0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n024.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 03:28:22 EDT 2022 0.12/0.34 % CPUTime : 1.58/1.80 ============================== Prover9 =============================== 1.58/1.80 Prover9 (32) version 2009-11A, November 2009. 1.58/1.80 Process 2163 was started by sandbox2 on n024.cluster.edu, 1.58/1.80 Tue Aug 9 03:28:24 2022 1.58/1.80 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_2003_n024.cluster.edu". 1.58/1.80 ============================== end of head =========================== 1.58/1.80 1.58/1.80 ============================== INPUT ================================= 1.58/1.80 1.58/1.80 % Reading from file /tmp/Prover9_2003_n024.cluster.edu 1.58/1.80 1.58/1.80 set(prolog_style_variables). 1.58/1.80 set(auto2). 1.58/1.80 % set(auto2) -> set(auto). 1.58/1.80 % set(auto) -> set(auto_inference). 1.58/1.80 % set(auto) -> set(auto_setup). 1.58/1.80 % set(auto_setup) -> set(predicate_elim). 1.58/1.80 % set(auto_setup) -> assign(eq_defs, unfold). 1.58/1.80 % set(auto) -> set(auto_limits). 1.58/1.80 % set(auto_limits) -> assign(max_weight, "100.000"). 1.58/1.80 % set(auto_limits) -> assign(sos_limit, 20000). 1.58/1.80 % set(auto) -> set(auto_denials). 1.58/1.80 % set(auto) -> set(auto_process). 1.58/1.80 % set(auto2) -> assign(new_constants, 1). 1.58/1.80 % set(auto2) -> assign(fold_denial_max, 3). 1.58/1.80 % set(auto2) -> assign(max_weight, "200.000"). 1.58/1.80 % set(auto2) -> assign(max_hours, 1). 1.58/1.80 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.58/1.80 % set(auto2) -> assign(max_seconds, 0). 1.58/1.80 % set(auto2) -> assign(max_minutes, 5). 1.58/1.80 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.58/1.80 % set(auto2) -> set(sort_initial_sos). 1.58/1.80 % set(auto2) -> assign(sos_limit, -1). 1.58/1.80 % set(auto2) -> assign(lrs_ticks, 3000). 1.58/1.80 % set(auto2) -> assign(max_megs, 400). 1.58/1.80 % set(auto2) -> assign(stats, some). 1.58/1.80 % set(auto2) -> clear(echo_input). 1.58/1.80 % set(auto2) -> set(quiet). 1.58/1.80 % set(auto2) -> clear(print_initial_clauses). 1.58/1.80 % set(auto2) -> clear(print_given). 1.58/1.80 assign(lrs_ticks,-1). 1.58/1.80 assign(sos_limit,10000). 1.58/1.80 assign(order,kbo). 1.58/1.80 set(lex_order_vars). 1.58/1.80 clear(print_given). 1.58/1.80 1.58/1.80 % formulas(sos). % not echoed (868 formulas) 1.58/1.80 1.58/1.80 ============================== end of input ========================== 1.58/1.80 1.58/1.80 % From the command line: assign(max_seconds, 960). 1.58/1.80 1.58/1.80 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.58/1.80 1.58/1.80 % Formulas that are not ordinary clauses: 1.58/1.80 1 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),A_1))) # label(fact_607_Int__lower1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 2 (all X all Y (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 3 (all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))))) # label(fact_136_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 4 (all P_1 all Q_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1))) # label(fact_583_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 5 (all G_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1)))))) # label(fact_303_finite__UnI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 6 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,hAPP_f547518321e_bool(cOMBB_1170234304e_bool(fequal1531560888_state),F)),hAPP_f1308959284_state(F,X_2)))))) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) & is_fun_pname_bool(X_2)))))) # label(fact_248_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 7 (all Com1_1 all Com2_1 all Pname semi(Com1_1,Com2_1) != hAPP_pname_com(body_1,Pname)) # label(fact_505_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 8 (all P_1 (is_fun_pname_bool(P_1) -> hAPP_f759274231e_bool(collect_pname,P_1) = P_1)) # label(fact_178_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 9 (all B_1 all C (hBOOL(hAPP_com_bool(wt,while(B_1,C))) -> hBOOL(hAPP_com_bool(wt,C)))) # label(fact_493_WTs__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 10 (all A all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1)) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))))) # label(fact_427_le__supE) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 11 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)))) # label(fact_526_predicate1I) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 12 (all G_1 all C (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1055319631e_bool))))) # label(fact_534_MGT__alternI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 13 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_115_set__mp) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 14 (all X all Y (is_pname(Y) & is_pname(X) -> -hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 15 (all N all H all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> ((all X_2 all Y_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f921536533e_bool(H,X_2)),hAPP_f921536533e_bool(H,Y_2)) = hAPP_f921536533e_bool(H,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2))) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,N)) -> (bot_bo1325454745l_bool != N -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(image_505022149e_bool(H),N)) = hAPP_f921536533e_bool(H,hAPP_f772567431e_bool(Fa,N))))))) # label(fact_486_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 16 (all P all Q (is_pname(P) -> hAPP_H1344248906_pname(cOMBK_588224941_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 17 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_43_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 18 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))) # label(fact_654_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 19 (all Fa all G_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1))))) # label(fact_308_finite__Un) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 20 (all B_1_1 all B_2_1 is_bool(finite1282449217_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 21 (all P all Q all R hAPP_H1632039476e_bool(hAPP_f833390165e_bool(cOMBB_1456120487_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1344248906_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_016) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 22 (all B bot_bo1055319631e_bool = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),B)) # label(fact_571_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 23 hBOOL(hoare_298929751gleton) -> (all T_2 -(all S_3 T_2 = S_3)) # label(fact_411_single__stateE) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 24 (all B_1_1 all B_2_1 is_bool(finite774711482_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 25 (all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> A_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) # label(fact_695_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 26 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) # label(fact_421_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 27 (all B_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_88_insertI2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 28 (all P_1 all G_1 all P_2 all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_1)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_381_conseq1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 29 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_376_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 30 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)))) # label(fact_525_predicate1I) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 31 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,hAPP_f833390165e_bool(cOMBB_1456120487_state(fequal_pname),F)),hAPP_H1344248906_pname(F,X_2))))))))))) # label(fact_251_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 32 (all F all X_1 all Y_1 (hAPP_p799580910on_com(F,X_1) = some_com(Y_1) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F))) # label(fact_39_insert__dom) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 33 (all A_1 all B (is_fun_pname_bool(B) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))))) # label(fact_322_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 34 (all Y_1 all A_1 all X_1 (is_pname(Y_1) & is_pname(X_1) -> (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_pname_bool(A_1,X_1))))) # label(fact_92_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 35 (all B_1_1 all B_2_1 is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 36 (all Q_1 all G_1 all P_1 all C all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_2)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_382_conseq2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 37 (all A all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),B)) # label(fact_329_insert__def) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 38 (all A all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_105_insert__compr) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 39 (all G_1 all T all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) & hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 40 (all Q_1 all P_1 all G_1 all P_2 all C all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_2)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> (all S_4 ((all Z_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_4)))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_399_conseq12) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 41 (all P all Q all R hAPP_H1645666623e_bool(P,hAPP_H563960305_state(Q,R)) = hAPP_H1645666623e_bool(hAPP_f1844318385e_bool(cOMBB_291471741_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___029) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 42 (all B all A_1 all F all Fa (is_fun_pname_bool(B) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (bot_bo844097828e_bool != B -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> hAPP_f1297739591_pname(Fa,A_1) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A_1)))))))) # label(fact_467_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 43 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1)))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & hBOOL(hAPP_pname_bool(P_1,X_1)))) # label(fact_586_Int__Collect) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 44 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 45 (all P_1 (hAPP_f921536533e_bool(collec727977250_state,P_1) = bot_bo1055319631e_bool <-> (all X_2 -hBOOL(hAPP_H513860823e_bool(P_1,X_2))))) # label(fact_71_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 46 (all P all Q all R hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) = hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.58/1.80 47 (all N all H all F all Fa (is_fun1661590463l_bool(N) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> ((all X_2 all Y_2 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H,X_2)),hAPP_f759274231e_bool(H,Y_2)))) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N)) -> (bot_bo1649642514l_bool != N -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H),N)) = hAPP_f759274231e_bool(H,hAPP_f674760225e_bool(Fa,N)))))))) # label(fact_485_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 48 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_63_subsetD) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 49 (all F all B all A_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_2)),B))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),B)))) # label(fact_263_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 50 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_273_UnE) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 51 (all A_1 ((all X_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))) <-> bot_bo1055319631e_bool = A_1)) # label(fact_81_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 52 (all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))))))) # label(fact_80_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 53 (all P_1 hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1) # label(fact_177_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 54 (all P all Q all R hAPP_H521649881_state(hAPP_p964374716_state(P,R),hAPP_p1842370726_state(Q,R)) = hAPP_p80247908_state(hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__030) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 55 (all F all C all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A)) -> (C = hAPP_f921536533e_bool(F,B_1) -> ((all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),hAPP_f921536533e_bool(F,A))))))) # label(fact_549_xt1_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 56 (all A all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)))) # label(fact_155_finite__insert) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 57 (all P all Q hAPP_s1806633685e_bool(cOMBK_631994958_state(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 58 (all A_1 all B_1 all F all X_1 (hAPP_H1344248906_pname(F,X_1) = B_1 -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))))) # label(fact_64_image__eqI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 59 (all H all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(H),Fa))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 60 (all P_1 (bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,P_1) <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_68_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 61 (all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),X_1))) # label(fact_265_order__refl) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 62 (all X_1 all Y_1 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1))) # label(fact_97_insert__commute) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 63 (all A_1 all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_169_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 64 (all B all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1))) # label(fact_609_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 65 (all X_1 all Y_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> X_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)))) # label(fact_639_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 66 (all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_335_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 67 (all P all Q all R hAPP_H1645666623e_bool(P,hAPP_f1308959284_state(Q,R)) = hAPP_f631639356e_bool(hAPP_f547518321e_bool(cOMBB_1170234304e_bool(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___028) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 68 (all B_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_182_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 69 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H),Fa))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 70 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> ((all X_2 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) -> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1))),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,B),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))))) # label(fact_673_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 71 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1508101115l_bool(P,R),hAPP_f1760790145l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 72 (all F all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))))) # label(fact_665_image__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 73 (all A_1 A_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),A_1)) # label(fact_295_Un__absorb) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 74 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,hAPP_f1862834069l_bool(cOMBB_1239130257_state(fequal1746921144e_bool),F)),hAPP_H1645666623e_bool(F,X_2))))))))))) # label(fact_255_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 75 (all B_1 all A all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)))) # label(fact_636_le__infI1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 76 (all A_1 all B all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),C_1))) # label(fact_666_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 77 (all A_1 all X_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) -> A_1 = bot_bo844097828e_bool | hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) = A_1))) # label(fact_51_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 78 (all B_1_1 (is_bool(B_1_1) -> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 79 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,hAPP_f376825399l_bool(cOMBB_1722165949_state(fequal533582459e_bool),F)),hAPP_H1632039476e_bool(F,X_2)))))) & hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))))))) # label(fact_254_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 80 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1)) # label(fact_310_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 81 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 82 (all B all X_1 all A_1 (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) <-> A_1 = B))))) # label(fact_90_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 83 (all P_1 all A ((-hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1)) = bot_bo844097828e_bool) & (hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1))))) # label(fact_202_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 84 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))))) # label(fact_521_Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 85 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),B))) # label(fact_605_Int__lower2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 86 (all C -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool))) # label(fact_72_empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 87 (all R_1 all S (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,R_1),S)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S))))) # label(fact_396_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 88 (all X_1 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) # label(fact_98_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 89 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(cOMBB_647938656_pname(P),Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 90 (all X all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 91 (all A all P_1 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(collect_pname,P_1))) # label(fact_100_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 92 (all B_1 all A (is_pname(B_1) & is_pname(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) -> A = B_1))) # label(fact_143_singletonE) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 93 (all P all Q all R hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 94 (all B_1 all D all A all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D)))))) # label(fact_429_sup__mono) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 95 (all A_1 all B (B = A_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)))) # label(fact_123_equalityD1) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 96 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))))) # label(fact_693_insert__Diff) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 97 (all P_1 ((all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))) <-> bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) # label(fact_69_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 98 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),B))) # label(fact_606_Int__lower2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 99 (all N all H all F all Fa (is_fun_pname_bool(N) -> (hBOOL(finite89670078_pname(F,Fa)) -> ((all X_2 all Y_2 (is_pname(Y_2) & is_pname(X_2) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X_2)),hAPP_pname_pname(H,Y_2)) = hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N)) -> (bot_bo844097828e_bool != N -> hAPP_pname_pname(H,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H),N)))))))) # label(fact_487_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 100 (all A A = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),A)) # label(fact_426_sup_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 101 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)))) # label(fact_581_IntD2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 102 (all B all A all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_616_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 103 (all A all A_2 (A_2 = A <-> some_com(A_2) = some_com(A))) # label(fact_358_option_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 104 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z)) # label(fact_413_sup__assoc) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 105 (all P all Q all R hAPP_H248360617l_bool(hAPP_f1862834069l_bool(cOMBB_1239130257_state(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_036) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 106 (all A all P_1 hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fimplies),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)))),P_1))) # label(fact_101_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 107 (all P all Q all R hAPP_f921536533e_bool(hAPP_f481659057e_bool(cOMBB_1099197107e_bool(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_f2143211163_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___033) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 108 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) != bot_bo1055319631e_bool) # label(fact_150_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 109 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 110 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> (exists X_2 (is_pname(X_2) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,hAPP_f567934427l_bool(cOMBB_408569982_pname(fequal533582459e_bool),F)),hAPP_p61793385e_bool(F,X_2)))))) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))))))) # label(fact_245_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 111 (all P all Q all R hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q) = hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 112 (all A_1 all B (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))))) # label(fact_166_finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 113 (all P_1 all Fa (is_fun_pname_bool(Fa) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (bot_bo844097828e_bool != Fa -> ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))))) -> ((all X_2 all F_1 (is_pname(X_2) & is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (F_1 != bot_bo844097828e_bool -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))))) # label(fact_474_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 114 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_286_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 115 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_561_IntE) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 116 (all B_1 all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (B_1 = hAPP_p1842370726_state(F,X_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))))) # label(fact_129_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 117 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A))) # label(fact_365_bot__least) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 118 (all B all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))) # label(fact_324_Un__upper2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 119 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_580_IntD2) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 120 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 121 (all B B = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B)) # label(fact_301_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 122 (all P all Q hAPP_p1842370726_state(cOMBK_90103121_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption]. 