_bool(hAPP_P2049543454l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_081) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 866 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_fun1651000642t_bool(hAPP_P1116266031t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__075) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 867 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),hAPP_P1116266031t_bool(B_1,X_1)))))) # label(fact_120_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 868 (all X_1 all Xs (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> insert897399838t_bool(X_1,Xs) = hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs))) # label(fact_617_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 869 (all Pa all Xs all Y_2 all Ys_1 (-hBOOL(hAPP_A1120018583t_bool(Pa,Y_2)) & hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,takeWh1545314552le_alt(Pa,Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)) = Xs <-> hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1) = dropWh1165804960le_alt(Pa,Xs))) # label(fact_425_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 870 (all Xs all Ys_1 (nil_Ar1135217151le_alt = Ys_1 <-> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = Xs)) # label(fact_378_self__append__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 871 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___066) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 872 (all Xs all X_1 all Y_2 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Xs))),hAPP_f664322981t_bool(listre868094907le_alt,R_1))))) # label(fact_414_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 873 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,hAPP_f2062029545l_bool(cOMBK_753699544t_bool,B_1)))))) # label(fact_195_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 874 (all X_1 all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) & Ys_1 = Xs | X_1 = Y_2 & hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))))) # label(fact_411_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 875 (all Pa ((all X1 (is_Pro1004667236le_alt(X1) -> hBOOL(hAPP_P1813625415t_bool(Pa,X1)))) <-> (all A all B (is_Arr723427730le_alt(A) & is_Arr723427730le_alt(B) -> hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B))))))) # label(fact_14_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 876 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),hAPP_b1461182872l_bool(B_1,X_1)))))) # label(fact_142_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 877 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Ys_1)))) | hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Xs)))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1))))))) # label(fact_582_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 878 (all P all Q all R hAPP_f890578273l_bool(hAPP_l1493471510l_bool(P,R),Q) = hAPP_l300482276t_bool(hAPP_f4315714t_bool(hAPP_f921250311t_bool(cOMBC_1827582133l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_100) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 879 (all Zs_1 all Ys_1 all R_1 all Xs ((all X_2 all Y_1 all Z (is_Pro1004667236le_alt(Y_1) & is_Pro1004667236le_alt(Z) & is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs))) -> (hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,X_2),Y_1)),R_1)) -> (hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,Y_1),Z)),R_1)) -> hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,X_2),Z)),R_1))))))) -> (hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Xs),Ys_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1))) -> (hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Ys_1),Zs_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1))) -> hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Xs),Zs_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1))))))) # label(fact_630_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 880 (all P all Q all R hAPP_l1148780281le_alt(hAPP_f670565125le_alt(hAPP_f351228915le_alt(cOMBC_72147604le_alt,P),Q),R) = hAPP_f1216999144le_alt(hAPP_l486475401le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_121) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 881 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),hAPP_f3167870t_bool(B_1,X_2)))))) -> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))))) # label(fact_155_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 882 (all P all Q (is_bool(P) -> P = hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl_087) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 883 (all Ys_1 all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Ys_1)))) | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs)))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1))))))) # label(fact_584_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 884 (all F all B_1 all A_1 ((all X_2 (is_fun20916972t_bool(X_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),B_1))))) -> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B_1)))))) # label(fact_193_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 885 (all B_1_1 all B_2_1 is_bool(hAPP_f2078996785l_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]. 