0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n013.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % DateTime : Tue Jul 13 15:29:18 EDT 2021 0.13/0.35 % CPUTime : 6.12/6.10 ============================== Prover9 =============================== 6.12/6.10 Prover9 (32) version 2009-11A, November 2009. 6.12/6.10 Process 25270 was started by sandbox2 on n013.cluster.edu, 6.12/6.10 Tue Jul 13 15:29:23 2021 6.12/6.10 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_25117_n013.cluster.edu". 6.12/6.10 ============================== end of head =========================== 6.12/6.10 6.12/6.10 ============================== INPUT ================================= 6.12/6.10 6.12/6.10 % Reading from file /tmp/Prover9_25117_n013.cluster.edu 6.12/6.10 6.12/6.10 set(prolog_style_variables). 6.12/6.10 set(auto2). 6.12/6.10 % set(auto2) -> set(auto). 6.12/6.10 % set(auto) -> set(auto_inference). 6.12/6.10 % set(auto) -> set(auto_setup). 6.12/6.10 % set(auto_setup) -> set(predicate_elim). 6.12/6.10 % set(auto_setup) -> assign(eq_defs, unfold). 6.12/6.10 % set(auto) -> set(auto_limits). 6.12/6.10 % set(auto_limits) -> assign(max_weight, "100.000"). 6.12/6.10 % set(auto_limits) -> assign(sos_limit, 20000). 6.12/6.10 % set(auto) -> set(auto_denials). 6.12/6.10 % set(auto) -> set(auto_process). 6.12/6.10 % set(auto2) -> assign(new_constants, 1). 6.12/6.10 % set(auto2) -> assign(fold_denial_max, 3). 6.12/6.10 % set(auto2) -> assign(max_weight, "200.000"). 6.12/6.10 % set(auto2) -> assign(max_hours, 1). 6.12/6.10 % assign(max_hours, 1) -> assign(max_seconds, 3600). 6.12/6.10 % set(auto2) -> assign(max_seconds, 0). 6.12/6.10 % set(auto2) -> assign(max_minutes, 5). 6.12/6.10 % assign(max_minutes, 5) -> assign(max_seconds, 300). 6.12/6.10 % set(auto2) -> set(sort_initial_sos). 6.12/6.10 % set(auto2) -> assign(sos_limit, -1). 6.12/6.10 % set(auto2) -> assign(lrs_ticks, 3000). 6.12/6.10 % set(auto2) -> assign(max_megs, 400). 6.12/6.10 % set(auto2) -> assign(stats, some). 6.12/6.10 % set(auto2) -> clear(echo_input). 6.12/6.10 % set(auto2) -> set(quiet). 6.12/6.10 % set(auto2) -> clear(print_initial_clauses). 6.12/6.10 % set(auto2) -> clear(print_given). 6.12/6.10 assign(lrs_ticks,-1). 6.12/6.10 assign(sos_limit,10000). 6.12/6.10 assign(order,kbo). 6.12/6.10 set(lex_order_vars). 6.12/6.10 clear(print_given). 6.12/6.10 6.12/6.10 % formulas(sos). % not echoed (4589 formulas) 6.12/6.10 6.12/6.10 ============================== end of input ========================== 6.12/6.10 6.12/6.10 % From the command line: assign(max_seconds, 1200). 6.12/6.10 6.12/6.10 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 6.12/6.10 6.12/6.10 % Formulas that are not ordinary clauses: 6.12/6.10 1 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(R) <-> p(Q)) -> Q = R))))) # label(boolext) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 2 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(G,X) = ap(F,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 4 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 5 (all A all B all F (mem(F,arr(A,B)) -> (all X (mem(X,A) -> mem(ap(F,X),B))))) # label(ap_tp) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 6 (all A all Y all X (mem(X,A) -> ap(k(A,Y),X) = Y)) # label(kbeta) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 7 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Emin_2E_3D) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 8 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) -> p(R)) <-> p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 9 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Emin_2E_40) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 10 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> Y = X))))))) # label(ax_eq_p) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 11 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((-p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) & (-p(V2Q) -> (p(V0P) <-> p(V1P_27))) -> (p(V0P) | p(V2Q) <-> p(V1P_27) | p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 12 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((all V4x (mem(V4x,A_27a) -> p(V1Q))) | (all V3x (mem(V3x,A_27a) -> p(V0P))) <-> (all V2x (mem(V2x,A_27a) -> p(V1Q) | p(V0P)))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 13 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x)) = ap(f11(A_27a,V0P),V1x)))) # label(lameq_f11) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 14 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(Q) & p(R) <-> p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))))))) # label(ax_and_p) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 15 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((all X (mem(X,A) -> p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_21(A),Q))))))) # label(ax_all_p) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 16 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> (p(ap(V0P,c_2Ebool_2Ethe__value(A_27a))) -> (all V1i (mem(V1i,ty_2Ebool_2Eitself(A_27a)) -> p(ap(V0P,V1i))))))))) # label(conj_thm_2Ebool_2Eitself__induction) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 17 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (p(ap(V0P,V1a)) <-> (exists V2x (p(ap(V0P,V2x)) & V2x = V1a & mem(V2x,A_27a)))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 18 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x ((p(ap(V0P,V2x)) -> p(V1Q)) & mem(V2x,A_27a))) <-> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 19 (all A_27a all V0P ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) # label(lameq_f2) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 20 (all V0P (mem(V0P,arr(bool,bool)) -> ((all V1b (mem(V1b,bool) -> p(ap(V0P,V1b)))) <-> p(ap(V0P,c_2Ebool_2EF)) & p(ap(V0P,c_2Ebool_2ET))))) # label(conj_thm_2Ebool_2EFORALL__BOOL) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 21 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> ((-p(V1x) -> -p(V0y)) <-> (p(V0y) -> p(V1x))))))) # label(conj_thm_2Ebool_2EMONO__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 22 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0M (mem(V0M,arr(A_27a,A_27b)) -> V0M = f47(A_27b,A_27a,V0M))))))) # label(conj_thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 23 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)))) & p(V0P) <-> (all V3x (mem(V3x,A_27a) -> p(V0P) & p(ap(V1Q,V3x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2ELET) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 25 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> (p(V1t2) -> p(V0t1) & p(V1t2))))))) # label(conj_thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 26 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2x ap(f58(A_27a,V0P,V1Q),V2x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V2x)),ap(V1Q,V2x))))))) # label(lameq_f58) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 27 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V1f)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) -> p(ap(V1f,V2x)))))))))))) # label(conj_thm_2Ebool_2ERES__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 28 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f34) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 29 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Emin_2E_40(A_27a),f51(A_27a,V0x)) = V0x)))) # label(conj_thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 30 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EARB(A_27a),A_27a))) # label(mem_c_2Ebool_2EARB) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 31 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1))))) # label(lameq_f20) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 32 (all V0t (mem(V0t,bool) -> ($T <-> $T | p(V0t)) & (p(V0t) <-> p(V0t) | p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) | $T <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 33 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 34 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V1B) & p(V0A) | p(V2C) & p(V0A) <-> (p(V2C) | p(V1B)) & p(V0A)))))))) # label(conj_thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 35 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))))) # label(mem_c_2Ebool_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 36 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (p(ap(V0P,ap(ap(c_2Ebool_2ELET(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M))) <-> p(ap(ap(c_2Ebool_2ELET(A_27a,bool),f54(A_27b,A_27a,V1N,V0P)),V2M))))))))))))) # label(conj_thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 37 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) <-> p(V0A) | p(V1B)) <-> (p(V1B) -> p(V0A))))))) # label(conj_thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 38 (all A_27b all A_27c all A_27a all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V2b (mem(V2b,A_27b) -> (all V4x