1.58/1.81 123 (all U all C_2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U)) -> U = T_1))) # label(fact_543_com__det) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 124 (all B all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_612_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 125 (all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1))))) # label(fact_131_imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 126 (all A all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)))) # label(fact_154_finite__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 127 (all A all A_1 bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)) # label(fact_149_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 128 (all G_1 all C all Q_1 all P_1 ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,cOMBK_631994958_state(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),cOMBK_631994958_state(hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))))) # label(fact_379_escape) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 129 (all A_1 all B (B = A_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)))) # label(fact_122_equalityD1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 130 (all P all Q all R hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q) = hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 131 (all Fa all G_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1))))) # label(fact_306_finite__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 132 (all X_2 all Xa hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X_2))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),Xa)) # label(fact_140_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 133 (all B_1 all A all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1))))) # label(fact_434_le__supI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 134 (all B bot_bo844097828e_bool = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B)) # label(fact_570_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 135 (all F all A all B hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,A)),hAPP_f631639356e_bool(image_275883510_state(F),B))) # label(fact_192_image__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 136 (all P all Q all R hAPP_pname_com(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 137 (all B all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))))) # label(fact_690_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 138 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 139 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) -> bot_bo1055319631e_bool = A)) # label(fact_362_le__bot) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 140 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_118_in__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 141 (all B_1_1 all B_2_1 is_bool(hAPP_state_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 142 (all B all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),B))))) # label(fact_688_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 143 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))) # label(fact_417_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 144 (all F all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> (exists C_3 (hAPP_f1874607724l_bool(image_505480954e_bool(F),C_3) = B & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & is_fun_pname_bool(C_3)))))) # label(fact_233_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 145 (all X_1 set_Ho1831989999_state(some_H1133819688_state(X_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) # label(fact_403_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 146 (all X all Y (hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 147 (all A_1 all B (A_1 = bot_bo1055319631e_bool & B = bot_bo1055319631e_bool <-> bot_bo1055319631e_bool = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) # label(fact_297_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 148 (all P_1 all Q_1 hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1)) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1))) # label(fact_585_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 149 (all X_1 all A_1 all F all Fa (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> hAPP_f674760225e_bool(Fa,A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)))))) # label(fact_483_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 150 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)))))) # label(fact_646_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 151 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,hAPP_f2081555625l_bool(cOMBB_44445098_pname(fequal1746921144e_bool),F)),hAPP_p877885514e_bool(F,X_2))))))))))) # label(fact_246_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 152 (all X all Y X = hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fTrue),X),Y)) # label(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 153 (all X all Y (X = Y | -hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)))) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 154 (all A_1 bot_bo1055319631e_bool = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),bot_bo1055319631e_bool)) # label(fact_569_Int__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 155 (all P all Q all R hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) = hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 156 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))))) # label(fact_633_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 157 (all P all Q all R hAPP_c1546227244_state(P,hAPP_pname_com(Q,R)) = hAPP_p1842370726_state(hAPP_f1758910594_state(cOMBB_422605457_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 158 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 159 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_687_DiffE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 160 (all B all A all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)))) # label(fact_611_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 161 (all A_1 all B ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (all Xa (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B)) -> Xa != X_2)))) <-> bot_bo1055319631e_bool = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) # label(fact_567_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 162 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1))) # label(fact_624_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 163 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(image_650584225_state(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,hAPP_f1844318385e_bool(cOMBB_291471741_state(fequal1531560888_state),F)),hAPP_H563960305_state(F,X_2))))))))))) # label(fact_247_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 164 (all X_1 all Y_1 (Y_1 = X_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)))) # label(fact_357_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 165 (all F all A all B hAPP_f1745235422e_bool(image_1925245338_pname(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,A)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B))) # label(fact_191_image__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 166 (all F all A_1 (bot_bo844097828e_bool = hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_159_image__is__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 167 (all P_1 (is_fun1661590463l_bool(P_1) -> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1)) # label(fact_179_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 168 (all G_1 all P_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),skip),P_1)),bot_bo1055319631e_bool)))) # label(fact_469_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 169 (all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) -> B_1 = A)) # label(fact_144_singletonE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 170 (all X_1 all A_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> X_1 = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1))))))) # label(fact_680_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 171 (all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1))) # label(fact_264_order__refl) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 172 (all B all A all A_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))) # label(fact_621_Int__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 173 (all A hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(fequal1746921144e_bool,A))) # label(fact_212_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 174 (all Com1 all Com2 skip != semi(Com1,Com2)) # label(fact_508_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 175 (all B all A_1 all F all Fa (is_fun1661590463l_bool(A_1) & is_fun1661590463l_bool(B) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (bot_bo1649642514l_bool != A_1 -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (bot_bo1649642514l_bool != B -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)))))))))) # label(fact_554_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 176 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),A_1))) # label(fact_127_subset__refl) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 177 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) # label(fact_289_Un__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 178 (all B all A_1 all X_1 (hBOOL(hAPP_H513860823e_bool(A_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_394_sup1I1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 179 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1))) # label(fact_630_inf__le2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 180 (all A_1 ((all Y_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_2),A_1))) -> A_1 = bot_bo1055319631e_bool)) # label(fact_532_equals0I) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 181 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 182 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_453_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 183 (all Fun all Com_1 while(Fun,Com_1) != skip) # label(fact_502_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 184 (all C all A all B_1 (B_1 = A -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))))) # label(fact_348_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 185 (all X_1 all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1))))) # label(fact_650_le__infE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 186 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2)))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)))) # label(fact_372_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 187 (all B_1 all D all A all C (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C),D)))))) # label(fact_430_sup__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 188 (all G_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) | hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,Fa),G_1))))) # label(fact_563_finite__Int) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 189 (all R_1 all S all X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S))) <-> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)))) # label(fact_590_inf__Int__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 190 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = X_1)) # label(fact_436_sup__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 191 (all X_1 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))))) # label(fact_368_le__funE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 192 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) <-> A = bot_bo1055319631e_bool)) # label(fact_364_bot__unique) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 193 (all B all A_1 (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> B = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))) # label(fact_601_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 194 (all P_1 (hAPP_f759274231e_bool(collect_pname,P_1) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_74_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 195 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 196 (all C (hBOOL(hoare_298929751gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_53_MGF) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 197 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) = hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_017) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 198 (all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_168_finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 199 (all A all M_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))) -> (exists B_3 hAPP_p799580910on_com(M_1,A) = some_com(B_3)))) # label(fact_259_domD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 200 (all C all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool) = hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1))) # label(fact_38_image__constant) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 201 (all P all Q all R hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___034) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 202 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D_1)))))) # label(fact_597_Int__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 203 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_281_UnI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 204 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (bot_bo844097828e_bool != A_1 -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1))))))) # label(fact_470_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 205 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H),Fa))))) # label(fact_14_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 206 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_339_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 207 (all X_1 all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))))) # label(fact_649_le__infE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 208 (all Ts all G_1 all T (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 209 (all P_1 all A ((-hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1))) & (hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)))) # label(fact_203_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 210 (all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> -(all B_2 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_2) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_2)))))) # label(fact_530_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 211 (all P_1 all Fa (is_fun1661590463l_bool(Fa) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (Fa != bot_bo1649642514l_bool -> ((all X_2 (is_fun_pname_bool(X_2) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),bot_bo1649642514l_bool))))) -> ((all X_2 all F_1 (is_fun1661590463l_bool(F_1) & is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (bot_bo1649642514l_bool != F_1 -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))))) # label(fact_476_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 212 (all B all A all C_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)))) # label(fact_619_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 213 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(P,R),Q) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_024) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 214 (all P all Q all R hAPP_f1863945078e_bool(P,hAPP_s1806633685e_bool(Q,R)) = hAPP_s336103912e_bool(hAPP_f249262236e_bool(cOMBB_1476898461_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_018) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 215 (all C all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A)) -> (C = B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A))))) # label(fact_345_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 216 (all Y_1 all X_1 (is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = Y_1))) # label(fact_641_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 217 (all P all Q all R hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) = hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBB_307249310e_bool(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 218 (all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),B) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) # label(fact_330_insert__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 219 (all P_1 all A ((-hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1))) & (hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1))))) # label(fact_204_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 220 (all F all A_1 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(fequal_pname),F)),hAPP_f1008690464_pname(F,X_2)))))) & hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1))))))) # label(fact_253_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 221 (all X_1 all Y_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = Y_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)))) # label(fact_446_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 222 (all P all Q all R hAPP_p1164893188on_com(hAPP_f755519727on_com(cOMBB_1394247784_pname(P),Q),R) = hAPP_b1679505845on_com(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 223 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool) # label(fact_659_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 224 (all C all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B_1)) -> (C = B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))))) # label(fact_347_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 225 (all B_1 all A all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C))) # label(fact_418_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 226 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)))) # label(fact_634_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 227 (all B all F all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_47_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 228 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_45_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 229 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_658_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 230 (all X_1 hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) = set_com(some_com(X_1))) # label(fact_404_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 