1.61/2.08 886 (exists X_2 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)) & is_fun48324065t_bool(X_2))) # label(fact_362_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 887 (all Xs all Ys_1 all R_1 all X_1 all Y_2 (hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_1),Y_2)) -> (hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs),Ys_1)) -> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)))))) # label(fact_468_listrelp_OCons) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 888 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) & is_fun20916972t_bool(B_1_1) -> is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__074) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 889 (all X_1 (hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_1)) <-> hBOOL(top_top_bool))) # label(fact_331_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 890 (all B_1_1 all B_2_1 is_bool(hAPP_f2099712241l_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]. 1.61/2.08 891 (all F all B_1 all A_1 ((all X_2 (is_Pro1004667236le_alt(X_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))))) # label(fact_182_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 892 (all X_1 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool))) # label(fact_315_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 893 (exists X_2 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) & is_bool(X_2))) # label(fact_356_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 894 (all X_1 all Xs ((hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> insert1409495663t_bool(X_1,Xs) = Xs) & (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) -> insert1409495663t_bool(X_1,Xs) = hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs)))) # label(fact_610_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 895 (all Ys_1 all Pa all Xs ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs))) -> hBOOL(hAPP_A416869060i_bool(Pa,X_2))))) -> takeWh1088896635e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),takeWh1088896635e_indi(Pa,Ys_1)))) # label(fact_641_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 896 (all M_1 all N_1 (M_1 = 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_eq_nat,M_1),N_1)))) # label(fact_688_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 897 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_665_le__refl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 898 (all Pa all Xs hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,size_s2106320494le_alt(takeWh1545314552le_alt(Pa,Xs))),Xs) = dropWh1165804960le_alt(Pa,Xs)) # label(fact_481_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 899 (all P all Q (is_fun1420103068l_bool(P) -> P = hAPP_b805997823l_bool(hAPP_f118515775l_bool(cOMBK_1028572856l_bool,P),Q))) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 900 (all As (As != nil_Pr1710246567le_alt -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,last_P1076199502le_alt(As)),set_Pr1756729158le_alt(As))))) # label(fact_573_last__in__set) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 901 (all Ys_1 all Xs all Us_1 all Vs_1 all X_1 all Y_2 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) -> (Xs = hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Vs_1)) -> (Ys_1 = hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Vs_1)) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))))))) # label(fact_416_listrel1I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 902 (all B_1_1 all B_2_1 is_bool(hAPP_f1472889102l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsu) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 903 (all Xs all Ys_1 (nil_Ar1135217151le_alt = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) <-> nil_Ar1135217151le_alt = Ys_1 & Xs = nil_Ar1135217151le_alt)) # label(fact_380_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 904 (all Aa all List_2 all A_2 all List_1 (is_Arr723427730le_alt(A_2) & is_Arr723427730le_alt(Aa) -> (hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),List_2) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_2),List_1) <-> A_2 = Aa & List_2 = List_1))) # label(fact_41_list_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 905 (all B_1_1 all B_2_1 is_bool(hAPP_f1484382710l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_051) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 906 (all B_1_1 all B_2_1 is_bool(hAPP_f2031902329l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____061) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 