ap(f56(A_27b,A_27c,A_27a,V0N,V2b),V4x) = ap(ap(V0N,V4x),V2b)))))) # label(lameq_f56) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 39 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V1M (mem(V1M,A_27a) -> (all V2b (mem(V2b,A_27b) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27c),f56(A_27b,A_27c,A_27a,V0N,V2b)),V1M) = ap(ap(ap(c_2Ebool_2Eliteral__case(A_27a,arr(A_27b,A_27c)),f55(A_27c,A_27b,A_27a,V0N)),V1M),V2b))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 40 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((p(V0P) -> (all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x))))) <-> (all V2x (mem(V2x,A_27a) -> (p(V0P) -> p(ap(V1Q,V2x)))))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 41 (all A_27a all V0p f43(A_27a,V0p) = ap(f44(A_27a),V0p)) # label(lameq_f44) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 42 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,bool)) -> (all V3g (mem(V3g,arr(A_27a,bool)) -> (V1Q = V0P -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1Q)) -> (p(ap(V2f,V4x)) <-> p(ap(V3g,V4x)))))) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V2f)) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1Q),V3g))))))))))))))) # label(conj_thm_2Ebool_2ERES__FORALL__CONG) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 43 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,A_27a) -> (all V2t2 ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t))))))) # label(lameq_f16) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 44 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1y ap(ap(c_2Emin_2E_3D(A_27a),V1y),V0x) = ap(f50(A_27a,V0x),V1y)))) # label(lameq_f50) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 45 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F_21) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 46 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) -> p(V1B)) <-> p(V1B) | -p(V0A)))))) # label(conj_thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 47 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y))))) # label(lameq_f23) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 48 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(A_27a),V0x))))))) # label(conj_thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 49 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V3x ap(f53(A_27b,A_27a,V1N),V3x) = ap(V1N,V3x)))) # label(lameq_f53) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 50 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x ((p(ap(V0P,V2x)) | p(ap(V1Q,V2x))) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x)))) | (exists V4x (mem(V4x,A_27a) & p(ap(V1Q,V4x))))))))))) # label(conj_thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 51 (all V0bool (mem(V0bool,arr(bool,arr(bool,bool))) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0bool,c_2Ebool_2ET),c_2Ebool_2EF)))))) # label(conj_thm_2Ebool_2EDATATYPE__BOOL) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 52 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ($T <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),k(A_27a,c_2Ebool_2ET)))))))) # label(conj_thm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 53 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> ((p(V0t1) & p(V1t2) -> p(V2t3)) <-> (p(V0t1) -> (p(V1t2) -> p(V2t3)))))))))) # label(conj_thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 54 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t) = V1t)))))) # label(conj_thm_2Ebool_2ECOND__ID) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 55 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((exists V1x (p(V0t) & mem(V1x,A_27a))) <-> p(V0t)))))) # label(conj_thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 56 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> ap(V1g,V2x) = ap(V0f,V2x))) -> V1g = V0f))))))))) # label(conj_thm_2Ebool_2EEQ__EXT) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 57 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V3x (mem(V3x,A_27a) & (p(ap(V0P,V3x)) | p(V1Q)))) <-> p(V1Q) | (exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x))))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 58 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(V1m,V2x) = ap(f40(A_27a,V1m),V2x)))) # label(lameq_f40) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 59 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (exists V1x (mem(V1x,A_27a) & V1x = V0a)))))) # label(conj_thm_2Ebool_2EEXISTS__REFL) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 60 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(V0f,V1x) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Ebool_2Eliteral__case__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 61 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V4x ap(V1Q,V4x) = ap(f60(A_27a,V1Q),V4x)))) # label(lameq_f60) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 62 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) & p(V0t1) <-> p(V1t2) & p(V0t1)))))) # label(conj_thm_2Ebool_2ECONJ__COMM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 63 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) <-> p(V0x)) & (p(V1x_27) -> (p(V2y) <-> p(V3y_27))) -> ((p(V0x) -> p(V2y)) <-> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 64 (all A_27b all A_27a all V0M (mem(V0M,arr(A_27a,A_27b)) -> (all V1x ap(f47(A_27b,A_27a,V0M),V1x) = ap(V0M,V1x)))) # label(lameq_f47) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 65 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1))))) # label(lameq_f4) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 66 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((p(V0P) -> (exists V3x (p(ap(V1Q,V3x)) & mem(V3x,A_27a)))) <-> (exists V2x (mem(V2x,A_27a) & (p(V0P) -> p(ap(V1Q,V2x)))))))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 67 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27a) -> (V2y = V1x <-> p(ap(V0P,V2y))))) -> ap(c_2Emin_2E_40(A_27a),V0P) = V1x))))))) # label(conj_thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 68 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,A_27b)) -> (all V1x ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x)))) # label(lameq_f31) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 69 (all V0t (mem(V0t,bool) -> (($F <-> p(V0t)) <-> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F__EQ__F) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 70 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27b) -> (all V2x ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x)) = ap(f22(A_27b,A_27a,V0f,V1y),V2x)))))) # label(lameq_f22) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 71 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a))) # label(ax_thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 72 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) -> p(V1t2) | p(V0t1)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 73 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (-p(ap(V0P,V2x)) & mem(V2x,A_27a))) <-> -(all V1x (mem(V1x,A_27a) -> p(ap(V0P,V1x))))))))) # label(conj_thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 74 (exists V0f (mem(V0f,arr(ind,ind)) & p(ap(c_2Ebool_2EONE__ONE(ind,ind),V0f)) & -p(ap(c_2Ebool_2EONTO(ind,ind),V0f)))) # label(ax_thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 75 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (exists V1f (mem(V1f,arr(ty_2Ebool_2Eitself(A_27a),A_27b)) & V0e = ap(V1f,c_2Ebool_2Ethe__value(A_27a)))))))))) # label(conj_thm_2Ebool_2Eitself__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 76 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> ((all V1x (mem(V1x,ty_2Ebool_2Eitself(A_27a)) -> p(ap(V0P,V1x)))) <-> p(ap(V0P,c_2Ebool_2Ethe__value(A_27a)))))))) # label(conj_thm_2Ebool_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 77 (all V4b ap(f65,V4b) = ap(c_2Ebool_2E_7E,V4b)) # label(lameq_f65) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 78 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V3x (mem(V3x,A_27a) & (p(V0P) | p(ap(V1Q,V3x))))) <-> (exists V2x (p(ap(V1Q,V2x)) & mem(V2x,A_27a))) | p(V0P)))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.12/6.10 79 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x)))) | p(V0P) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)) | p(V0P)))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 80 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 81 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 82 (all A_27a (ne(A_27a) -> k(A_27a,c_2Ebool_2ET) = c_2Ebool_2EDATATYPE(A_27a))) # label(ax_thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 83 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V2z) -> p(V3w)) & (p(V0y) -> p(V1x)) -> ((p(V1x) -> p(V2z)) -> (p(V0y) -> p(V3w)))))))))))) # label(conj_thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 84 (all V1t2 (mem(V1t2,bool) -> (all V0t1 (mem(V0t1,bool) -> (all V2t ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t)))))) # label(lameq_f3) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 85 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> V3y = V2x)))) & p(V0t) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),k(A_27a,V0t)))))))) # label(conj_thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 86 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_21(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 87 (all V0t1 f7(V0t1) = ap(f8,V0t1)) # label(lameq_f8) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 88 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t) & p(V0t)) & ($F & p(V0t) <-> $F) & ($F <-> p(V0t) & $F))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 89 i(bool) = i(bool) <-> $T # label(ax_thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 90 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 ap(f19(A_27b,A_27a,V0f,V1x1),V2x2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2))))))) # label(lameq_f19) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 91 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> ((all V2x_27 (mem(V2x_27,A_27b) -> (all V3x_27_27 (mem(V3x_27_27,A_27b) -> (ap(V1rep,V2x_27) = ap(V1rep,V3x_27_27) -> V2x_27 = V3x_27_27))))) & (all V4x (mem(V4x,A_27a) -> (p(ap(V0P,V4x)) <-> (exists V5x_27 (mem(V5x_27,A_27b) & V4x = ap(V1rep,V5x_27)))))) <-> p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),V0P),V1rep))))))))))) # label(conj_thm_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 92 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> V0t1 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2))))) & (all V2t1 (mem(V2t1,A_27a) -> (all V3t2 (mem(V3t2,A_27a) -> V3t2 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2))))))) # label(conj_thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 93 (all A_27b all A_27a all V0P f29(A_27b,A_27a,V0P) = ap(f30(A_27b,A_27a),V0P)) # label(lameq_f30) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 94 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) & (p(V2C) | p(V1B)) <-> p(V2C) & p(V0A) | p(V1B) & p(V0A)))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 95 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f63(A_27a,V1f,V0P),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f62(A_27a,V1f,V3x))))))) # label(lameq_f63) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 96 (all A_27b all A_27a all V1t (mem(V1t,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2u (mem(V2u,A_27b) -> (all V3x ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V0a)),V1t),V2u) = ap(f67(A_27b,A_27a,V1t,V0a,V2u),V3x)))))))) # label(lameq_f67) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 97 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1f ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x)))) # label(lameq_f32) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 98 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1f)) <-> (exists V2x (mem(V2x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) & p(ap(V1f,V2x))))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 99 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27))))) # label(lameq_f26) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 100 (all A_27a all V0a (mem(V0a,A_27a) -> (all V1x ap(f57(A_27a,V0a),V1x) = ap(ap(c_2Emin_2E_3D(A_27a),V1x),V0a)))) # label(lameq_f57) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 101 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> ((all V2x (mem(V2x,A_27a) -> (V2x = V1v -> p(ap(V0f,V2x))))) <-> p(ap(V0f,V1v))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 102 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),f58(A_27a,V0P,V1Q))) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f59(A_27a,V0P))) | p(ap(c_2Ebool_2E_3F_21(A_27a),f60(A_27a,V1Q)))))))))) # label(conj_thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 103 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V4x ap(V0P,ap(V1N,V4x)) = ap(f54(A_27b,A_27a,V1N,V0P),V4x)))))) # label(lameq_f54) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 104 (all A_27a all V0t ap(f18(A_27a),V0t) = f17(A_27a,V0t)) # label(lameq_f18) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 105 (all A_27a all V0p f38(A_27a,V0p) = ap(f39(A_27a),V0p)) # label(lameq_f39) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 106 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f24(A_27a,A_27b) = c_2Ebool_2EONTO(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 107 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V1x) = ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2ELET__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 108 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2EIN) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 109 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x (p(ap(V1Q,V2x)) & p(V0P) & mem(V2x,A_27a))) <-> p(V0P) & (exists V3x (mem(V3x,A_27a) & p(ap(V1Q,V3x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 110 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 111 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> ap(V0f,V2x) = ap(V1g,V2x))) <-> V1g = V0f))))))))) # label(conj_thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 112 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V1B) & p(V2C) | p(V0A) <-> (p(V1B) | p(V0A)) & (p(V2C) | p(V0A))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 113 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (p(ap(c_2Ebool_2EONE__ONE(A_27a,A_27b),V0f)) <-> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 (mem(V2x2,A_27a) -> (ap(V0f,V1x1) = ap(V0f,V2x2) -> V1x1 = V2x2)))))))))))) # label(conj_thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 114 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))))))) # label(mem_c_2Ebool_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 115 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27b) -> V0t1 = ap(k(A_27b,V0t1),V1t2))))))))) # label(conj_thm_2Ebool_2EABS__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 116 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)))) # label(mem_c_2Ebool_2Ethe__value) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 117 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5y_27 (mem(V5y_27,A_27a) -> ((p(V1Q) -> V2x = V3x_27) & (-p(V1Q) -> V4y = V5y_27) & (p(V1Q) <-> p(V0P)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y)))))))))))))))) # label(conj_thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 118 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) <-> p(V1t2) & p(V0t1)))))) # label(conj_thm_2Ebool_2ECONJ__SYM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 119 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x (mem(V4x,A_27a) -> (all V5x_27 ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27))))))) # label(lameq_f27) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 120 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((all V2x (mem(V2x,A_27a) -> (p(V0P) -> p(V1Q)))) <-> ((exists V3x (mem(V3x,A_27a) & p(V0P))) -> (all V4x (mem(V4x,A_27a) -> p(V1Q))))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 121 (all A_27a (ne(A_27a) -> f39(A_27a) = c_2Ebool_2ERES__EXISTS(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 122 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(V1f,V2x) = ap(f61(A_27a,V1f),V2x)))) # label(lameq_f61) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 123 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V3y (mem(V3y,A_27b) -> (all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),V3y)))))) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESWAP__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 124 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> (exists V2fn (V0t1 = ap(V2fn,c_2Ebool_2ET) & V1t2 = ap(V2fn,c_2Ebool_2EF) & mem(V2fn,arr(bool,A_27a)))))))))) # label(conj_thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 125 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m)) = ap(f38(A_27a,V0p),V1m)))) # label(lameq_f38) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 126 (all A_27a all V1t1 (mem(V1t1,A_27a) -> (all V2t2 (mem(V2t2,A_27a) -> (all V0t (mem(V0t,bool) -> (all V3x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2))) = ap(f15(A_27a,V1t1,V2t2,V0t),V3x)))))))) # label(lameq_f15) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 127 (all A_27b all A_27a all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> (all V3x ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)) = ap(f52(A_27b,A_27a,V0b,V1f,V2g),V3x)))))))) # label(lameq_f52) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 128 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 129 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> f52(A_27b,A_27a,V0b,V1f,V2g) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g))))))))))) # label(conj_thm_2Ebool_2ECOND__ABS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 