231 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 232 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 233 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> (bot_bo1649642514l_bool = hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) -> hAPP_f674760225e_bool(Fa,A_1) = X_1) & (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) = hAPP_f674760225e_bool(Fa,A_1))))))) # label(fact_678_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.81 234 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),hAPP_f921536533e_bool(collec727977250_state,Q_1))))))) # label(fact_671_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 235 (all P_1 all F all G all S hAPP_f631639356e_bool(image_275883510_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,hAPP_f1405979047_state(cOMBB_707293872_pname(if_Hoa533980679_state),P_1)),F)),G)),S) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f631639356e_bool(image_275883510_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1)))))) # label(fact_668_if__image__distrib) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 236 (all A_1 bot_bo844097828e_bool = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),bot_bo844097828e_bool)) # label(fact_568_Int__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 237 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(H),Fa))))) # label(fact_16_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 238 (all B_1_1 all B_2_1 is_bool(finite132673334e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 239 (all C all A all B_1 (B_1 = A -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))))) # label(fact_350_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 240 (all P_1 hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = P_1) # label(fact_180_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 241 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f780887186e_bool(image_936554724_state(F),C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1)) & is_fun1661590463l_bool(C_3)))))) # label(fact_225_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 242 (all B all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_116_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 243 (all P_1 all Q_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1))) # label(fact_274_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 244 (all B all C_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))))) # label(fact_600_Int__greatest) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 245 (all P all Q all R hAPP_H737849090l_bool(hAPP_f376825399l_bool(cOMBB_1722165949_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H1632039476e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 246 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),D_1)))))) # label(fact_315_Un__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 247 (all A_1 all A all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) # label(fact_312_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 248 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> (bot_bo1325454745l_bool != hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)))) = hAPP_f772567431e_bool(Fa,A_1)) & (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,A_1) = X_1))))) # label(fact_679_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 249 (all P_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (Fa != bot_bo1325454745l_bool -> ((all X_2 hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),bot_bo1325454745l_bool)))) -> ((all X_2 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (bot_bo1325454745l_bool != F_1 -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1)))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa))))))) # label(fact_477_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 250 (all B all F all A_1 ((exists AA (is_fun_pname_bool(AA) & B = hAPP_f631639356e_bool(image_275883510_state(F),AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1)))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))))) # label(fact_196_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 251 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_573_Int__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 252 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___023) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 253 (all A all C_1 all D_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),D_1))))) # label(fact_173_insert__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 254 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_119_in__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 255 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B)))))) # label(fact_685_DiffI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 256 (all Ts all G_1 all Ts_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 257 (all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool)) <-> bot_bo844097828e_bool = A_1))) # label(fact_157_subset__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 258 (all C1 all S2 all C0 all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0),S1_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_1),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0,C1)),S0),S2))))) # label(fact_541_evalc_OSemi) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 259 (all X_3 hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) # label(fact_491_the__elem__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 260 (all A all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))))) # label(fact_153_finite__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 261 (all A_1 all B (B = A_1 -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))))) # label(fact_110_equalityE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 262 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1))) # label(fact_592_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 263 (all A all B_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)))) # label(fact_638_le__infI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 264 (all A_1 all B hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B)) # label(fact_574_Int__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 265 (all P all Q all R hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R)) = hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 266 (all P all Q (is_bool(P) -> hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 267 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) <-> X_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1))) # label(fact_632_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 268 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1))) # label(fact_21_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 269 (all A -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),bot_bo844097828e_bool))) # label(fact_54_emptyE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 270 (all Pname skip != hAPP_pname_com(body_1,Pname)) # label(fact_478_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 271 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1))) # label(fact_623_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 272 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(H),Fa))))) # label(fact_15_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 273 (all A hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)) # label(fact_208_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 274 (all X_1 all Y_1 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1))) # label(fact_96_insert__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 275 (all A all C_1 all D_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),C_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),D_1))))) # label(fact_174_insert__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 276 (all P_1 all A ((-hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1))) & (hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)))) # label(fact_200_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 277 (all P all Q all R hAPP_H513860823e_bool(hAPP_f631639356e_bool(P,R),Q) = hAPP_f1664156314l_bool(hAPP_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 278 (all A all B_1 (is_pname(B_1) & is_pname(A) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) -> A = B_1))) # label(fact_141_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 279 (all F all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool <-> hAPP_f631639356e_bool(image_275883510_state(F),A_1) = bot_bo1055319631e_bool))) # label(fact_160_image__is__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 280 (all A all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1))))) # label(fact_24_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 281 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1745235422e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_005) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 282 (all A hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) # label(fact_206_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 283 (all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))))) # label(fact_130_imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 284 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 285 (all P (is_bool(P) -> fFalse = P | P = fTrue)) # label(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 286 (all A_1 all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_165_finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 287 (all P_1 all Q_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))))) # label(fact_133_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 288 (all R_1 all S all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,R_1),S))) <-> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2)))) # label(fact_591_inf__Int__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 289 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1))) # label(fact_627_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 290 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_50_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 291 (all P_1 all F all G dom_pname_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,hAPP_f755519727on_com(cOMBB_1394247784_pname(if_option_com),P_1)),F)),G)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(G)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1))))) # label(fact_669_dom__if) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 292 (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),bot_bo1055319631e_bool)) <-> hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)))) # label(fact_388_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 293 (all G_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1)))))) # label(fact_304_finite__UnI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 294 (all P all Q all R hAPP_b589554111l_bool(P,hAPP_f1760790145l_bool(Q,R)) = hAPP_f1508101115l_bool(hAPP_f482022705l_bool(cOMBB_2020112947e_bool(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_021) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 295 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))))) # label(fact_522_Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 296 (all B_1_1 (is_bool(B_1_1) -> is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 297 (all B all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),B))))) # label(fact_689_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 298 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> A_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) # label(fact_604_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 299 (all A_1 all C all B ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_271_UnCI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 300 (all P all Q all R hAPP_H1645666623e_bool(P,hAPP_p1842370726_state(Q,R)) = hAPP_p877885514e_bool(hAPP_f998786331e_bool(cOMBB_799949246_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 301 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_272_UnE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 302 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f280588268e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It_009) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 303 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> B = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) # label(fact_321_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 304 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 305 (all A all B_1 all A_1 (is_pname(A) & is_pname(B_1) -> (A = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))))) # label(fact_94_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 306 (all C1 all C2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1,C2)),S_2),T_1)) -> -(all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_2),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)))))) # label(fact_544_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 307 (all B_1 all A all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)))) # label(fact_635_le__infI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 308 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_114_set__mp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 309 (all F all G ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)))) # label(fact_400_le__funI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 310 (all Y_1 all X_1 (is_fun_pname_bool(Y_1) & is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (Y_1 = X_1 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)))))) # label(fact_352_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 311 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) <-> B = A_1)) # label(fact_125_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 312 (all X_1 all Y_1 (is_fun_pname_bool(Y_1) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))))) # label(fact_445_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 313 (all A all B_1 all C all D (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D),bot_bo1055319631e_bool)) <-> B_1 = C & D = A | A = C & B_1 = D)) # label(fact_146_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 314 (all P_1 all A ((hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1))) & (-hBOOL(hAPP_pname_bool(P_1,A)) -> bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1))))) # label(fact_198_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 315 (all P all Q all R hAPP_f239102607l_bool(hAPP_f1269496639l_bool(P,R),Q) = hAPP_f239102607l_bool(hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 316 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_560_IntE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 317 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_pname_bool(P_1,X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_389_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 318 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))) <-> hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)))) # label(fact_588_Int__Collect) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 319 (all P all Q all R hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)) = hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 320 (all A all B hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),B) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B)) # label(fact_332_insert__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 321 (all A all X_1 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_439_le__supI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 322 (all B_1_1 all B_2_1 is_bool(finite506823037_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 323 (all Fun_1 all Com_2 all Fun all Com_1 (while(Fun_1,Com_2) = while(Fun,Com_1) <-> Com_2 = Com_1 & Fun_1 = Fun)) # label(fact_498_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 324 (all A all A_1 all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) # label(fact_617_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 325 (all C1 all C0 (hBOOL(hAPP_com_bool(wt,C0)) -> (hBOOL(hAPP_com_bool(wt,C1)) -> hBOOL(hAPP_com_bool(wt,semi(C0,C1)))))) # label(fact_506_WT_OSemi) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 326 (all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),bot_bo1055319631e_bool) = A_1) # label(fact_299_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 327 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_294_Un__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 328 (all X_1 (is_fun_pname_bool(X_1) -> X_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),bot_bo844097828e_bool))) # label(fact_457_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 329 (all P all Q all R hAPP_H513860823e_bool(hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H737849090l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___015) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 330 (all B_1_1 all B_2_1 is_bool(finite1626890877e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 331 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_171_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 332 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_pname(B_2_1) -> is_bool(hAPP_pname_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 333 (all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) <-> hBOOL(hAPP_H513860823e_bool(A_1,X_1)))) # label(fact_176_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 334 (all P_1 all Pn_1 all Q_1 all G_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))))) # label(fact_377_BodyN) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 335 (all A all B_1 all A_1 (is_pname(B_1) & is_pname(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1))) -> (A != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)))))) # label(fact_58_insertE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 336 (all X all Y (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X != Y)) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 337 (all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f631639356e_bool(image_275883510_state(F),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))) # label(fact_190_insert__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 338 (all P all Q (is_bool(P) -> P = hAPP_f1760790145l_bool(cOMBK_564432736e_bool(P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 339 (all A all A_1 bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) # label(fact_152_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 340 (all B all A all C_1 ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) & (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1)))) # label(fact_620_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 341 (all F all C all B_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A)) -> (C = hAPP_f759274231e_bool(F,B_1) -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A))))))) # label(fact_548_xt1_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 342 (all P (hBOOL(hAPP_bool_bool(fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 343 (all X_1 all Y_1 (bot_bo1055319631e_bool = Y_1 & bot_bo1055319631e_bool = X_1 <-> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = bot_bo1055319631e_bool)) # label(fact_456_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 344 (all F all A_1 (is_fun_pname_bool(A_1) -> (bot_bo844097828e_bool = A_1 <-> hAPP_f631639356e_bool(image_275883510_state(F),A_1) = bot_bo1055319631e_bool))) # label(fact_164_empty__is__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 345 (all A_1 ((exists X_2 exists B_2 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_2) = A_1 & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_2)))) <-> A_1 != bot_bo1055319631e_bool)) # label(fact_267_nonempty__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 346 (all A_1 all B (A_1 = B -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)))) # label(fact_121_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 347 (all B all A_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)))) # label(fact_223_subsetI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 348 (all Z all F all A_1 ((exists X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & Z = hAPP_p1842370726_state(F,X_2) & is_pname(X_2))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z),hAPP_f631639356e_bool(image_275883510_state(F),A_1))))) # label(fact_132_image__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 349 (all X_1 all Y_1 all Z hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))))) # label(fact_662_distrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 350 (all P all Q all R hAPP_H513860823e_bool(hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H1632039476e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 351 (all H all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(H),Fa))))) # label(fact_12_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 352 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_451_sup__ge1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 353 (all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))) # label(fact_189_insert__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 