907 (all F all B_1 all A_1 ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))))) # label(fact_243_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 908 (all B_1_1 is_fun1264457267t_bool(last_f1921219373t_bool(B_1_1))) # label(gsy_c_List_Olast_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oind) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 909 (all Xs_19 all X_11 Xs_19 = butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_19),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_11),nil_Ar1135217151le_alt)))) # label(fact_393_butlast__snoc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 910 (all X_1 all Xs (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Xs)))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))))) # label(fact_537_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 911 (all P all Q (is_fun_bool_bool(P) -> hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_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]. 1.61/2.08 912 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_009) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 913 (all Xs (Xs = nil_Ar1135217151le_alt <-> rotate184372300le_alt(Xs) = nil_Ar1135217151le_alt)) # label(fact_405_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 914 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),suc(M))))) # label(fact_684_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 915 (all B_1_1 all B_2_1 is_bool(hAPP_f1456773233l_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]. 1.61/2.08 916 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),M)) <-> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_682_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 917 (all X all Y (is_fun20916972t_bool(Y) & is_fun20916972t_bool(X) -> Y = X | -hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(fequal318101288t_bool,X),Y)))) # label(help_fequal_1_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 918 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) -> 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_1)),rev_bool(Xs)) = rev_bool(tl_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_1)),Xs)))))) # label(fact_500_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 919 (all S_1 all R_2 ((all X_2 all Xa (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),R_2)) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),S_1)))) <-> S_1 = R_2)) # label(fact_254_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 920 (all L_1 all X_1 all Y_2 (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Y_2) -> (Y_2 != X_1 -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,L_1),X_1),Y_2)),arrow_912654623le_Lin)))))) # label(fact_21_below__Lin) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 921 (all A_1 (is_fun_bool_bool(A_1) -> ((all X_2 (is_bool(X_2) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)))) -> top_to1647826457l_bool = A_1))) # label(fact_348_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 922 (all P all Q all R hAPP_P1373277879t_bool(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1373277879t_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]. 1.61/2.08 923 (all P all Q all R hAPP_A64811457t_bool(hAPP_f1092358369t_bool(hAPP_f1682340965t_bool(cOMBB_333235735le_alt,P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___122) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 924 (all B_1_1 all B_2_1 (is_fun292781289l_bool(B_2_1) -> is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_046) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 925 (all A_7 all B_5 all A_6 all B_4 (hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_6),B_4) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_7),B_5) -> -(A_7 = A_6 -> B_5 != B_4))) # label(fact_17_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 926 (all B_1_1 all B_2_1 is_bool(hAPP_l1642116416t_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]. 1.61/2.08 927 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),hAPP_b651754310l_bool(B_1,X_1))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))))) # label(fact_61_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 928 (all Ys_1 all Pa all Xs ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs))) -> hBOOL(hAPP_f446648900l_bool(Pa,X_2))))) -> hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),takeWh1268567035t_bool(Pa,Ys_1)) = takeWh1268567035t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)))) # label(fact_643_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 929 (all U all X_1 all Y_2 all Aa all Ba