130 (all V0t (mem(V0t,bool) -> (-p(V0t) -> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 131 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-p(V1B) | -p(V0A) <-> -(p(V0A) & p(V1B))) & (-p(V1B) & -p(V0A) <-> -(p(V1B) | p(V0A))))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 132 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> ((p(V1t1) | -p(V0b)) & (p(V2t2) | p(V0b)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 133 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0P),V1f) = ap(c_2Emin_2E_40(A_27a),f64(A_27a,V0P,V1f)))))))) # label(conj_thm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 134 (all A_27a all V0P ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET)) = ap(f1(A_27a),V0P)) # label(lameq_f1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 135 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> (p(V0t) <-> (all V1x (mem(V1x,A_27a) -> p(V0t)))))))) # label(conj_thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 136 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep))) = ap(f29(A_27b,A_27a,V0P),V1rep)))) # label(lameq_f29) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 137 (all V0t (mem(V0t,bool) -> -(p(V0t) & -p(V0t)))) # label(conj_thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 138 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 139 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F(A_27a),V0f)) <-> (exists V1x (p(ap(V0f,V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Ebool_2EEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 140 (all V0t (mem(V0t,bool) -> p(V0t))) <-> $F # label(ax_thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 141 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1y ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y) = ap(f51(A_27a,V0x),V1y)))) # label(lameq_f51) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 142 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y -> V0x = V1y))))))) # label(conj_thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 143 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)) & p(V1Q))) <-> p(V1Q) & (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x))))))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 144 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V1M (mem(V1M,A_27a) -> (all V2b (mem(V2b,A_27b) -> ap(ap(ap(c_2Ebool_2ELET(A_27a,arr(A_27b,A_27c)),f55(A_27c,A_27b,A_27a,V0N)),V1M),V2b) = ap(ap(c_2Ebool_2ELET(A_27a,A_27c),f56(A_27b,A_27c,A_27a,V0N,V2b)),V1M))))))))))))) # label(conj_thm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 145 (all A0 (ne(A0) -> ne(ty_2Ebool_2Eitself(A0)))) # label(ne_ty_2Ebool_2Eitself) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 146 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) -> p(V0t1)))))) # label(conj_thm_2Ebool_2EAND1__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 147 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) & (p(V2Q) -> (p(V1P_27) <-> p(V0P))) -> (p(V3Q_27) & p(V1P_27) <-> p(V2Q) & p(V0P))))))))))) # label(conj_thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 148 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2R (mem(V2R,bool) -> ((p(V0P) | p(V1Q) -> p(V2R)) <-> (p(V0P) -> p(V2R)) & (p(V1Q) -> p(V2R))))))))) # label(conj_thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 149 (all A_27c all A_27b all A_27a all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V3x ap(V0N,V3x) = ap(f55(A_27c,A_27b,A_27a,V0N),V3x)))) # label(lameq_f55) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 150 (all A_27a all V0p f45(A_27a,V0p) = ap(f46(A_27a),V0p)) # label(lameq_f46) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 151 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> V0x = V0x))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 152 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 & ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 153 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,A_27b) -> V0b = ap(ap(c_2Ebool_2Eitself__case(A_27a,A_27b),c_2Ebool_2Ethe__value(A_27a)),V0b))))))) # label(ax_thm_2Ebool_2Eitself__case__thm) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 154 (all A_27a (ne(A_27a) -> c_2Ebool_2E_21(A_27a) = f1(A_27a))) # label(ax_thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 155 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m))))) # label(lameq_f45) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 156 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V1rep (mem(V1rep,arr(A_27b,A_27a)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),V0P),V1rep)))) -> (exists V2rep (mem(V2rep,arr(A_27b,A_27a)) & (exists V3abs ((all V4a (mem(V4a,A_27b) -> V4a = ap(V3abs,ap(V2rep,V4a)))) & (all V5r (mem(V5r,A_27a) -> (V5r = ap(V2rep,ap(V3abs,V5r)) <-> p(ap(V0P,V5r))))) & mem(V3abs,arr(A_27a,A_27b))))))))))))) # label(conj_thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 157 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m)) = ap(f35(A_27a,V0p),V1m)))) # label(lameq_f35) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 158 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V0P) <-> p(V1P_27)) & (-p(V1P_27) -> (p(V2Q) <-> p(V3Q_27))) -> (p(V3Q_27) | p(V1P_27) <-> p(V0P) | p(V2Q))))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 159 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2z (mem(V2z,A_27a) -> (V1y = V0x & V1y = V2z -> V2z = V0x))))))))) # label(conj_thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 160 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y))))))) # label(lameq_f10) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 161 (all A_27a (ne(A_27a) -> f18(A_27a) = c_2Ebool_2ECOND(A_27a))) # label(ax_thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 162 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f37) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 163 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> p(ap(V1Q,V4x)))) & (all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)) & p(ap(V0P,V2x))))))))))) # label(conj_thm_2Ebool_2EFORALL__AND__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 164 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z) = ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)))))))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ap(ap(V0f,V5y),V4x) = ap(ap(V0f,V4x),V5y))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> ap(ap(V0f,V7y),ap(ap(V0f,V6x),V8z)) = ap(ap(V0f,V6x),ap(ap(V0f,V7y),V8z)))))))))))))) # label(conj_thm_2Ebool_2ELCOMM__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 165 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2))))) # label(lameq_f7) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 166 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(f49(A_27a,V0P),V1x) = ap(V0P,V1x)))) # label(lameq_f49) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 167 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) -> p(V1t2)))))) # label(conj_thm_2Ebool_2EAND2__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 168 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ((all V1y (mem(V1y,A_27b) -> (exists V2x (mem(V2x,A_27a) & V1y = ap(V0f,V2x))))) <-> p(ap(c_2Ebool_2EONTO(A_27a,A_27b),V0f))))))))) # label(conj_thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 169 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((all V3x (mem(V3x,A_27a) -> p(V1Q) & p(ap(V0P,V3x)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x)))) & p(V1Q)))))))) # label(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 170 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & ($T <-> (p(V0t) -> $T)) & ($T <-> ($F -> p(V0t))) & (-p(V0t) <-> -p(V0t)) & ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 171 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(f62(A_27a,V1f,V3x),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1f,V3x)),ap(V1f,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y))))))) # label(lameq_f62) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 172 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1Q,V4x)))))))))))) # label(conj_thm_2Ebool_2EMONO__ALL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 173 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t) = V1t)))))) # label(conj_thm_2Ebool_2Ebool__case__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 174 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x)))) # label(lameq_f13) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 175 (all A_27b all A_27c all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27b,A_27c)) -> (all V4x ap(V0P,ap(V1N,V4x)) = ap(f66(A_27b,A_27c,A_27a,V1N,V0P),V4x)))))) # label(lameq_f66) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 176 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))))) # label(mem_c_2Ebool_2ECOND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 177 