354 (all P_1 all A ((-hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = bot_bo1649642514l_bool) & (hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)))) # label(fact_199_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 355 (all A_1 ((exists X_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))) <-> bot_bo1055319631e_bool != A_1)) # label(fact_79_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 356 (all X_1 all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)))))) # label(fact_473_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 357 (all Q all P (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | -hBOOL(Q) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 358 (all A_1 all C all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_280_UnI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 359 (all P all Q (is_bool(P) -> P = hAPP_H513860823e_bool(cOMBK_1079618832_state(P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 360 (all B all A all A_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) # label(fact_615_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 361 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (bot_bo1649642514l_bool = hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = X_1) & (bot_bo1649642514l_bool != hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1))))))) # label(fact_682_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 362 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),A_1))) # label(fact_608_Int__lower1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 363 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) <-> X_1 = Y_1))) # label(fact_356_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 364 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))) # label(fact_596_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 365 (all A (A = bot_bo1055319631e_bool | (exists A_4 exists A_3 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_4)) & hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_4) = A)) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)))) # label(fact_244_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 366 (all C all A all B_1 (B_1 = A -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A))))) # label(fact_349_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 367 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_572_Int__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 368 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) <-> bot_bo844097828e_bool = A | (exists A_4 exists A_3 (is_pname(A_3) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4)) & hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),A_4) = A & is_fun_pname_bool(A_4)))))) # label(fact_243_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 369 (all B_1 all A all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1))))) # label(fact_433_le__supI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 370 (all X_1 all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f2143211163_state(Fa,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)))))) # label(fact_482_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 371 (all Y_1 all X_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> X_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_435_sup__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 372 (all A all B hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) # label(fact_107_insert__compr) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 373 (all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A))) # label(fact_366_bot__least) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 374 (all P_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool)) -> ((all X_2 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa)))))) # label(fact_240_finite__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 375 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> (exists C_3 (B = hAPP_f280588268e_bool(image_636285904_pname(F),C_3) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3)) & hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1)))))))) # label(fact_228_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 376 (all X_1 all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (bot_bo1055319631e_bool != A_1 -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)))))) # label(fact_471_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 377 (all A hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)) # label(fact_211_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 378 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 379 (all X_1 all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> hAPP_f772567431e_bool(Fa,A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)))))) # label(fact_484_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 380 (all Y_1 all X_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> X_1 = Y_1)))) # label(fact_338_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 381 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) | hBOOL(Q) | -hBOOL(P))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 382 (all P_1 all Q_1 all C (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_383_MGF__complete) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 383 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f42430548e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 384 (all P_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all X_2 all F_1 (is_fun_pname_bool(F_1) & is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1)))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))) # label(fact_239_finite__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 385 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 386 (all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (bot_bo1055319631e_bool != A_1 -> ((all X_2 all Y_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(Fa,A_1)),A_1))))))) # label(fact_516_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 387 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 388 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1))) # label(fact_625_inf__le1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 389 (all A hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))) # label(fact_207_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 390 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),B)))) # label(fact_185_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 391 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = bot_bo844097828e_bool <-> A_1 = bot_bo844097828e_bool & B = bot_bo844097828e_bool))) # label(fact_296_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 392 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))) # label(fact_653_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 393 (all B_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)))))) # label(fact_644_le__infI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 394 (all A_1 all B hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B))) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)) # label(fact_293_Un__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 395 (all A_1 all B (bot_bo844097828e_bool = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) <-> (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (all Xa (is_pname(Xa) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B)) -> Xa != X_2)))))))) # label(fact_566_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 396 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))) # label(fact_87_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 397 (all Fun all Com_1 all Com1_3 all Com2_3 semi(Com1_3,Com2_3) != while(Fun,Com_1)) # label(fact_496_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 398 (all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A_1)))))) # label(fact_11_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 399 (all B_1 all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)))))) # label(fact_643_le__infI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 400 (all B_1 all D all A all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D)))))) # label(fact_647_inf__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 401 (all B_1_1 all B_2_1 is_bool(hAPP_f1904669497l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 402 (all X_1 all Xo (is_option_pname(Xo) -> (some_pname(X_1) = Xo <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo)))))) # label(fact_405_elem__set) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 403 (all X_1 all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> (bot_bo1649642514l_bool != A_1 -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)))))))) # label(fact_511_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 404 (all G_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_1))))) # label(fact_562_finite__Int) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 405 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1760790145l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 406 (all X all Y Y = hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fFalse),X),Y)) # label(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 407 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)))) # label(fact_108_insertI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 408 (all G_1 all P_1 all B_1 all C hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),while(B_1,C)),P_1)),bot_bo1055319631e_bool)))) # label(fact_489_LoopF) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 409 (all F all A_1 all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)) & hAPP_f748867288l_bool(image_1259634916e_bool(F),C_3) = B)))))) # label(fact_229_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 410 (all Q_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)))))) # label(fact_34_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 411 (all B all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_117_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 412 (all A all B hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) # label(fact_104_insert__compr) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 413 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) <-> B = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) # label(fact_323_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 414 (all Com1_3 all Com2_3 all Com1_2 all Com2_2 (semi(Com1_2,Com2_2) = semi(Com1_3,Com2_3) <-> Com2_3 = Com2_2 & Com1_2 = Com1_3)) # label(fact_497_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 415 (all P all Q all R hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R)) = hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_026) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 416 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> B = A_1)))) # label(fact_60_equalityI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 417 (all Y_1 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_449_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 418 (all B all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (B != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)))))))) # label(fact_464_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 419 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = Y_1)) # label(fact_642_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 420 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1)) & hAPP_f1745235422e_bool(image_1925245338_pname(F),C_3) = B & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)))))))) # label(fact_231_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 421 (all A_1 all B (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = A_1))) # label(fact_603_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 422 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) # label(fact_419_sup__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 423 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))) # label(fact_416_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 424 (all C all A_1 ((bot_bo1055319631e_bool = A_1 -> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = bot_bo844097828e_bool) & (bot_bo1055319631e_bool != A_1 -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) = hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1)))) # label(fact_35_image__constant__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 425 (all Fa all G_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1))))) # label(fact_307_finite__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.82 426 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (A_1 != bot_bo1055319631e_bool -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1))))))) # label(fact_510_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 427 (all X_1 X_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),X_1)) # label(fact_425_sup__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 428 (all A_1 (is_fun_pname_bool(A_1) -> A_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool))) # label(fact_298_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 429 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> -(all X_2 (hAPP_H1344248906_pname(F,X_2) = B_1 -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))))))) # label(fact_216_imageE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 430 (all Y_1 all Z all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Z),X_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)),X_1)) # label(fact_656_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 431 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_275_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 432 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 433 (all A_1 (bot_bo1055319631e_bool = A_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool)))) # label(fact_158_subset__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 434 (all B_1_1 all B_2_1 is_bool(hAPP_f239102607l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 435 (all B all A_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)))) # label(fact_224_subsetI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 436 (all X_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) = set_pname(some_pname(X_1))) # label(fact_402_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 437 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1935169308e_bool(cOMBB_1036740637_state(P),Q),R) = hAPP_f1012183542e_bool(P,hAPP_s336103912e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 438 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)) # label(fact_424_sup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 439 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)) # label(fact_423_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 440 (all X_1 all A_1 (is_fun_pname_bool(A_1) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A_1))) # label(fact_694_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 441 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_686_DiffE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 442 (all P_1 all Q_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))) # label(fact_277_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 443 (all A all P_1 hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),hAPP_f1970439265l_bool(collec111528142e_bool,P_1)) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fimplies),hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(fNot),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)))),P_1))) # label(fact_102_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 444 (all B_1 all C all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),T)) -> ((T = S_1 -> hBOOL(hAPP_state_bool(B_1,S_1))) -> -(hBOOL(hAPP_state_bool(B_1,S_1)) -> (all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_1),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1),T)))))))) # label(fact_545_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 445 (all H all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(H),Fa))))) # label(fact_17_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 446 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) <-> B = A_1))) # label(fact_124_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 447 (all G_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 448 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) # label(fact_290_Un__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 449 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D_1)))))) # label(fact_314_Un__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 450 (all X_1 (hBOOL(bot_bot_bool) <-> hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1)))) # label(fact_374_bot__apply) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 451 (all R_1 all S (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,R_1),S)))) # label(fact_395_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 452 (all B all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = A_1))) # label(fact_318_Un__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 453 (all A_1 all B (B = A_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)))) # label(fact_120_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 454 (all A all A_1 (A_1 = bot_bo1055319631e_bool -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)))) # label(fact_67_equals0D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 455 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> (A_1 != bot_bo1325454745l_bool -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)) = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1))))))) # label(fact_512_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 456 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1))) # label(fact_22_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 457 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Fa),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool)) -> ((all A_3 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),F_1)))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa))))))) # label(fact_221_finite__subset__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 458 (all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f1904669497l_bool(finite1586217244l_bool,hAPP_f1987093l_bool(collec1277803610l_bool,hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,ord_le1076702565l_bool),A_1)))))) # label(fact_9_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 459 (all A all B_1 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) -> A = B_1)) # label(fact_142_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 460 (all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))))) # label(fact_170_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 461 (all Q_1 all P_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))) | hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)))))) # label(fact_33_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 462 (all B all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (bot_bo1055319631e_bool != A_1 -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (bot_bo1055319631e_bool != B -> (bot_bo1055319631e_bool = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)) = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))))))) # label(fact_557_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 463 (all Y_1 -(all Fun1 all Com all Fun2 Y_1 != hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2))) # label(fact_519_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 464 (all B all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_188_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 465 (all P all Q all R hAPP_o334540577on_com(hAPP_p1164893188on_com(P,R),hAPP_p799580910on_com(Q,R)) = hAPP_p1086945780on_com(hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__019) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 466 (all B_1 all F all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> -(all X_2 (is_pname(X_2) -> (hAPP_p1842370726_state(F,X_2) = B_1 -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))))))) # label(fact_217_imageE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 467 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = B)) # label(fact_602_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 468 (all A all P_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,P_1))) # label(fact_103_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 469 (all B all A_1 all F all Fa (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))))))) # label(fact_552_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 470 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))) # label(fact_327_Un__upper1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 471 (all G_1 all C (hBOOL(hoare_298929751gleton) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))))) # label(fact_533_MGT__alternD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 472 (all A all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))))) # label(fact_25_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 473 (all B all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (B != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),A_1)) -> hAPP_f772567431e_bool(Fa,A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,B)),hAPP_f772567431e_bool(Fa,A_1))))))) # label(fact_466_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 474 (all F all B all A_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_2)),B)))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),B)))) # label(fact_262_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 475 (all B_1 all A all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) -> B_1 = A) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_56_insertCI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 476 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> Y_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) # label(fact_438_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 477 (all X_1 all Y_1 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))))) # label(fact_661_distrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 478 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_pname(hAPP_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 479 (all A all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),B)) # label(fact_331_insert__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 480 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_213_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 481 (all Q_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)))))) # label(fact_31_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 482 (all A all A_1 (bot_bo844097828e_bool = A_1 -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)))) # label(fact_66_equals0D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 483 (all Y_1 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_447_sup__ge2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 484 (all B all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) != bot_bo1055319631e_bool -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B))))))) # label(fact_553_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 485 (all A all B hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B)))) # label(fact_106_insert__compr) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 486 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_167_finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 487 (all B all A all A_1 ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) & (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))))) # label(fact_622_Int__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 488 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,hAPP_f998786331e_bool(cOMBB_799949246_pname(fequal1531560888_state),F)),hAPP_p1842370726_state(F,X_2)))))) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & is_pname(X_2)))))) # label(fact_256_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 489 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 490 (all R_1 all S all X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S))) <-> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)))) # label(fact_397_sup__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 491 (all A all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)))) # label(fact_696_insert__Diff__single) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 492 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_454_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 493 (all C all A all F all B_1 (hAPP_f921536533e_bool(F,B_1) = A -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,C)),A)))))) # label(fact_547_xt1_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 494 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all A_3 all F_1 (is_fun_pname_bool(A_3) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),F_1))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa))))))) # label(fact_218_finite__subset__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 495 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_369_le__funD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 496 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1)) # label(fact_334_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 497 (all B all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1))))) # label(fact_317_Un__least) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 498 (all B all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),C_1))))) # label(fact_316_Un__least) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 499 hBOOL(hoare_298929751gleton) <-> (exists S_3 exists T_2 T_2 != S_3) # label(fact_412_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 500 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & hAPP_f631639356e_bool(image_275883510_state(F),C_3) = B & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & is_fun_pname_bool(C_3)))))) # label(fact_235_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 501 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> (exists B_2 (A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B_2)) & is_fun_pname_bool(B_2)))))) # label(fact_527_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 502 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> B = A_1))) # label(fact_61_equalityI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 503 (all Fun_1 all Com_2 all Pname_1 hAPP_pname_com(body_1,Pname_1) != while(Fun_1,Com_2)) # label(fact_500_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 504 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_H737849090l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_003) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 505 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),B)))) # label(fact_186_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 506 (all X all Y (hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 507 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = A_1))) # label(fact_692_insert__Diff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 508 (all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) <-> B_1 = A)) # label(fact_148_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 509 (all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) <-> (all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))))) # label(fact_371_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 510 (all Q_1 all P_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) | hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1)))))) # label(fact_32_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 511 (all B all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (bot_bo1055319631e_bool != B -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,B)),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,A_1)))))) # label(fact_468_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 512 (all P all Q all R hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) = hAPP_p393069232l_bool(hAPP_f1402196763l_bool(cOMBB_675860798_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 513 (all P all Q all R hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 514 (all X_2 all Xa hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),Xa) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),X_2))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),Xa)))) # label(fact_138_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 515 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> (exists X_2 (is_fun_pname_bool(X_2) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,hAPP_f1385420507e_bool(cOMBB_598082538e_bool(fequal_pname),F)),hAPP_f1297739591_pname(F,X_2)))))) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))))))) # label(fact_252_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 516 (all B_1 all C (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_com_bool(wt,while(B_1,C))))) # label(fact_501_While) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 517 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool))))) & (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool -> X_1 = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)))))) # label(fact_683_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 518 (all A_1 all B all X_1 (hBOOL(hAPP_H513860823e_bool(B,X_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_393_sup1I2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 519 (all A_1 all B_1 all F all X_1 (hAPP_p1842370726_state(F,X_1) = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))))) # label(fact_65_image__eqI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 520 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B))))) # label(fact_193_image__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 521 (all X_1 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> -(all B_2 (is_fun_pname_bool(B_2) -> (A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_2)))))))) # label(fact_529_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 522 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)))) # label(fact_444_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 523 (all B_1_1 all B_2_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]. 1.59/1.83 524 (all A_1 all B all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)) -> (-hBOOL(hAPP_H513860823e_bool(A_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(B,X_1))))) # label(fact_384_sup1E) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 525 (all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (bot_bo844097828e_bool != A_1 -> ((all X_2 all Y_2 (is_pname(X_2) & is_pname(Y_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A_1)),A_1)))))))) # label(fact_515_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 526 (all B (is_fun_pname_bool(B) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B)) # label(fact_300_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 527 (all Ts all G_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 528 (all Y_1 all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_450_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 529 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_f748867288l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_006) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 530 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),bot_bo1055319631e_bool) = X_1) # label(fact_458_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 531 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)))) # label(fact_579_IntD1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 532 (all P all Q all R hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)) = hAPP_f759274231e_bool(hAPP_f1385420507e_bool(cOMBB_598082538e_bool(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_012) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 533 (all B all F all A_1 (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) <-> (exists AA (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,AA),A_1)) & hAPP_f1745235422e_bool(image_1925245338_pname(F),AA) = B))))) # label(fact_195_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 534 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1))))) # label(fact_337_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 535 (all F all A_1 all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & hAPP_f434788991l_bool(image_47868345e_bool(F),C_3) = B & is_fun_pname_bool(C_3))))))) # label(fact_232_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 536 (all B all X_1 all A_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))))) # label(fact_183_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 537 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) # label(fact_422_sup__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 538 (all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_380_Body__sound__lemma) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 539 (all P all Q all R hAPP_f239102607l_bool(hAPP_f105100493l_bool(P,R),Q) = hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_031) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 540 (all X_2 (hBOOL(bot_bot_bool) <-> hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)))) # label(fact_375_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 541 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1)))) <-> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) & hBOOL(hAPP_f1760790145l_bool(P_1,X_1)))) # label(fact_589_Int__Collect) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 542 (all X_1 all Y_1 X_1 = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1))) # label(fact_652_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 543 (all X_1 X_1 = hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) # label(fact_261_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 544 (all B all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 545 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))))) # label(fact_26_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 546 (all F all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)) & hAPP_f854625363l_bool(image_277167759e_bool(F),C_3) = B & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1))))))) # label(fact_230_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 547 (all B all A all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)))) # label(fact_610_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 548 (all C_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))))) # label(fact_112_subset__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 549 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_H513860823e_bool(P_1,X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_1))))) # label(fact_390_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 550 (all H all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(H),Fa))))) # label(fact_13_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 551 (all C all A all B_1 (B_1 = A -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))))) # label(fact_351_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 552 (all X all Y (-hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 553 (all X_3 hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(cOMBB_1653402815_state(hAPP_f854625363l_bool(fequal1746921144e_bool,X_3)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool))) = hAPP_f2143211163_state(the_el23965208_state,X_3)) # label(fact_492_the__elem__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 554 (all P all Q all R hAPP_f1949912908_state(P,hAPP_p1637813682e_bool(Q,R)) = hAPP_p2032835427_state(hAPP_f950918952_state(cOMBB_2123334001_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___035) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 555 (all A_1 all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_292_Un__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 556 (all A all B_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) | A = B_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1))))) # label(fact_95_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 557 (all C all A_1 (is_fun_pname_bool(A_1) -> (bot_bo844097828e_bool != A_1 -> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool)) & (bot_bo844097828e_bool = A_1 -> bot_bo1055319631e_bool = hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1)))) # label(fact_36_image__constant__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 558 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)))) # label(fact_578_IntD1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 559 (all P_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (bot_bo1055319631e_bool != Fa -> ((all X_2 hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) -> ((all X_2 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (F_1 != bot_bo1055319631e_bool -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1)))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa))))))) # label(fact_475_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 560 (all A_1 all B all C_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),C_1) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1)))) # label(fact_667_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 561 (all B all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1) <-> B = A_1)))) # label(fact_91_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 562 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))))) # label(fact_340_order__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 563 (all B_1 all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_89_insertI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 564 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 565 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_62_subsetD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 566 (all A all X_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_440_le__supI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 567 (all P all Q all R hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 568 (all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> ((all X_2 all Y_2 hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2)),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,Y_2),bot_bo1325454745l_bool))))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f772567431e_bool(Fa,A_1)),A_1))))))) # label(fact_518_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 569 (all F all G all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))) <-> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_1)))) # label(fact_410_sup__apply) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 570 (all P_1 all A_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,Fa),A_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool)) -> ((all A_3 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),A_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),F_1)))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa))))))) # label(fact_219_finite__subset__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 571 (all P_1 ((all X_2 -hBOOL(hAPP_f1760790145l_bool(P_1,X_2))) <-> bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,P_1))) # label(fact_76_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 572 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1))) # label(fact_288_Un__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 573 (all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1)) -> S_2 = T_1)) # label(fact_538_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 574 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1))) # label(fact_629_inf__le2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 575 (all Y_1 all Z all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Z),X_1))) # label(fact_655_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 576 (all P all Q all R hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 577 (all P all Q all R hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 578 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) & hBOOL(hAPP_H513860823e_bool(P_1,X_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1)))))) # label(fact_587_Int__Collect) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 579 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z)),X_1))))) # label(fact_431_sup__least) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 580 (all P_1 all A_1 all B ((exists X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) & hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) <-> (exists X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) & hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)))) | (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)) & hBOOL(hAPP_H513860823e_bool(P_1,X_2)))))) # label(fact_284_bex__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 581 (all B_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_181_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 582 (all X_1 all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1))))))) # label(fact_472_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 583 (all X all Y Y = hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fFalse),X),Y)) # label(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 584 (all P all Q all R hAPP_pname_bool(hAPP_f1745235422e_bool(P,R),Q) = hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 585 (all S_2 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2))) # label(fact_542_evalc_OSkip) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 586 (all P_1 all A_1 all B ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) <-> (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) & (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))))) # label(fact_283_ball__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 587 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all A_3 all F_1 (is_fun_pname_bool(F_1) & is_pname(A_3) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),F_1))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa))))))) # label(fact_220_finite__subset__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 588 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 589 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (bot_bo844097828e_bool != A_1 -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)))))))) # label(fact_509_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 590 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))))) # label(fact_41_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 591 (all X_4 hAPP_option_com_com(the_com,some_com(X_4)) = X_4) # label(fact_268_the_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 592 (all A all B_1 all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C)) # label(fact_415_sup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 593 (all B_1_1 (is_option_pname(B_1_1) -> is_fun_pname_bool(set_pname(B_1_1)))) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 594 (all P all Q all R hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q) = hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_013) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 595 (all A (A = bot_bo1325454745l_bool | (exists A_4 exists A_3 (A = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),A_4) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_4)))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)))) # label(fact_242_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 596 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z))))) # label(fact_341_order__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 597 (all A_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) -> A_1 = bot_bo1055319631e_bool | hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool) = A_1)) # label(fact_52_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 598 (all P all Q all R hAPP_H513860823e_bool(hAPP_p877885514e_bool(P,R),Q) = hAPP_pname_bool(hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 599 (all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) <-> (exists A_4 exists A_3 (is_fun_pname_bool(A_3) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4)) & A = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),A_4) & is_fun1661590463l_bool(A_4))) | bot_bo1649642514l_bool = A))) # label(fact_241_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 600 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1)) # label(fact_285_Un__assoc) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 601 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f759274231e_bool(image_pname_pname(F),C_3) & is_fun_pname_bool(C_3))))))) # label(fact_234_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 602 (all A hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) # label(fact_210_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 603 (all B all A all C_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1))) # label(fact_614_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption]. 