all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)),R_1)) -> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,U),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Aa),X_1))),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,U),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Ba),Y_2)))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))))) # label(fact_396_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 930 (all F all B_1 all A_1 ((all X_2 (is_fun48324065t_bool(X_2) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B_1,X_2)))))) -> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))))) # label(fact_232_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 931 (all X_1 all F all A_1 all B_1 (hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),hAPP_A990651116l_bool(B_1,X_1))) -> -hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))))) # label(fact_58_PiE) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 932 (all Ys_1 all Pa all X_1 all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) -> (-hBOOL(hAPP_f446648900l_bool(Pa,X_1)) -> takeWh1268567035t_bool(Pa,Xs) = takeWh1268567035t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1))))) # label(fact_568_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 933 (all X_17 all Xs_34 (is_Arr723427730le_alt(X_17) -> (Xs_34 = nil_Ar1135217151le_alt -> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_17),Xs_34)) = X_17))) # label(fact_293_last__ConsL) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 934 (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]. 1.61/2.08 935 (all X_1 all Xs all Y_2 all Ys_1 all R_1 (hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(lex_li910676976le_alt,R_1))) <-> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) & size_s101148091le_alt(Ys_1) = size_s101148091le_alt(Xs) | hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(lex_li910676976le_alt,R_1))) & Y_2 = X_1)) # label(fact_423_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 936 (all P all Q hAPP_f1681297285t_bool(hAPP_f684471657t_bool(cOMBK_509674590t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___110) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 937 (all X_1 all Pa all Xs (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(takeWh1268567035t_bool(Pa,Xs)))) -> hBOOL(hAPP_f446648900l_bool(Pa,X_1)) & hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))))) # label(fact_527_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 938 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1))))) # label(fact_685_le__SucI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 939 (all B_1_1 all B_2_1 is_bool(hAPP_f140107297l_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]. 1.61/2.08 940 (all X_1 all Xs (hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) -> takeWh1813199437t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),rev_fu313987494t_bool(Xs)) = rev_fu313987494t_bool(tl_fun542205423t_bool(dropWh2056378277t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),Xs)))))) # label(fact_503_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 941 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 942 (all B_1_1 all B_2_1 (is_fun1264457267t_bool(B_2_1) -> is_Arr723427730le_alt(hAPP_f1287961430le_alt(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__020) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 943 (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]. 1.61/2.08 944 (all A_1 (is_fun1420103068l_bool(A_1) -> ((all X_2 (is_fun20916972t_bool(X_2) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)))) -> A_1 = top_to846262053l_bool))) # label(fact_353_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 945 (all F all B_1 all A_1 ((all X_2 (is_fun1264457267t_bool(X_2) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,hAPP_f498119908l_bool(cOMBK_874213703t_bool,B_1)))))) # label(fact_191_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 946 (all F all B_1 all A_1 ((all X_2 (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B_1))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B_1)))))) # label(fact_217_funcsetI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 947 (all B_1_1 all B_2_1 is_bool(hAPP_f784749731l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 948 (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_eq_nat,suc(N)),M)))) # label(fact_699_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 949 (all B_1_1 all B_2_1 (is_Pro1004667236le_alt(B_2_1) -> is_fun_bool_bool(hAPP_P1122857141l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__077) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 950 (all B_1_1 all B_2_1 is_bool(hAPP_f891725169l_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]. 