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0P,V4y)) & p(ap(V0P,V3x)) -> V3x = V4y))))) & (exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),f49(A_27a,V0P)))))))) # label(conj_thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 178 (all A_27a (ne(A_27a) -> (all V0Q (mem(V0Q,bool) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V1P,V3x)))) | p(V0Q) <-> (all V2x (mem(V2x,A_27a) -> p(V0Q) | p(ap(V1P,V2x))))))))))) # label(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 179 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))))))) # label(mem_c_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 180 (all V0P (mem(V0P,arr(bool,bool)) -> (p(ap(V0P,c_2Ebool_2EF)) & p(ap(V0P,c_2Ebool_2ET)) -> (all V1b (mem(V1b,bool) -> p(ap(V0P,V1b))))))) # label(conj_thm_2Ebool_2Ebool__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 181 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (mem(V2x,A_27a) & (p(V0P) -> p(V1Q)))) <-> ((all V3x (mem(V3x,A_27a) -> p(V0P))) -> (exists V4x (mem(V4x,A_27a) & p(V1Q))))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 182 (all V0v (mem(V0v,bool) -> ($T <-> p(ap(c_2Ebool_2EBOUNDED,V0v))))) # label(conj_thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 183 (all A_27a (ne(A_27a) -> f33(A_27a) = c_2Ebool_2EIN(A_27a))) # label(ax_thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2Eliteral__case) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 185 (all A_27a all V0P ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P)))) # label(lameq_f12) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 186 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((exists X (mem(X,A) & p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_3F(A),Q))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 187 -($F <-> $T) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 188 -($T <-> $F) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 189 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1t (mem(V1t,A_27a) -> ((all V2x (mem(V2x,A_27a) -> (V1t = V2x -> p(ap(V0P,V2x))))) -> p(ap(c_2Ebool_2E_3F(A_27a),V0P))))))))) # label(conj_thm_2Ebool_2EJRH__INDUCT__UTIL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 190 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(R) | p(Q)))))) # label(ax_or_p) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 191 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 192 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p)))))) # label(lameq_f43) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 193 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.10 194 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (((p(V0P) -> p(V1Q)) -> p(V0P)) -> p(V0P)))))) # label(conj_thm_2Ebool_2EPEIRCE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 195 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x ap(f28(A_27b,A_27a,V0P,V1rep),V4x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x)))))))) # label(lameq_f28) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 196 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V5x (p(V1Q) & p(ap(V0P,V5x)) & mem(V5x,A_27a))) <-> (exists V4x (p(ap(V0P,V4x)) & mem(V4x,A_27a))) & p(V1Q)) & ((exists V6x (mem(V6x,A_27a) & p(ap(V0P,V6x)))) & p(V1Q) <-> (exists V7x (p(V1Q) & p(ap(V0P,V7x)) & mem(V7x,A_27a)))) & ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(V1Q)))) <-> ((exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 197 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y <-> V1y = V0x))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 198 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 199 $T <-> -$F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 200 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 201 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (-p(V1t2) & -p(V0t1) | p(V0t1) & p(V1t2) <-> (p(V0t1) <-> p(V1t2))))))) # label(conj_thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 202 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V0x) -> p(V1y)) & (p(V2z) -> p(V3w)) -> (p(V2z) & p(V0x) -> p(V1y) & p(V3w))))))))))) # label(conj_thm_2Ebool_2EMONO__AND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 203 (all V0t1 ap(f5,V0t1) = f4(V0t1)) # label(lameq_f5) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 204 (all A_27a (ne(A_27a) -> f44(A_27a) = c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 205 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,A_27b)) -> V0t = f31(A_27b,A_27a,V0t))))))) # label(ax_thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 206 (all V0P (mem(V0P,arr(arr(bool,bool),bool)) -> (p(ap(V0P,k(bool,c_2Ebool_2ET))) & p(ap(V0P,f65)) & p(ap(V0P,i(bool))) & p(ap(V0P,k(bool,c_2Ebool_2EF))) -> (all V5f (mem(V5f,arr(bool,bool)) -> p(ap(V0P,V5f))))))) # label(conj_thm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 207 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V0t1) -> p(V1t2)) -> ((p(V1t2) -> p(V0t1)) -> (p(V1t2) <-> p(V0t1)))))))) # label(conj_thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 208 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> ((exists V2x (mem(V2x,A_27a) & V1a = V2x & p(ap(V0P,V2x)))) <-> p(ap(V0P,V1a))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 209 (all A_27b all A_27a all V0f f13(A_27b,A_27a,V0f) = ap(f14(A_27b,A_27a),V0f)) # label(lameq_f14) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 210 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(V0P,V1x)) -> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(ax_thm_2Ebool_2ESELECT__AX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 211 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (all V3N (mem(V3N,A_27a) -> (V2M = V3N & (all V4x (mem(V4x,A_27a) -> (V4x = V3N -> ap(V0f,V4x) = ap(V1g,V4x)))) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V1g),V3N) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V0f),V2M)))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 212 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> (all V3x (mem(V3x,A_27a) -> ap(ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)))))))))))))) # label(conj_thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 213 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2R (mem(V2R,bool) -> ((p(V0P) -> p(V1Q)) & (p(V0P) -> p(V2R)) <-> (p(V0P) -> p(V2R) & p(V1Q))))))))) # label(conj_thm_2Ebool_2EIMP__CONJ__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 214 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1)))) # label(lameq_f17) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 215 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1f)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f61(A_27a,V1f))) & p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f63(A_27a,V1f,V0P)))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 216 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((-p(V0A) -> p(V1B)) <-> p(V0A) | p(V1B)))))) # label(conj_thm_2Ebool_2EDISJ__EQ__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 217 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V3p (mem(V3p,arr(A_27a,bool)) -> (all V4m1 (mem(V4m1,arr(A_27a,A_27b)) -> (all V5m2 (mem(V5m2,arr(A_27a,A_27b)) -> ((all V6x (mem(V6x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),V3p)) -> ap(V4m1,V6x) = ap(V5m2,V6x)))) -> ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V3p),V4m1) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V3p),V5m2)))))))) & (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)) -> ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m),V2x) = ap(V1m,V2x)))))))))))) # label(ax_thm_2Ebool_2ERES__ABSTRACT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 218 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 (mem(V2x_27,A_27b) -> (all V3x_27_27 ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27))))))) # label(lameq_f25) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 219 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> (p(V0t1) & p(V1t2) & p(V2t3) <-> p(V0t1) & p(V2t3) & p(V1t2)))))))) # label(conj_thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 220 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 221 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = V0x)))) # label(conj_thm_2Ebool_2EEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 222 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 223 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a))) # label(ax_thm_2Ebool_2ERES__FORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 224 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)))) # label(mem_c_2Ebool_2EDATATYPE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 225 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) = ap(f41(A_27a,V1m,V3x),V4y)))))) # label(lameq_f41) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 226 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> p(V0t1) | p(V1t2)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 227 (all V0t (mem(V0t,bool) -> (p(V0t) <-> ($T <-> p(V0t))) & (p(V0t) <-> (p(V0t) <-> $T)) & ((p(V0t) <-> $F) <-> -p(V0t)) & (-p(V0t) <-> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 228 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) <-> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),f49(A_27a,V0P))))))))) # label(conj_thm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 229 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f57(A_27a,V0a))))))) # label(conj_thm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 230 (all V0t ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF) = ap(f9,V0t)) # label(lameq_f9) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 231 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f14(A_27b,A_27a) = c_2Ebool_2Eliteral__case(A_27a,A_27b))))) # label(ax_thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 232 (all A_27a (ne(A_27a) -> (exists V0rep (mem(V0rep,arr(ty_2Ebool_2Eitself(A_27a),A_27a)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,ty_2Ebool_2Eitself(A_27a)),ap(c_2Emin_2E_3D(A_27a),c_2Ebool_2EARB(A_27a))),V0rep)))))) # label(ax_thm_2Ebool_2Eitself__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 233 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V2z) -> p(V3w)) & (p(V0x) -> p(V1y)) -> (p(V2z) | p(V0x) -> p(V3w) | p(V1y))))))))))) # label(conj_thm_2Ebool_2EMONO__OR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 234 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> ((exists V1x (mem(V1x,ty_2Ebool_2Eitself(A_27a)) & p(ap(V0P,V1x)))) <-> p(ap(V0P,c_2Ebool_2Ethe__value(A_27a)))))))) # label(conj_thm_2Ebool_2EEXISTS__itself) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 235 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((all V5x (mem(V5x,A_27a) -> p(ap(V0P,V5x)) & p(V1Q))) <-> p(V1Q) & (all V4x (mem(V4x,A_27a) -> p(ap(V0P,V4x))))) & ((all V7x (mem(V7x,A_27a) -> p(V1Q) & p(ap(V0P,V7x)))) <-> p(V1Q) & (all V6x (mem(V6x,A_27a) -> p(ap(V0P,V6x))))) & ((p(V1Q) -> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x))))) <-> (all V3x (mem(V3x,A_27a) -> (p(V1Q) -> p(ap(V0P,V3x)))))))))))) # label(conj_thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 236 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a))))) # label(ax_thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 237 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2)) <-> p(V2t2) & -p(V0b) | p(V0b) & p(V1t1)))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 238 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(V0f,V1v)) <-> (all V2x (mem(V2x,A_27a) -> (V1v = V2x -> p(ap(V0f,V2x)))))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 239 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> (all V4b (mem(V4b,bool) -> ((p(V0x) -> p(V1y)) -> ((p(V2z) -> p(V3w)) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V4b),V0x),V2z)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V4b),V1y),V3w))))))))))))))) # label(conj_thm_2Ebool_2EMONO__COND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 240 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))))))) # label(mem_c_2Ebool_2Eitself__case) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 241 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V3f ((all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),ap(V3f,V4x))))) & mem(V3f,arr(A_27a,A_27b)))) <-> (all V1x (mem(V1x,A_27a) -> (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 242 (all A_27b all A_27a all V0f ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f)) = ap(f21(A_27b,A_27a),V0f)) # label(lameq_f21) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 243 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,bool)) -> (all V3g (mem(V3g,arr(A_27a,bool)) -> (V0P = V1Q -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1Q)) -> (p(ap(V3g,V4x)) <-> p(ap(V2f,V4x)))))) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1Q),V3g)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V2f))))))))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 244 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V0P) <-> p(V1P_27)) & (p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) -> (p(V2Q) & p(V0P) <-> p(V1P_27) & p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 245 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V1t2) <-> p(V0t1)) <-> (p(V0t1) -> p(V1t2)) & (p(V1t2) -> p(V0t1))))))) # label(conj_thm_2Ebool_2EEQ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 246 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ($F <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),k(A_27a,c_2Ebool_2EF)))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 247 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(V0P,V3x) = ap(f59(A_27a,V0P),V3x)))) # label(lameq_f59) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 248 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-(p(V0A) -> p(V1B)) <-> p(V0A) & -p(V1B)))))) # label(conj_thm_2Ebool_2ENOT__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 249 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONE__ONE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 250 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27c)) -> (all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> ap(V0P,ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M)) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27c),f66(A_27b,A_27c,A_27a,V1N,V0P)),V2M))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 251 (all A_27a (ne(A_27a) -> f2(A_27a) = c_2Ebool_2E_3F(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 252 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1Q,V3x))))) & (exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) -> p(ap(V1Q,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(conj_thm_2Ebool_2ESELECT__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 253 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONTO) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 254 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> ((exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a))) -> (exists V4x (p(ap(V1Q,V4x)) & mem(V4x,A_27a))))))))))) # label(conj_thm_2Ebool_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 255 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> ((p(V0y) -> p(V1x)) -> (-p(V1x) -> -p(V0y))))))) # label(conj_thm_2Ebool_2EMONO__NOT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 256 (all A_27a all V0p f35(A_27a,V0p) = ap(f36(A_27a),V0p)) # label(lameq_f36) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 257 (all A_27a (ne(A_27a) -> (all V0i (mem(V0i,ty_2Ebool_2Eitself(A_27a)) -> c_2Ebool_2Ethe__value(A_27a) = V0i)))) # label(conj_thm_2Ebool_2EITSELF__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 258 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> (((exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x)))) -> p(V1Q)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(V1Q))))))))))) # label(conj_thm_2Ebool_2ELEFT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 259 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27a) -> ap(f48(A_27b,A_27a,V0f),V1y) = ap(V0f,V1y))))))))) # label(conj_thm_2Ebool_2EBETA__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 260 (all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(V1t1) | p(V2t2) -> ((p(V1t1) -> p(V0t)) -> ((p(V2t2) -> p(V0t)) -> p(V0t)))))))))) # label(conj_thm_2Ebool_2EOR__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 261 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_21) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 262 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t)) = ap(f6(V0t1,V1t2),V2t)))))) # label(lameq_f6) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 263 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) | p(V2C) | p(V1B) <-> p(V2C) | p(V1B) | p(V0A)))))))) # label(conj_thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 264 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f14(A_27b,A_27a) = c_2Ebool_2ELET(A_27a,A_27b))))) # label(ax_thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 265 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V3x ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x))))))) # label(lameq_f42) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 266 (all A_27a all V0x f32(A_27a,V0x) = ap(f33(A_27a),V0x)) # label(lameq_f33) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 267 (all V0f (mem(V0f,arr(bool,bool)) -> V0f = k(bool,c_2Ebool_2ET) | V0f = k(bool,c_2Ebool_2EF) | V0f = f65 | i(bool) = V0f)) # label(conj_thm_2Ebool_2EBOOL__FUN__CASES__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 268 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $T) | ($F <-> p(V0t)))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 269 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 270 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 