1.59/1.83 604 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = X_1) # label(fact_651_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 605 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) # label(fact_420_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 606 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> (hBOOL(hAPP_pname_bool(P_1,X_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_391_predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 607 (all X_1 all Y_1 (Y_1 = X_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)))) # label(fact_354_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 608 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> X_1 = hAPP_f2143211163_state(Fa,A_1)) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))))))))) # label(fact_677_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 609 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),X_1) = bot_bo1055319631e_bool) # label(fact_660_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 610 (all P_1 all Q_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))) # label(fact_582_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 611 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_291_Un__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 612 (all Pn_1 all G_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo1055319631e_bool))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 613 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(hAPP_f674760225e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_007) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 614 (all P_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all X_2 all F_1 (is_fun_pname_bool(X_2) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1)))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))) # label(fact_237_finite__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 615 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1)) & B = hAPP_f772567431e_bool(image_774712299_state(F),C_3) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3))))))) # label(fact_226_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 616 (all B all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))) # label(fact_325_Un__upper2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 617 (all A_1 all B hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B)))) # label(fact_575_Int__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 618 (all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,ord_le1720872323e_bool),A_1)))))) # label(fact_10_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 619 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_209_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 620 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = bot_bo844097828e_bool <-> X_1 = bot_bo844097828e_bool & bot_bo844097828e_bool = Y_1))) # label(fact_455_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 621 (all A all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) != bot_bo844097828e_bool) # label(fact_151_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 622 (all A_1 (is_fun_pname_bool(A_1) -> ((all Y_2 (is_pname(Y_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A_1)))) -> bot_bo844097828e_bool = A_1))) # label(fact_531_equals0I) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 623 (all A all B_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1))) -> (A != B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))))) # label(fact_59_insertE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 624 (all C -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),bot_bo1055319631e_bool))) # label(fact_73_empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 625 (all A_1 all B (A_1 = B -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))))) # label(fact_111_equalityE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 626 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) -> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2)))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))) # label(fact_524_Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 627 (all Pname_1 all Fun_1 all Com_2 hAPP_pname_com(body_1,Pname_1) != while(Fun_1,Com_2)) # label(fact_499_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 628 (all B all C_1 all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1))) # label(fact_593_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 629 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2)))))) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & is_pname(X_2)))))) # label(fact_250_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 630 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1))) # label(fact_126_subset__refl) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 631 (all Q all P (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 632 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))))) # label(fact_691_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 633 (all X_2 all Xa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa)))) # label(fact_137_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 634 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_343_order__antisym) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 635 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))))) # label(fact_44_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 636 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),hAPP_f759274231e_bool(collect_pname,Q_1))))))) # label(fact_670_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 637 (all F all G all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))) <-> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_2)))) # label(fact_409_sup__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 638 (all P (hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P))) -> -(all Y_2 hAPP_p799580910on_com(body,P) != some_com(Y_2)))) # label(fact_222_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 639 (all X_1 all Y_1 all Z ((all X_2 all Y_2 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_2),Z_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)))) # label(fact_674_distrib__imp1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 640 (all P all Q all R hAPP_p799580910on_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,P),Q),R) = hAPP_o356497025on_com(hAPP_p1086945780on_com(P,R),hAPP_p799580910on_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 641 (all B_1_1 all B_2_1 is_pname(hAPP_f1008690464_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 642 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1))) # label(fact_595_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 643 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))))) # label(fact_558_IntI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 644 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1))) # label(fact_626_inf__le1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 645 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),Z)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z)))) # label(fact_443_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 646 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(H),Fa))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 647 (all F all A_1 (hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) = bot_bo844097828e_bool <-> bot_bo1055319631e_bool = A_1)) # label(fact_163_empty__is__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 648 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> (exists C_3 (is_fun1661590463l_bool(C_3) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1)))))))) # label(fact_227_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 649 (all Pname_2 all Pname_1 (is_pname(Pname_1) & is_pname(Pname_2) -> (hAPP_pname_com(body_1,Pname_2) = hAPP_pname_com(body_1,Pname_1) <-> Pname_2 = Pname_1))) # label(fact_257_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 650 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,P),Q),R)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 651 (all X_1 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1))) # label(fact_99_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 652 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 653 (all P all Q all R hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) = hAPP_f1476298914l_bool(hAPP_f143162813l_bool(cOMBB_2095475776e_bool(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 654 (all F all A_1 all B hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))) # label(fact_328_image__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 655 (all A all B all C_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1)) # label(fact_311_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 656 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 657 (all A all A_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)) # label(fact_333_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 658 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z)) # label(fact_414_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 659 (all B_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_442_le__supI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 660 (all Com1_3 all Com2_3 all Fun all Com_1 while(Fun,Com_1) != semi(Com1_3,Com2_3)) # label(fact_495_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 661 (all Q_1 all P_1 ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))) # label(fact_523_Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 662 (all X_1 all Xo (Xo = some_com(X_1) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo))))) # label(fact_407_elem__set) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 663 (all B all F all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_49_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 664 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> X_1 = Y_1)))) # label(fact_342_order__antisym) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 665 (all G_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_1))))) # label(fact_564_finite__Int) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 666 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool)) -> bot_bo844097828e_bool = A))) # label(fact_361_le__bot) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 667 (all X_1 (hBOOL(bot_bot_bool) <-> hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)))) # label(fact_373_bot__apply) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 668 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_584_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 669 (all N all H all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> ((all X_2 all Y_2 hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_H563960305_state(H,X_2)),hAPP_H563960305_state(H,Y_2))) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N)) -> (N != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(image_650584225_state(H),N)) = hAPP_H563960305_state(H,hAPP_f2143211163_state(Fa,N))))))) # label(fact_488_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 670 (all F all G all M all N (N = M -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N)) -> hAPP_p1842370726_state(G,X_2) = hAPP_p1842370726_state(F,X_2)))) -> hAPP_f631639356e_bool(image_275883510_state(F),M) = hAPP_f631639356e_bool(image_275883510_state(G),N)))) # label(fact_520_image__cong) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 671 (all P_1 all Q_1 all G_1 all P_2 all C0_1 all Q_2 all U_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1)) -> ((all P_3 (is_pname(P_3) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_2,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_2,P_3))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_1,P_3))),bot_bo1055319631e_bool)))))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_2)),C0_1)),Q_2)),U_1))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_378_finite__pointwise) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 672 (all Pname hAPP_pname_com(body_1,Pname) != skip) # label(fact_479_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 673 (all B_1_1 all B_2_1 is_pname(hAPP_H1344248906_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 674 (all R_1 all S all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,R_1),S))) <-> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2)))) # label(fact_398_sup__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 675 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))))) # label(fact_576_Int__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 676 (all P_1 ((all X_2 -hBOOL(hAPP_H513860823e_bool(P_1,X_2))) <-> hAPP_f921536533e_bool(collec727977250_state,P_1) = bot_bo1055319631e_bool)) # label(fact_77_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 677 (all B_1_1 (is_pname(B_1_1) -> is_option_pname(some_pname(B_1_1)))) # label(gsy_c_Option_Ooption_OSome_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 678 (all A all B_1 all C all D (is_pname(A) & is_pname(B_1) & is_pname(D) & is_pname(C) -> (D = A & B_1 = C | D = B_1 & A = C <-> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool))))) # label(fact_145_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 679 (all B all C_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))))) # label(fact_599_Int__greatest) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 680 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1))))) # label(fact_336_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 681 (all G_1 all P_1 all C all Q_1 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),C_1)),C),Q_1)),bot_bo1055319631e_bool))))) # label(fact_359_constant) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 682 (all P all Q all R hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R)) = hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_014) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 683 (all Y_1 all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_448_sup__ge2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 684 (all P all Q all R hAPP_f1745235422e_bool(hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1008690464_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_022) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 685 (all A_1 all C all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_279_UnI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 686 (all P (is_bool(P) -> P = fFalse | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 687 (all B all A_1 all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (bot_bo844097828e_bool != B -> (bot_bo844097828e_bool = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))))))))) # label(fact_556_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 688 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B_1)) -> (C = B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))))) # label(fact_346_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 689 (all B all A all C_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))) # label(fact_613_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 690 (all F hAPP_f631639356e_bool(image_275883510_state(F),bot_bo844097828e_bool) = bot_bo1055319631e_bool) # label(fact_162_image__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 691 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))) # label(fact_326_Un__upper1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 692 (all X_1 all Y_1 all Z hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))))) # label(fact_664_distrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 693 (all M_1 all A all B_1 (hAPP_p799580910on_com(M_1,A) = some_com(B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))))) # label(fact_197_domI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 694 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))))) # label(fact_577_Int__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 695 (all Fun all Com_1 while(Fun,Com_1) != skip) # label(fact_503_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 696 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = X_1)) # label(fact_640_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 697 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,B),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))))) # label(fact_672_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 698 (all P_1 all A ((hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1))) & (-hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1)) = bot_bo1055319631e_bool))) # label(fact_205_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 699 (all A_1 all A all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) # label(fact_313_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 700 (all B all A_1 all F all Fa (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (bot_bo1649642514l_bool != hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B)))))))) # label(fact_550_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 701 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_1_1) & is_fun_pname_bool(B_2_1) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 702 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)) -> (hBOOL(hAPP_H513860823e_bool(P_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_1))))) # label(fact_392_predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 703 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B)))))) # label(fact_684_DiffI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 704 (all B_1 all A all B ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B)) -> B_1 = A) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_57_insertCI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 705 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1))) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> X_1 = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)))))) # label(fact_681_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 706 (all F all A_1 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> (exists X_2 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,hAPP_f481659057e_bool(cOMBB_1099197107e_bool(fequal1531560888_state),F)),hAPP_f2143211163_state(F,X_2)))))) & hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1))))))) # label(fact_249_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 707 