1.61/2.08 951 (all Xs all Ys_1 all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) -> -(all X_2 all Y_1 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_1) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1)) -> (all Us all Vs (hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Vs)) = Xs -> Ys_1 != hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Vs))))))))) # label(fact_418_listrel1E) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 952 (all X_1 all Pa all Xs (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(takeWh808795006le_alt(Pa,Xs)))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) & hBOOL(hAPP_P1813625415t_bool(Pa,X_1)))) # label(fact_530_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 953 (all X_1 all U all V all R_1 (hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,U),V)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) -> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),U)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),V))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))))) # label(fact_392_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 954 (all B_1_1 (is_fun866579754t_bool(B_1_1) -> is_fun20916972t_bool(produc278404511t_bool(B_1_1)))) # label(gsy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 955 (all Xs_18 all X_10 (is_Arr723427730le_alt(X_10) -> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_18),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_10),nil_Ar1135217151le_alt))) = X_10)) # label(fact_394_last__snoc) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 956 (exists L_2 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_2),arrow_912654623le_Lin)) & is_fun20916972t_bool(L_2))) # label(fact_40_linear__alt) # label(axiom) # label(non_clause). [assumption]. 1.61/2.08 957 -(all I (is_Arr859726945e_indi(I) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),c)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,hAPP_A340536322t_bool(p,I)),c),b))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_A340536322t_bool(p,I)))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 1.61/2.08 1.61/2.08 ============================== end of process non-clausal formulas === 3.60/3.88 3.60/3.88 ============================== PROCESS INITIAL CLAUSES =============== 3.60/3.88 3.60/3.88 ============================== PREDICATE ELIMINATION ================= 3.60/3.88 3.60/3.88 ============================== end predicate elimination ============= 3.60/3.88 3.60/3.88 Auto_denials: (non-Horn, no changes). 3.60/3.88 3.60/3.88 Term ordering decisions: 3.60/3.88 Function symbol KB weights: member720722004le_alt=1. member1373125444le_alt=1. cons_A77766063le_alt=1. produc1456060119le_alt=1. produc2031778509le_alt=1. nil_Ar1135217151le_alt=1. append28105492le_alt=1. member1704306684t_bool=1. member1265098019t_bool=1. member1619170513t_bool=1. member694465108le_alt=1. produc1707341143le_alt=1. member2080870050le_alt=1. cons_l882637220le_alt=1. member161528657e_indi=1. member_bool=1. ord_less_nat=1. arrow_583275979e_Prof=1. arrow_912654623le_Lin=1. lexord807118444le_alt=1. listre1913026136le_alt=1. ord_less_eq_nat=1. fNot=1. listre1769678631le_alt=1. listre868094907le_alt=1. distin85347314le_alt=1. lexord717456039le_alt=1. listre870705708le_alt=1. arrow_207701375_below=1. f=1. nil_li7342420le_alt=1. lexord1008325386le_alt=1. lexord1145600903t_bool=1. lexord1692326342t_bool=1. lexord1918670343e_indi=1. lexord373145049t_bool=1. lexord_bool=1. member1058364180t_bool=1. member1353676180le_alt=1. member1477971960t_bool=1. member200634580t_bool=1. member912023252e_indi=1. member976989780t_bool=1. produc1067887767t_bool=1. produc1134856577t_bool=1. produc1787549079le_alt=1. produc1849892183e_indi=1. produc436944087t_bool=1. produc49085783t_bool=1. append1413540863le_alt=1. arrow_885770895le_IIA=1. append1735936098le_alt=1. append2131097198t_bool=1. append352340785t_bool=1. append1480696031t_bool=1. append968919903e_indi=1. append_bool=1. b=1. cOMBK_1918246033t_bool=1. top_to846262053l_bool=1. top_top_bool=1. a=1. lex_Ar1264540259le_alt=1. lexord170366202le_alt=1. member1024929995t_bool=1. member104322770t_bool=1. member1194332074t_bool=1. member1258284266t_bool=1. member1402889547l_bool=1. member1423816203t_bool=1. member1464733303le_alt=1. member1618799570e_indi=1. member1687274886le_alt=1. member1805745300le_alt=1. member1935624595e_indi=1. member1953881075le_alt=1. member2021375116l_bool=1. member2074697974le_alt=1. member2142449782le_alt=1. member219620739le_alt=1. member220564739e_indi=1. member234310528e_indi=1. member300433020le_alt=1. member385159430le_alt=1. member39203141le_alt=1. member442467260le_alt=1. member48503289l_bool=1. member567993161le_alt=1. member689634176t_bool=1. member821152697t_bool=1. member930088569t_bool=1. produc499297815le_alt=1. append1768277586le_alt=1. arrow_1486210539le_alt=1. arrow_1549387998ctator=1. fTrue=1. top_to1849101472l_bool=1. top_to186242507t_bool=1. top_to207207712i_bool=1. top_to935749874l_bool=1. arrow_1550141362nimity=1. 