271 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)),ap(V1f,V2x)) = ap(f64(A_27a,V0P,V1f),V2x)))))) # label(lameq_f64) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 272 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1t (mem(V1t,A_27b) -> (all V2u (mem(V2u,A_27b) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f67(A_27b,A_27a,V1t,V0a,V2u)),V0a) = V1t)))))))))) # label(conj_thm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 273 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f21(A_27b,A_27a) = c_2Ebool_2EONE__ONE(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 274 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (p(V0P) & p(V1Q) & mem(V2x,A_27a))) <-> (exists V3x (p(V0P) & mem(V3x,A_27a))) & (exists V4x (mem(V4x,A_27a) & p(V1Q)))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 275 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5y_27 (mem(V5y_27,A_27a) -> ((p(V1Q) <-> p(V0P)) & (-p(V1Q) -> V4y = V5y_27) & (p(V1Q) -> V2x = V3x_27) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27)))))))))))))))) # label(conj_thm_2Ebool_2Ebool__case__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 276 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2)) <-> (-p(V0b) -> p(V2t2)) & (p(V0b) -> p(V1t1))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 277 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (all V3N (mem(V3N,A_27a) -> (V2M = V3N & (all V4x (mem(V4x,A_27a) -> (V4x = V3N -> ap(V1g,V4x) = ap(V0f,V4x)))) -> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V1g),V3N) = ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V2M)))))))))))))) # label(conj_thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 278 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x ap(V0f,V2x) = ap(f48(A_27b,A_27a,V0f),V2x)))) # label(lameq_f48) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 279 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V2C) & p(V1B) | p(V0A) <-> (p(V1B) | p(V0A)) & (p(V2C) | p(V0A))))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 280 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V3y ((exists V4x (p(ap(ap(V0P,V4x),V3y)) & mem(V4x,A_27a))) & mem(V3y,A_27b))) <-> (exists V1x (mem(V1x,A_27a) & (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESWAP__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 281 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (-(exists V1x (mem(V1x,A_27a) & p(ap(V0P,V1x)))) <-> (all V2x (mem(V2x,A_27a) -> -p(ap(V0P,V2x))))))))) # label(conj_thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 282 (all A_27a (ne(A_27a) -> f12(A_27a) = c_2Ebool_2E_3F_21(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 283 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Emin_2E_40(A_27a),f50(A_27a,V0x)))))) # label(conj_thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 284 (all A_27a all A_27b all V0f ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f))) # label(lameq_f24) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 285 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1b (mem(V1b,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ap(V0f,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1b),V2x),V3y)) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V1b),ap(V0f,V2x)),ap(V0f,V3y)))))))))))))) # label(conj_thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 286 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (all V2x_27 (mem(V2x_27,bool) -> (all V3y (mem(V3y,bool) -> (all V4y_27 (mem(V4y_27,bool) -> ((p(V0c) -> (p(V2x_27) -> p(V1x))) & (-p(V0c) -> (p(V4y_27) -> p(V3y))) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V2x_27),V4y_27)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),V3y)))))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__cond) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 287 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(c_2EConseqConv_2EASM__MARKER,V0y),V1x)) <-> p(V1x)))))) # label(conj_thm_2EConseqConv_2EASM__MARKER__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 288 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V3y_27) -> (p(V0x) -> p(V1x_27))) & (p(V0x) -> (p(V3y_27) -> p(V2y))) -> ((p(V1x_27) -> p(V3y_27)) -> (p(V0x) -> p(V2y)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 289 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 290 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2s (mem(V2s,A_27a) -> (p(ap(V0P,V2s)) <-> p(ap(V1Q,V2s))))) -> ((all V3s (mem(V3s,A_27a) -> p(ap(V0P,V3s)))) <-> (all V4s (mem(V4s,A_27a) -> p(ap(V1Q,V4s)))))))))))) # label(conj_thm_2EConseqConv_2Eforall__eq__thm) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 291 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> ((-p(V0c) -> p(V1x)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2ET),V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 292 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(V0c) & p(V1x) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2EF))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 293 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V0x) -> p(V1x_27)) & (p(V1x_27) -> (p(V3y_27) -> p(V2y))) -> ((p(V1x_27) -> p(V3y_27)) -> (p(V0x) -> p(V2y)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 294 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 295 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 296 (all V0t (mem(V0t,bool) -> (p(V0t) -> $T))) # label(conj_thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 297 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2ET)) <-> (p(V0c) -> p(V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 298 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V2y) -> (p(V0x) -> p(V1x_27))) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> (p(V0x) & p(V2y) -> p(V3y_27) & p(V1x_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 299 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V3y_27) -> p(V2y))) & (p(V2y) -> (p(V1x_27) -> p(V0x))) -> (p(V3y_27) & p(V1x_27) -> p(V2y) & p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 300 (all V0t (mem(V0t,bool) -> ($F & p(V0t) <-> $F))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 301 -$F <-> $T # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 302 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> p(V0x)) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 303 (all V0t (mem(V0t,bool) -> ($F <-> $F & p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 304 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (all V2x_27 (mem(V2x_27,bool) -> (all V3y (mem(V3y,bool) -> (all V4y_27 (mem(V4y_27,bool) -> ((p(V4y_27) -> p(V3y)) & (p(V2x_27) -> p(V1x)) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V2x_27),V4y_27)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),V3y)))))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__cond__simple) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 305 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V0x) -> (p(V2y) -> p(V3y_27))) & (-p(V3y_27) -> (p(V1x_27) -> p(V0x))) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 306 (all V0t (mem(V0t,bool) -> (p(V0t) & p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 307 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 308 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 309 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 310 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 311 -$T <-> $F # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 312 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> V1t = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 313 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> $T)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 314 (all V0t (mem(V0t,bool) -> (-p(V0t) <-> -p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 315 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 316 (all V0t (mem(V0t,bool) -> (p(V0t) | p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 317 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2EF),V1x)) <-> p(V1x) & -p(V0c)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 318 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 319 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2s (mem(V2s,A_27a) -> (p(ap(V1Q,V2s)) <-> p(ap(V0P,V2s))))) -> ((exists V3s (mem(V3s,A_27a) & p(ap(V0P,V3s)))) <-> (exists V4s (p(ap(V1Q,V4s)) & mem(V4s,A_27a))))))))))) # label(conj_thm_2EConseqConv_2Eexists__eq__thm) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 320 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V1x_27) -> (p(V2y) -> p(V3y_27))) & (-p(V2y) -> (p(V0x) -> p(V1x_27))) -> (p(V2y) | p(V0x) -> p(V3y_27) | p(V1x_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__disj__weaken) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 321 (all V0t (mem(V0t,bool) -> ($T <-> ($F -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 322 