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1))) # label(fact_628_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 708 (all X_1 all Xo (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),set_Ho1831989999_state(Xo))) <-> some_H1133819688_state(X_1) = Xo)) # label(fact_406_elem__set) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 709 (all A all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)))) # label(fact_637_le__infI2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 710 (all G_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs)))))) # label(fact_258_MGT__Body) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 711 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_657_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 712 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_287_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 713 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = A_1)) # label(fact_319_Un__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 714 (all X_1 all P_1 all A_1 ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A_1))) -> hBOOL(hAPP_com_bool(P_1,X_2)))) -> (some_com(X_1) = A_1 -> hBOOL(hAPP_com_bool(P_1,X_1))))) # label(fact_408_ospec) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 715 (all X_1 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))))) # label(fact_370_le__funD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 716 (all B all A_1 all F all Fa (is_fun1661590463l_bool(B) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (bot_bo1649642514l_bool != B -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1))))))) # label(fact_465_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 717 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_40_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 718 (all A_1 all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) # label(fact_698_Diff__insert2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 719 (all C all B_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A)) -> (C = B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))))) # label(fact_344_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 720 (all X_1 all Y_1 all Z ((all X_2 all Y_2 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)))) # label(fact_675_distrib__imp2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 721 (all B all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_48_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 722 (all P all Q all R hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R)) = hAPP_p338031245l_bool(hAPP_f567934427l_bool(cOMBB_408569982_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 723 (all B_1_1 all B_2_1 is_bool(finite1268145088e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 724 (all F all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))))) # label(fact_194_image__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 725 (all P all Q all R hAPP_pname_bool(hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 726 (all G_1 all P_1 all Pn_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))))) # label(fact_269_weak__Body) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 727 (all X all Y hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 728 (all X_1 all Y_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) <-> X_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)))) # label(fact_631_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 729 (all P all Q all R hAPP_p1617973726l_bool(hAPP_f2081555625l_bool(cOMBB_44445098_pname(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_p877885514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_032) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 730 (all P all Q all R hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R)) = hAPP_H513860823e_bool(hAPP_f1456107715e_bool(cOMBB_1653402815_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 731 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1))))) # label(fact_432_sup__least) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 732 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_452_sup__ge1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 733 (all A all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))))) # label(fact_23_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 734 (all B_1_1 all B_2_1 is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_001) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 735 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)))) # label(fact_156_finite__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 736 (all P_1 all A ((-hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = bot_bo1055319631e_bool) & (hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))) # label(fact_201_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 737 (all B_1_1 all B_2_1 is_bool(finite959343283e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Hoare____Mirabelle____ddpg) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 738 (all X_1 all A_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (bot_bo844097828e_bool = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) -> X_1 = hAPP_f1297739591_pname(Fa,A_1)) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,A_1) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))))))) # label(fact_676_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 739 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (Fun1_2 = Fun1_1 & Com_2 = Com_1 & Fun2_2 = Fun2_1 <-> hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_2),Com_2),Fun2_2) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_1),Com_1),Fun2_1))) # label(fact_278_triple_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 740 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_008) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 741 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))) # label(fact_697_insert__Diff__single) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 742 (all B all C_1 all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)),A_1)) # label(fact_594_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 743 (all P all Q all R hAPP_b798484845_state(P,hAPP_pname_bool(Q,R)) = hAPP_p964374716_state(hAPP_f1405979047_state(cOMBB_707293872_pname(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 744 (all B all A_1 all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (B != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))))))) # label(fact_463_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 745 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_f854625363l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_027) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 746 (all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> ((all X_2 all Y_2 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_2) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A_1)),A_1)))))))) # label(fact_517_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 747 (all Pname all Com1_1 all Com2_1 hAPP_pname_com(body_1,Pname) != semi(Com1_1,Com2_1)) # label(fact_504_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 748 (all B all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (bot_bo1325454745l_bool != A_1 -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (bot_bo1325454745l_bool != B -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = bot_bo1325454745l_bool -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B))))))))) # label(fact_555_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 749 (all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A_1)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 750 (all P all Q all R hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___020) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 751 (all P_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool)) -> ((all X_2 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa)))))) # label(fact_238_finite__induct) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 752 (all X all P (-hBOOL(hAPP_f327114704l_bool(fAll_state,P)) | hBOOL(hAPP_state_bool(P,X)))) # label(help_fAll_1_1_fAll_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 753 (all A all B hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_109_insertI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 754 (all B all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B)))))) # label(fact_184_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 755 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_1) = X_1)) # label(fact_459_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 756 (all P all Q (hBOOL(P) | hBOOL(Q) | -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 757 (all C all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),S_1)))) # label(fact_539_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 758 (all C1 all C2 (hBOOL(hAPP_com_bool(wt,semi(C1,C2))) -> -(hBOOL(hAPP_com_bool(wt,C1)) -> -hBOOL(hAPP_com_bool(wt,C2))))) # label(fact_494_WTs__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 759 (all X all Y (is_fun_pname_bool(X) & is_fun_pname_bool(Y) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) | Y = X)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 760 (all P all Q all R hAPP_p1712839024_state(hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,P),Q),R) = hAPP_c408625258_state(hAPP_p2032835427_state(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 761 (all B_1 all D all A all C (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C),D)))))) # label(fact_648_inf__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 762 (all X_1 all A_1 all F all Fa (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1))))) # label(fact_481_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 763 (all X_1 all Y_1 (is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> Y_1 = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_437_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 764 (all A -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),bot_bo1055319631e_bool))) # label(fact_55_emptyE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 765 (all P_1 ((all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))) <-> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = bot_bo1649642514l_bool)) # label(fact_75_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 766 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_42_finite__surj) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 767 (all Y_1 all A_1 all X_1 (Y_1 = X_1 | hBOOL(hAPP_H513860823e_bool(A_1,X_1)) <-> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1),X_1)))) # label(fact_93_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 768 (all C_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1))))) # label(fact_113_subset__trans) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 769 (all X_2 all Xa hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),Xa) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),X_2))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),Xa)))) # label(fact_139_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 770 (all P (is_bool(P) -> P = fFalse | P = fTrue)) # label(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 771 (all P all Q all R hAPP_f327114704l_bool(P,hAPP_s1806633685e_bool(Q,R)) = hAPP_state_bool(hAPP_f1012183542e_bool(cOMBB_1911358915_state(P),Q),R)) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 772 (all Pn all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0),S1_1)))) # label(fact_536_evalc_OBody) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 773 (all B_1_1 is_fun_pname_bool(dom_pname_com(B_1_1))) # label(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom) # label(hypothesis) # label(non_clause). [assumption]. 1.59/1.84 774 (all X_1 all Y_1 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z))))) # label(fact_663_distrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 775 (all G_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1)))))) # label(fact_302_finite__UnI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 776 (all P all Q (is_bool(P) -> P = hAPP_pname_bool(cOMBK_bool_pname(P),Q))) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 777 (all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),Ts)))) # label(fact_386_hoare__sound) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 778 (all X_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> X_1 = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))) # label(fact_513_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 779 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_215_WT__bodiesD) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 780 (all A_1 all C all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_270_UnCI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 781 (all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))))) # label(fact_363_bot__unique) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 782 (all X_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> X_1 = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) # label(fact_514_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 783 (all B_1_1 all B_2_1 is_bool(hAPP_f327114704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 784 (all P_1 all Q_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1))) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))) # label(fact_134_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.84 785 (all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) <-> hBOOL(hAPP_pname_bool(A_1,X_1)))) # label(fact_175_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 786 (all P all Q all R hAPP_f588507005_state(hAPP_p1712839024_state(P,R),hAPP_p1637813682e_bool(Q,R)) = hAPP_p1842370726_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,P),Q),R)) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 787 (all C all G_1 (hBOOL(hoare_298929751gleton) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo1055319631e_bool)))))) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_214_MGF__lemma1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 788 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)))) # label(fact_86_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 789 (all F hAPP_f1745235422e_bool(image_1925245338_pname(F),bot_bo1055319631e_bool) = bot_bo844097828e_bool) # label(fact_161_image__empty) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 790 (all Fa all G_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1))))) # label(fact_309_finite__Un) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 791 (all A all A_1 all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) # label(fact_618_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 792 (all B_1 all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hAPP_H1344248906_pname(F,X_1) = B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))))) # label(fact_128_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 793 (all B all A_1 all F all Fa (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A_1) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (bot_bo1649642514l_bool != A_1 -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (bot_bo1649642514l_bool != B -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B))))))))) # label(fact_461_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 794 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> (exists B_2 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_2)) & A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_2))))) # label(fact_528_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 795 (all B_1 all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_441_le__supI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 796 (all D all R_1 all G_1 all P_1 all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Q_1),D),R_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),semi(C,D)),R_1)),bot_bo1055319631e_bool)))))) # label(fact_490_Comp) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 797 (all C hAPP_c1546227244_state(hoare_Mirabelle_MGT,C) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,fequal_state),C),evalc(C))) # label(fact_535_MGT__def) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 798 (all B_1 all A (is_pname(A) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) <-> A = B_1))) # label(fact_147_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 799 (all P_1 (hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = bot_bo1325454745l_bool <-> (all X_2 -hBOOL(hAPP_f1760790145l_bool(P_1,X_2))))) # label(fact_70_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 800 (all C all A all F all B_1 (hAPP_f759274231e_bool(F,B_1) = A -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A)))))) # label(fact_546_xt1_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 801 (all B all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)))) # label(fact_187_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 802 (all B_1_1 all B_2_1 is_bool(hAPP_f990396704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 803 (all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B))) # label(fact_320_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 804 (all C all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) = hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1))) # label(fact_37_image__constant) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 805 (all B all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (bot_bo1325454745l_bool != hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B))),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B)))))))) # label(fact_551_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 806 (all A_1 (is_fun_pname_bool(A_1) -> (bot_bo844097828e_bool != A_1 <-> (exists X_2 exists B_2 (is_pname(X_2) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)) & is_fun_pname_bool(B_2)))))) # label(fact_266_nonempty__iff) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 807 (all A_1 (is_fun_pname_bool(A_1) -> (bot_bo844097828e_bool != A_1 <-> (exists X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & is_pname(X_2)))))) # label(fact_78_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 808 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_2),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 809 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1632039476e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_002) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 810 (all X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),bot_bo844097828e_bool)) <-> hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)))) # label(fact_387_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 811 (all Pn_1 all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procs)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo1055319631e_bool)))))) # label(fact_360_Body1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 812 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_1) = X_1) # label(fact_460_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 813 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_367_le__funE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 814 (all P_1 all Q_1 hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1)) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) # label(fact_276_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 815 (all G_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) | hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Fa),G_1))))) # label(fact_565_finite__Int) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 816 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 817 (all S2_1 all C all S1_2 all B_1 all S0_1 (hBOOL(hAPP_state_bool(B_1,S0_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1_2)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1_2),S2_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S0_1),S2_1)))))) # label(fact_540_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 818 (all G_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1)))))) # label(fact_305_finite__UnI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 819 (all X_1 (is_pname(X_1) -> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1)) # label(fact_260_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 820 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)))) # label(fact_401_le__funI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 821 (all A_1 all B all X_1 ((-hBOOL(hAPP_H513860823e_bool(B,X_1)) -> hBOOL(hAPP_H513860823e_bool(A_1,X_1))) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_385_sup1CI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 822 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),D_1)))))) # label(fact_598_Int__mono) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 823 (all B_1_1 all B_2_1 is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_004) # label(hypothesis) # label(non_clause). [assumption]. 