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insert1409495663t_bool=1. insert1683711393le_alt=1. insert1731565726e_indi=1. insert22093680t_bool=1. insert531176721le_alt=1. insert897399838t_bool=1. insert_bool=1. partit1336600824le_alt=1. hAPP_A2054143614e_indi=1. hAPP_A785351481e_indi=1. hAPP_P1099469545l_bool=1. hAPP_P1109943007le_alt=1. hAPP_P1374173745l_bool=1. hAPP_P1435933929l_bool=1. hAPP_P1725284223le_alt=1. hAPP_P1891191097le_alt=1. hAPP_P1919864457l_bool=1. hAPP_P1992806581l_bool=1. hAPP_P29732487le_alt=1. hAPP_P626359285l_bool=1. hAPP_P738148045l_bool=1. hAPP_P937918807le_alt=1. hAPP_b1115999851l_bool=1. hAPP_b2048821609l_bool=1. hAPP_b2116075462i_bool=1. hAPP_b287951269t_bool=1. hAPP_f1092358369t_bool=1. hAPP_f1224738111l_bool=1. hAPP_f1265889019t_bool=1. hAPP_f1418100887l_bool=1. hAPP_f1503353479t_bool=1. hAPP_f1585690341l_bool=1. hAPP_f1596466233t_bool=1. hAPP_f1639289588t_bool=1. hAPP_f1682340965t_bool=1. hAPP_f1747206697l_bool=1. hAPP_f1785736029t_bool=1. hAPP_f18365135le_alt=1. hAPP_f1837837439t_bool=1. hAPP_f1893731349l_bool=1. hAPP_f1895633847t_bool=1. hAPP_f1997384703t_bool=1. hAPP_f1999636669t_bool=1. hAPP_f268020663le_alt=1. hAPP_f274832101l_bool=1. hAPP_f38433022t_bool=1. hAPP_f775987425t_bool=1. hAPP_l784127213t_bool=1. hAPP_A1202525278t_bool=1. hAPP_A1849759038le_alt=1. hAPP_A643475905l_bool=1. hAPP_A64811457t_bool=1. hAPP_A85603248t_bool=1. hAPP_f1124725731le_alt=1. hAPP_f1216999144le_alt=1. hAPP_f1291634731le_alt=1. hAPP_f1427069397le_alt=1. hAPP_f1472889102l_bool=1. hAPP_f1504748473le_alt=1. hAPP_f1558754397le_alt=1. hAPP_f1654251593le_alt=1. hAPP_f1656652505l_bool=1. hAPP_f1660378693le_alt=1. hAPP_f1928725626le_alt=1. hAPP_f1949171529le_alt=1. hAPP_f2122335314le_alt=1. hAPP_f239458941le_alt=1. hAPP_f310101886le_alt=1. hAPP_f332249751le_alt=1. hAPP_f351228915le_alt=1. hAPP_f372913425t_bool=1. hAPP_f4315714t_bool=1. hAPP_f593033837le_alt=1. hAPP_f622637325l_bool=1. hAPP_f794134621le_alt=1. hAPP_f879032165le_alt=1. hAPP_f904937452le_alt=1. hAPP_f921250311t_bool=1. hAPP_f921948995le_alt=1. hAPP_l1244209582le_alt=1. hAPP_l1493471510l_bool=1. hAPP_l1693669363le_alt=1. hAPP_l1748807729l_bool=1. hAPP_l1791846092le_alt=1. hAPP_l2144750563t_bool=1. hAPP_l436896263le_alt=1. hAPP_l486097526le_alt=1. hAPP_l486475401le_alt=1. hAPP_l508185643t_bool=1. lexn_A19384479le_alt=1. hAPP_l1197505987l_bool=1. hAPP_n2058955628t_bool=1. hAPP_n2099236808t_bool=1. hAPP_n2100915976le_alt=1. hAPP_n2108195705le_alt=1. hAPP_n323901960le_alt=1. hAPP_n479129736t_bool=1. hAPP_n568645704e_indi=1. hAPP_n587545160t_bool=1. f2=1. f8=1. f9=1. f30=1. f37=1. f38=1. f45=1. f46=1. f63=1. f64=1. f77=1. f78=1. f82=1. f83=1. f102=1. f113=1. f130=1. f135=1. f149=1. f150=1. f197=1. f198=1. f199=1. f202=1. f203=1. f217=1. f218=1. f225=1. f234=1. f235=1. f236=1. f242=1. f243=1. f244=1. f245=1. f246=1. f266=1. f267=1. suc=1. set_Ar426477344le_alt=1. set_Pr2031705942le_alt=1. set_bool=1. set_fu222164517t_bool=1. set_fu444796538t_bool=1. set_Ar1035526739e_indi=1. set_fu1433968595t_bool=1. rev_Ar955429983le_alt=1. set_Pr1756729158le_alt=1. butlas123970891le_alt=1. last_A1066338328le_alt=1. listre1062185049le_alt=1. size_s2106320494le_alt=1. produc278404511t_bool=1. hd_Arr1814706386le_alt=1. produc616221118t_bool=1. tl_Arr314474198le_alt=1. produc1802641557t_bool=1. rotate184372300le_alt=1. size_s101148091le_alt=1. arrow_163947511_mkbot=1. arrow_312654597_mktop=1. butlas1168145387le_alt=1. butlas1808913499le_alt=1. butlas1811107560e_indi=1. butlas217264037t_bool=1. butlas423814760t_bool=1. butlas813551546t_bool=1. butlast_bool=1. collec612883262t_bool=1. rev_Ar758908116e_indi=1. rev_Pr1722970583le_alt=1. rev_Pr816629831le_alt=1. rev_bool=1. rev_fu101184185t_bool=1. rev_fu313987494t_bool=1. rev_fu580432980t_bool=1. collec279390863e_indi=1. collec591097828le_alt=1. if_Pro1659200999le_alt=1. in_rel1361124802le_alt=1. produc930723380t_bool=1. collec1376511890le_alt=1. collec1517527055t_bool=1. collec1567922785t_bool=1. hd_Arr1280875809e_indi=1. hd_Pro804272676le_alt=1. hd_bool=1. hd_fun1289819809t_bool=1. hd_fun1937506860t_bool=1. hd_fun780865267t_bool=1. in_rel264468792le_alt=1. last_A560832347e_indi=1. last_P15572062le_alt=1. last_bool=1. last_f1172522866t_bool=1. last_f1921219373t_bool=1. last_f584510683t_bool=1. listre1064220282le_alt=1. order_1844940151le_alt=1. hd_Pro53798164le_alt=1. last_P1076199502le_alt=1. produc1250814607le_alt=1. set_li1879521523le_alt=1. tl_Arr282712093e_indi=1. tl_Pro1439282464le_alt=1. tl_Pro645285392le_alt=1. tl_bool=1. tl_fun1131179056t_bool=1. tl_fun1512606109t_bool=1. tl_fun542205423t_bool=1. undefi1052853330e_indi=1. undefi1471133025le_alt=1. undefi1522782549le_alt=1. undefi396693458t_bool=1. undefi426827556t_bool=1. undefi541132219t_bool=1. undefined_bool=1. f12=1. f13=1. f20=1. f21=1. f22=1. f23=1. f35=1. f36=1. f52=1. f53=1. f54=1. f75=1. f76=1. f90=1. f91=1. f92=1. f93=1. f94=1. fAlarm clock 119.77/120.02 Prover9 interrupted 119.77/120.02 EOF