1.59/1.85 824 (all P all S_2 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_2),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_2),S1_1)))) # label(fact_537_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 825 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_282_UnI1) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 826 (all P all Q all R hAPP_p1842370726_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,P),Q),R) = hAPP_H563960305_state(hAPP_p80247908_state(P,R),hAPP_p1842370726_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption]. 1.59/1.85 827 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z)))))) # label(fact_645_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 828 (all A_1 all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_172_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 829 (all B all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (bot_bo1325454745l_bool != B -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)))))))) # label(fact_462_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 830 (all A all B_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1)) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1))))) # label(fact_428_le__supE) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 831 (all Com1 all Com2 skip != semi(Com1,Com2)) # label(fact_507_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 832 (all X all Y (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) | Y != X)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 833 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))))) # label(fact_559_IntI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 834 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (Y_1 = X_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))))) # label(fact_353_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 835 (all B_1_1 all B_2_1 is_bool(hAPP_com_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ocom_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 836 (all P_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1))) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1)))))) # label(fact_135_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 837 (all X_1 all Y_1 (Y_1 = X_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)))) # label(fact_355_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 1.59/1.90 1.59/1.90 ============================== end of process non-clausal formulas === 1.59/1.90 1.59/1.90 ============================== PROCESS INITIAL CLAUSES =============== 1.59/1.90 1.59/1.90 ============================== PREDICATE ELIMINATION ================= 1.59/1.90 838 -is_pname(A) | is_option_pname(some_pname(A)) # label(gsy_c_Option_Ooption_OSome_000tc__Com__Opname) # label(axiom). [clausify(677)]. 1.59/1.90 839 -is_option_pname(A) | some_pname(B) != A | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) # label(fact_405_elem__set) # label(axiom). [clausify(402)]. 1.59/1.90 840 -is_option_pname(A) | some_pname(B) = A | -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) # label(fact_405_elem__set) # label(axiom). [clausify(402)]. 2.18/2.48 841 -is_option_pname(A) | is_fun_pname_bool(set_pname(A)) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom). [clausify(593)]. 2.18/2.48 Derived: -is_pname(A) | some_pname(B) != some_pname(A) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(some_pname(A)))). [resolve(838,b,839,a)]. 2.18/2.48 Derived: -is_pname(A) | some_pname(B) = some_pname(A) | -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(some_pname(A)))). [resolve(838,b,840,a)]. 2.18/2.48 Derived: -is_pname(A) | is_fun_pname_bool(set_pname(some_pname(A))). [resolve(838,b,841,a)]. 2.18/2.48 2.18/2.48 ============================== end predicate elimination ============= 2.18/2.48 2.18/2.48 Auto_denials: (non-Horn, no changes). 2.18/2.48 2.18/2.48 Term ordering decisions: 2.18/2.48 Function symbol KB weights: ord_le313189616e_bool=1. ord_le1720872323e_bool=1. bot_bo1055319631e_bool=1. member1758697444_state=1. semila447562797e_bool=1. insert1835143293_state=1. bot_bo844097828e_bool=1. member_pname=1. finite_finite_pname=1. insert_pname=1. finite595471783e_bool=1. finite784854244_state=1. semila2145357127e_bool=1. finite899049100e_bool=1. semila1635148844e_bool=1. bot_bo1649642514l_bool=1. semila278973382e_bool=1. collect_pname=1. hoare_1575745797_state=1. collec1974731493e_bool=1. bot_bo1325454745l_bool=1. collec727977250_state=1. collec111528142e_bool=1. fconj=1. insert1325755072e_bool=1. insert1991711667e_bool=1. ord_le675606854l_bool=1. fdisj=1. member799430823e_bool=1. ord_le1076702565l_bool=1. member402455436e_bool=1. cOMBC_1058051404l_bool=1. cOMBC_764456866l_bool=1. body_1=1. cOMBS_1248383340l_bool=1. cOMBS_568398431l_bool=1. cOMBS_2138645332l_bool=1. cOMBS_350070575l_bool=1. semila1130628874l_bool=1. wt=1. body=1. hoare_Mirabelle_MGT=1. fequal1531560888_state=1. fequal_pname=1. semila1410775201l_bool=1. cOMBS_1401555724_state=1. cOMBS_1615712031_state=1. fequal1746921144e_bool=1. fequal533582459e_bool=1. minus_2076558538e_bool=1. minus_1015773161e_bool=1. the_com=1. fFalse=1. ord_less_eq_bool=1. semila1782091504l_bool=1. semila2055205435l_bool=1. bot_bot_bool=1. cOMBC_1018307482l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_1166591542l_bool=1. cOMBC_1284144636l_bool=1. cOMBC_1424981238e_bool=1. cOMBC_1988546018l_bool=1. fimplies=1. fNot=1. fequal_state=1. hoare_298929751gleton=1. minus_1290075917l_bool=1. minus_164259166l_bool=1. fTrue=1. cOMBC_952831051e_bool=1. cOMBS_1378840469l_bool=1. semila1168014441p_bool=1. skip=1. wT_bodies=1. bool=1. cOMBC_231445413l_bool=1. cOMBC_471052088e_bool=1. fAll_state=1. fa=1. if_Hoa533980679_state=1. if_option_com=1. member_com=1. pname=1. cOMBC_1004116266e_bool=1. cOMBC_1084925030l_bool=1. cOMBC_1123258281e_bool=1. cOMBC_1305755390e_bool=1. cOMBC_2027030106e_bool=1. cOMBC_2107548985e_bool=1. cOMBC_2140141647l_bool=1. cOMBC_290948233e_bool=1. cOMBC_367297061e_bool=1. cOMBC_488258100e_bool=1. cOMBC_498627897l_bool=1. cOMBC_725526061e_bool=1. cOMBC_7971162l_bool=1. cOMBS_1529518335on_com=1. cOMBS_381334199_state=1. cOMBS_843273363_state=1. cOMBS_904531235on_com=1. pn=1. the_el23965208_state=1. the_elem_pname=1. bot_bot_fun_com_bool=1. collec1277803610l_bool=1. collec1613912337l_bool=1. finite1586217244l_bool=1. finite786885583l_bool=1. insert_com=1. the_Ho10452358_state=1. the_pname=1. y=1. c1=1. c2=1. hAPP_f1760790145l_bool=1. hAPP_f921536533e_bool=1. hAPP_f1664156314l_bool=1. hAPP_f759274231e_bool=1. hAPP_f1583986009e_bool=1. hAPP_f434788991l_bool=1. hAPP_f854625363l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f1388330588e_bool=1. hAPP_H727730819e_bool=1. hAPP_f239102607l_bool=1. hAPP_H248360617l_bool=1. hAPP_f559147733l_bool=1. hAPP_p338031245l_bool=1. hAPP_f1970439265l_bool=1. hAPP_p905327722e_bool=1. hAPP_H513860823e_bool=1. hAPP_f631639356e_bool=1. hAPP_pname_bool=1. hAPP_state_bool=1. hAPP_s1806633685e_bool=1. hAPP_c408625258_state=1. hAPP_f1949912908_state=1. hAPP_f588507005_state=1. hAPP_f674760225e_bool=1. hAPP_f1297739591_pname=1. hAPP_f1745235422e_bool=1. hAPP_bool_bool=1. hAPP_f1320879424l_bool=1. hAPP_f772567431e_bool=1. hAPP_f230953622l_bool=1. hAPP_f510955609l_bool=1. hAPP_f2143211163_state=1. hAPP_f1587382801l_bool=1. hAPP_f601642911l_bool=1. hAPP_f1269496639l_bool=1. hAPP_b589554111l_bool=1. hAPP_p61793385e_bool=1. hAPP_H1645666623e_bool=1. hAPP_f1262649863e_bool=1. hAPP_f661147897e_bool=1. hAPP_H563960305_state=1. hAPP_com_bool=1. hAPP_f556039215l_bool=1. hAPP_pname_pname=1. hAPP_f1402196763l_bool=1. hAPP_f1558728829l_bool=1. hAPP_f649174806e_bool=1. hAPP_f760664097e_bool=1. hAPP_f105100493l_bool=1. hAPP_f143162813l_bool=1. hAPP_f1850463605l_bool=1. hAPP_f482022705l_bool=1. hAPP_f624840228l_bool=1. hAPP_p1842370726_state=1. hAPP_pname_com=1. while=1. hAPP_H521649881_state=1. hAPP_f1296386871_state=1. hAPP_f1777033564_state=1. hAPP_f2136041130_state=1. hAPP_f358330902_state=1. hAPP_f950918952_state=1. hAPP_p799580910on_com=1. hAPP_c1546227244_state=1. hAPP_p1170154830_pname=1. semi=1. finite1282449217_pname=1. finite1626890877e_bool=1. hAPP_H1344248906_pname=1. finite774711482_state=1. hAPP_f1874607724l_bool=1. hAPP_f780887186e_bool=1. finite132673334e_bool=1. hAPP_f1145991873l_bool=1. hAPP_f1297925993l_bool=1. hAPP_f2119687429l_bool=1. hAPP_f22061361e_bool=1. hAPP_f262880489e_bool=1. hAPP_f280588268e_bool=1. hAPP_f517001763l_bool=1. hAPP_f748867288l_bool=1. finite1268145088e_bool=1. finite89670078_pname=1. hAPP_p1637813682e_bool=1. hAPP_H1632039476e_bool=1. hAPP_option_com_com=1. finite506823037_state=1. finite959343283e_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1758910594_state=1. hAPP_f96342628me_com=1. hAPP_p877885514e_bool=1. hAPP_H737849090l_bool=1. hAPP_f1138284024e_bool=1. hAPP_f1759915619e_bool=1. hAPP_f915354021e_bool=1. hAPP_f990396704l_bool=1. hAPP_p1617973726l_bool=1. fun=1. hAPP_b1095269219e_bool=1. hAPP_b1679505845on_com=1. hAPP_b798484845_state=1. hAPP_c667411853l_bool=1. hAPP_f1008690464_pname=1. hAPP_f1863945078e_bool=1. hAPP_f1935169308e_bool=1. hAPP_f249262236e_bool=1. hAPP_f327114704l_bool=1. hAPP_f42430548e_bool=1. hAPP_f701449317e_bool=1. hAPP_f873506917e_bool=1. hAPP_o334540577on_com=1. hAPP_o356497025on_com=1. hAPP_s2001034685l_bool=1. hAPP_s58564346l_bool=1. hAPP_H226398757l_bool=1. hAPP_b2019457360e_bool=1. hAPP_f1012183542e_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1308959284_state=1. hAPP_f1336811455e_bool=1. hAPP_f137248406_state=1. hAPP_f1385420507e_bool=1. hAPP_f1405979047_state=1. hAPP_f1456107715e_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1508101115l_bool=1. hAPP_f1508257257l_bool=1. hAPP_f1558052123e_bool=1. hAPP_f1661207211_state=1. hAPP_f167292325e_bool=1. hAPP_f1673966486on_com=1. hAPP_f167506745e_bool=1. hAPP_f1721106985e_bool=1. hAPP_f180827860e_bool=1. hAPP_f1844318385e_bool=1. hAPP_f1862834069l_bool=1. hAPP_f1879335953l_bool=1. hAPP_f1904669497l_bool=1. hAPP_f1973135743e_bool=1. hAPP_f2070658331l_bool=1. hAPP_f2081555625l_bool=1. hAPP_f2082757169l_bool=1. hAPP_f2093196134on_com=1. hAPP_f2101567797_state=1. hAPP_f2123220539on_com=1. hAPP_f261382953l_bool=1. hAPP_f294904177e_bool=1. hAPP_f376825399l_bool=1. hAPP_f389811538l_bool=1. hAPP_f481659057e_bool=1. hAPP_f492098723l_bool=1. hAPP_f547518321e_bool=1. hAPP_f567934427l_bool=1. hAPP_f644196280e_bool=1. hAPP_f648377725on_com=1. hAPP_f698292281e_bool=1. hAPP_f755519727on_com=1. hAPP_f762269719e_bool=1. hAPP_f817621513e_bool=1. hAPP_f833390165e_bool=1. hAPP_f939130838_state=1. hAPP_f964290431e_bool=1. hAPP_f998786331e_bool=1. hAPP_p1086945780on_com=1. hAPP_p1164893188on_com=1. hAPP_p1712839024_state=1. hAPP_p2032835427_state=1. hAPP_p393069232l_bool=1. hAPP_p80247908_state=1. hAPP_p964374716_state=1. hAPP_s1226857760e_bool=1. hAPP_s1874344717e_bool=1. hAPP_s336103912e_bool=1. hAPP_c566651504m_bool=1. hAPP_f1682609283m_bool=1. hAPP_f1987093l_bool=1. hAPP_f783502055l_bool=1. f1=1. f2=1. f8=1. f9=1. f25=1. f26=1. f27=1. f31=1. f32=1. f33=1. f34=1. f38=1. f39=1. f40=1. f41=1. f43=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f53=1. f54=1. f55=1. f57=1. f59=1. f64=1. f71=1. f72=1. f74=1. f75=1. f78=1. f79=1. f83=1. f92=1. f98=1. f99=1. f100=1. f101=1. f107=1. f108=1. f109=1. f128=1. f129=1. f132=1. f133=1. f140=1. f147=1. f154=1. f155=1. f157=1. f158=1. f165=1. image_275883510_state=1. hoare_659004819_state=1. image_1925245338_pname=1. evalc=1. cOMBB_1382207997_state=1. cOMBB_675860798_pname=1. cOMBB_2020112947e_bool=1. cOMBB_2095475776e_bool=1. some_com=1. cOMBB_2123334001_pname=1. dom_pname_com=1. image_pname_pname=1. image_1283814551_pname=1. image_47868345e_bool=1. image_505480954e_bool=1. image_936554724_state=1. image_1259634916e_bool=1. image_277167759e_bool=1. image_636285904_pname=1. image_774712299_state=1. some_pname=1. cOMBB_1759179140_state=1. cOMBB_188601460_state=1. cOMBB_422605457_pname=1. cOMBB_923936821_pname=1. cOMBB_20296667_state=1. cOMBB_647938656_pname=1. cOMBK_588224941_state=1. cOMBK_90103121_pname=1. hoare_1065416081_state=1. set_com=1. set_pname=1. cOMBB_1036740637_state=1. cOMBB_1476898461_state=1. cOMBB_1757942702_state=1. cOMBB_1911358915_state=1. cOMBK_1857069011e_bool=1. cOMBK_631994958_state=1. cOMBK_bool_pname=1. image_2063528359e_bool=1. image_650584225_state=1. set_Ho1831989999_state=1. some_H1133819688_state=1. cOMBB_1099197107e_bool=1. cOMBB_1170234304e_bool=1. cOMBB_1239130257_state=1. cOMBB_1394247784_pname=1. cOMBB_1456120487_state=1. cOMBB_160679318_state=1. cOMBB_1653402815_state=1. cOMBB_1671808265e_bool=1. cOMBB_1722165949_state=1. cOMBB_1957242197e_bool=1. cOMBB_291471741_state=1. cOMBB_307249310e_bool=1. cOMBB_408569982_pname=1. cOMBB_416661851_state=1. cOMBB_44445098_pname=1. cOMBB_530759491_pname=1. cOMBB_542850580_pname=1. cOMBB_598082538e_bool=1. cOMBB_707293872_pname=1. cOMBB_799949246_pname=1. cOMBK_1079618832_state=1. cOMBK_564432736e_bool=1. image_505022149e_bool=1. undefi17486888e_bool=1. undefi64961550l_bool=1. undefined_pname=1. f5=1. f15=1. f19=1. f20=1. f23=1. f28=1. f42=1. f44=1. f62=1. f63=1. f66=1. f67=1. f68=1. f69=1. f70=1. f87=1. f88=1. f89=1. f114=1. f123=1. f124=1. f125=1. f126=1. f131=1. f135=1. f145=1. f156=1. f159=1. f162=1. f163=1. f164=1. f18=1. f37=1. f52=1. f56=1. f65=1. f73=1. f76=1. f77=1. f80=1. f81=1. f82=1. f85=1. f86=1. f90=1. f91=1. f95=1. f96=1. f97=1. f102=1. f103=1. f104=1. f105=1. f106=1. f110=1. f111=1. f112=1. f113=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f127=1. f130=1. f136=1. f137=1. f138=1. f139=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f3=1. f4=1. f16=1. f17=1. f21=1. f22=1. f24=1. f29=1. f30=1. f35=1. f36=1. f51=1. f58=1. f60=1. f61=1. f84=1. f93=1. f94=1. f134=1. f141=1. f142=1. f143=1. f146=1. f160=1. f161=1. f6=1. f7=1. f10=1. f11=1. f12=1. f13=1. f14=1. f144=1. 6.51/6.79 6.51/6.79 ============================== end of process initial clauses ======== 6.51/6.79 6.51/6.79 ============================== CLAUSES FOR SEARCH ==================== 6.51/6.79 6.51/6.79 ============================== end of clauses for search ============= 6.51/6.79 6.51/6.79 ============================== SEARCH ================================ 6.51/6.79 6.51/6.79 % Starting search at 0.82 seconds. 6.51/6.79 6.51/6.79 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 1.87 sec). 6.51/6.79 6.51/6.79 Low Water (keep): wt=42.000, iters=3578 6.51/6.79 6.51/6.79 Low Water (keep): wt=34.000, iters=3355 6.51/6.79 6.51/6.79 Low Water (keep): wt=33.000, iters=3420 6.51/6.79 6.51/6.79 Low Water (keep): wt=32.000, iters=3416 6.51/6.79 6.51/6.79 Low Water (keep): wt=31.000, iters=3419 6.51/6.79 6.51/6.79 Low Water (keep): wt=30.000, iters=3338 6.51/6.79 6.51/6.79 Low Water (keep): wt=29.000, iters=3339 6.51/6.79 6.51/6.79 Low Water (keep): wt=28.000, iters=3369 6.51/6.79 6.51/6.79 Low Water (keep): wt=27.000, iters=3345 6.51/6.79 6.51/6.79 Low Water (keep): wt=26.000, iters=3451 6.51/6.79 6.51/6.79 Low Water (keep): wt=25.000, iters=3349 6.51/6.79 6.51/6.79 Low Water (keep): wt=24.000, iters=3340 6.51/6.79 6.51/6.79 Low Water (keep): wt=23.000, iters=3340 6.51/6.79 6.51/6.79 Low Water (keep): wt=22.000, iters=3352 6.51/6.79 6.51/6.79 Low Water (keep): wt=21.000, iters=3391 6.51/6.79 6.51/6.79 Low Water (keep): wt=20.000, iters=3342 6.51/6.79 6.51/6.79 Low Water (keep): wt=19.000, iters=3369 6.51/6.79 6.51/6.79 Low Water (keep): wt=18.000, iters=3333 6.51/6.79 6.51/6.79 Low Water (keep): wt=17.000, iters=3344 6.51/6.79 6.51/6.79 Low Water (keep): wt=16.000, iters=3333 6.51/6.79 6.51/6.79 Low Water (keep): wt=15.000, iters=3335 6.51/6.79 6.51/6.79 Low Water (keep): wt=14.000, iters=3346 6.51/6.79 6.51/6.79 Low Water (keep): wt=13.000, iters=3333 6.51/6.79 6.51/6.79 Low Water (keep): wt=12.000, iters=3415 6.51/6.79 6.51/6.79 Low Water (displace): id=4696, wt=103.000 6.51/6.79 6.51/6.79 Low Water (displace): id=4695, wt=100.000 6.51/6.79 6.51/6.79 Low Water (displace): id=4064, wt=96.000 6.51/6.79 6.51/6.79 Low Water (displace): id=7797, wt=43.000 6.51/6.79 6.51/6.79 Low Water (displace): id=14903, wt=37.000 6.51/6.79 6.51/6.79 Low Water (displace): id=14923, wt=11.000 15.89/16.12 15.89/16.12 Low Water (displace): id=14939, wt=10.000 15.89/16.12 15.89/16.12 Low Water (displace): id=15101, wt=9.000 15.89/16.12 15.89/16.12 Low Water (keep): wt=11.000, iters=3336 15.89/16.12 15.89/16.12 Low Water (keep): wt=10.000, iters=3333 15.89/16.12 15.89/16.12 ============================== PROOF ================================= 15.89/16.12 % SZS status Theorem 15.89/16.12 % SZS output start Refutation 15.89/16.12 15.89/16.12 % Proof 1 at 14.23 (+ 0.24) seconds. 15.89/16.12 % Length of proof is 28. 15.89/16.12 % Level of proof is 7. 15.89/16.12 % Maximum clause weight is 16.000. 15.89/16.12 % Given clauses 6676. 15.89/16.12 15.89/16.12 53 (all P_1 hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1) # label(fact_177_Collect__def) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 145 (all X_1 set_Ho1831989999_state(some_H1133819688_state(X_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) # label(fact_403_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 196 (all C (hBOOL(hoare_298929751gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_53_MGF) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 373 (all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A))) # label(fact_366_bot__least) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 480 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_213_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 779 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_215_WT__bodiesD) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 808 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_2),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption]. 15.89/16.12 931 hAPP_f921536533e_bool(collec727977250_state,A) = A # label(fact_177_Collect__def) # label(axiom). [clausify(53)]. 15.89/16.12 1067 hBOOL(wT_bodies) # label(conj_1) # label(hypothesis). [assumption]. 15.89/16.12 1093 set_Ho1831989999_state(some_H1133819688_state(A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) # label(fact_403_Option_Oset_Osimps_I2_J) # label(axiom). [clausify(145)]. 15.89/16.12 1094 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = set_Ho1831989999_state(some_H1133819688_state(A)). [copy(1093),flip(a)]. 15.89/16.12 1172 -hBOOL(hoare_298929751gleton) | -hBOOL(wT_bodies) | -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,A)),bot_bo1055319631e_bool))) # label(fact_53_MGF) # label(axiom). [clausify(196)]. 15.89/16.12 1173 -hBOOL(hoare_298929751gleton) | -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),set_Ho1831989999_state(some_H1133819688_state(hAPP_c1546227244_state(hoare_Mirabelle_MGT,A))))). [copy(1172),rewrite([1094(15)]),unit_del(b,1067)]. 15.89/16.12 1463 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A)) # label(fact_366_bot__least) # label(axiom). [clausify(373)]. 15.89/16.12 1577 hBOOL(hoare_298929751gleton) # label(conj_0) # label(hypothesis). [assumption]. 15.89/16.12 1616 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) # label(fact_213_singleton__conv2) # label(axiom). [clausify(480)]. 15.89/16.12 1617 set_Ho1831989999_state(some_H1133819688_state(A)) = hAPP_H1645666623e_bool(fequal1531560888_state,A). [copy(1616),rewrite([1094(4),931(6)])]. 15.89/16.12 1765 hAPP_p799580910on_com(body,pn) = some_com(y) # label(conj_5) # label(hypothesis). [assumption]. 15.89/16.12 2083 -hBOOL(wT_bodies) | some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)) # label(fact_215_WT__bodiesD) # label(axiom). [clausify(779)]. 15.89/16.12 2084 some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)). [copy(2083),unit_del(a,1067)]. 15.89/16.12 2140 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(A),B)) | -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(C),B)) # label(fact_3_thin) # label(axiom). [clausify(808)]. 15.89/16.12 2167 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))) # label(conj_7) # label(negated_conjecture). [assumption]. 15.89/16.12 2168 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [copy(2167),rewrite([1094(16),1617(14)])]. 15.89/16.12 2254 -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,A)))). [back_unit_del(1173),rewrite([1617(11)]),unit_del(a,1577)]. 15.89/16.12 7127 hBOOL(hAPP_com_bool(wt,y)). [resolve(2084,a,1765,a(flip))]. 15.89/16.12 8696 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [resolve(7127,a,2254,a)]. 15.89/16.12 33833 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(A),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [resolve(8696,a,2140,a),unit_del(a,1463)]. 15.89/16.12 33834 $F. [resolve(33833,a,2168,a)]. 15.89/16.12 15.89/16.12 % SZS output end Refutation 15.89/16.12 ============================== end of proof ========================== 15.89/16.12 15.89/16.12 ============================== STATISTICS ============================ 15.89/16.12 15.89/16.12 Given=6676. Generated=300984. Kept=32726. proofs=1. 15.89/16.12 Usable=5875. Sos=9983. Demods=924. Limbo=0, Disabled=18179. Hints=0. 15.89/16.12 Megabytes=157.13. 15.89/16.12 User_CPU=14.23, System_CPU=0.24, Wall_clock=14. 15.89/16.12 15.89/16.12 ============================== end of statistics ===================== 15.89/16.12 15.89/16.12 ============================== end of search ========================= 15.89/16.12 15.89/16.12 THEOREM PROVED 15.89/16.12 % SZS status Theorem 15.89/16.12 15.89/16.12 Exiting with 1 proof. 15.89/16.12 15.89/16.12 Process 2163 exit (max_proofs) Tue Aug 9 03:28:38 2022 15.89/16.12 Prover9 interrupted 15.89/16.13 EOF