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V2y) -> (p(V1x_27) -> p(V0x))) & (-p(V1x_27) -> (p(V3y_27) -> p(V2y))) -> (p(V3y_27) | p(V1x_27) -> p(V2y) | p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 323 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 324 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 325 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 326 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (--(p(V0A) | p(V1B)) <-> (-p(V0A) -> --p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 327 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 328 (all V0A (mem(V0A,bool) -> (--p(V0A) <-> p(V0A)))) # label(conj_thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 329 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((-p(V0p) | -p(V1q)) & (p(V0p) | p(V1q)) <-> (p(V0p) <-> -p(V1q))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 330 (all V0A (mem(V0A,bool) -> (-p(V0A) & p(V0A) <-> $F))) # label(conj_thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 331 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V1q)) & (p(V1q) | -p(V0p) | p(V2r)) & (-p(V2r) | p(V0p)) <-> (p(V1q) | p(V2r) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 332 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 333 (all V0b (mem(V0b,bool) -> (p(V0b) -> (p(V0b) <-> $T)))) # label(conj_thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 334 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V0p)) & (p(V2r) | -p(V0p) | -p(V1q)) & (p(V0p) | -p(V2r)) <-> ((p(V1q) -> p(V2r)) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 335 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> p(V0p)))))) # label(conj_thm_2Esat_2Epth__ni1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 336 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V2r) | p(V0p)) & (-p(V1q) | -p(V2r) | p(V0p)) & (-p(V2r) | -p(V0p) | p(V1q)) & (p(V2r) | -p(V1q) | -p(V0p)) <-> (p(V0p) <-> (p(V2r) <-> p(V1q)))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 337 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (--(p(V0A) | p(V1B)) <-> (-p(V0A) -> --p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 338 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 339 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V1q) | -p(V2r)) & (p(V1q) | -p(V0p)) & (p(V2r) | -p(V0p)) <-> (p(V0p) <-> p(V2r) & p(V1q))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 340 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (--(-p(V0A) | p(V1B)) <-> (p(V0A) -> --p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 341 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (p(V0p) & p(V1q) -> p(V0p)))))) # label(conj_thm_2Esat_2Epth__an1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 342 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 343 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V0p)))))) # label(conj_thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 344 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> ((p(V1B) & p(V0A) -> p(V2C)) <-> (p(V0A) -> (p(V1B) -> p(V2C)))))))))) # label(conj_thm_2Esat_2EAND__IMP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 345 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 346 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (p(V0p) & p(V1q) -> p(V1q)))))) # label(conj_thm_2Esat_2Epth__an2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 347 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__ni2) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 348 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (all V3s (mem(V3s,bool) -> ((-p(V1q) | -p(V0p) | p(V2r)) & (p(V1q) | p(V3s) | -p(V0p)) & (-p(V2r) | -p(V3s) | p(V0p)) & (-p(V2r) | -p(V1q) | p(V0p)) & (-p(V3s) | p(V1q) | p(V0p)) <-> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V1q),V2r),V3s)) <-> p(V0p))))))))))) # label(conj_thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 349 (all V0b (mem(V0b,bool) -> (-p(V0b) -> (p(V0b) <-> $F)))) # label(conj_thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 350 (all A_27a (ne(A_27a) -> mem(c_2EnormalForms_2EUNIV__POINT(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 351 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p))) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0p,V1x))))))))) # label(conj_thm_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 352 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) -> V1g = V0f))))))))) # label(ax_thm_2EnormalForms_2EEXT__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 353 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),A_27a))))))) # label(mem_c_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 354 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (V0f = V1g <-> ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g))))))))))) # label(conj_thm_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 355 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p))) -> (all V1x (mem(V1x,A_27a) -> p(ap(V0p,V1x))))))))) # label(ax_thm_2EnormalForms_2EUNIV__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 356 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) & p(V1q) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p)) & (p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p)) & (p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p)))))))) # label(conj_thm_2Emarker_2Emove__left__conj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 357 (all V0lab (mem(V0lab,ind) -> (all V1argument (mem(V1argument,bool) -> (p(V1argument) <-> p(ap(ap(c_2Emarker_2E_3A_2D,V0lab),V1argument))))))) # label(ax_thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 358 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Emarker_2Estmarker(A_27a),V0x))))) # label(ax_thm_2Emarker_2Estmarker__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 359 (all V0x (mem(V0x,bool) -> (p(V0x) <-> p(ap(c_2Emarker_2ECong,V0x))))) # label(ax_thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 360 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q)) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q) <-> p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p)) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__right__disj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 361 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Emarker_2Eunint(A_27a),V0x) = V0x)))) # label(ax_thm_2Emarker_2Eunint__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 362 p(c_2Emarker_2EIfCases) <-> $T # label(ax_thm_2Emarker_2EIfCases__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 363 (all A_27a (ne(A_27a) -> mem(c_2Emarker_2Estmarker(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Emarker_2Estmarker) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 364 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V1q) | p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V1q) | p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) | p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 365 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) <-> p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) <-> p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 366 (all A_27a (ne(A_27a) -> mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Emarker_2Eunint) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 367 (all V0b1 (mem(V0b1,bool) -> (all V1b2 (mem(V1b2,bool) -> (p(V1b2) & p(V0b1) <-> p(ap(ap(c_2Emarker_2EAC,V0b1),V1b2))))))) # label(ax_thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 368 (all V0x (mem(V0x,bool) -> (p(ap(c_2Emarker_2EAbbrev,V0x)) <-> p(V0x)))) # label(ax_thm_2Emarker_2EAbbrev__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 369 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ap(ap(V0f,V1x),V2y) = ap(ap(V0f,V2y),V1x))))) <-> p(ap(c_2Ecombin_2ECOMM(A_27a,A_27b),V0f))))))))) # label(ax_thm_2Ecombin_2ECOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 370 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> (all V1x ap(ap(V0f,V1x),V1x) = ap(f75(A_27b,A_27a,V0f),V1x)))) # label(lameq_f75) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 371 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),ap(V0f,V1a)),V0f) = V0f)))))))) # label(conj_thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 372 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> V0x = ap(ap(c_2Ecombin_2EK(A_27a,A_27b),V0x),V1y))))))))) # label(conj_thm_2Ecombin_2EK__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 373 (all A_27b all A_27a all V0x k(A_27b,V0x) = ap(f68(A_27b,A_27a),V0x)) # label(lameq_f68) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 374 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2ES(A_27a,bool,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(bool,bool),bool),c_2Emin_2E_3D_3D_3E),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Emarker_2EAbbrev),ap(ap(c_2Ecombin_2EC(A_27a,A_27a,bool),c_2Emin_2E_3D(A_27a)),V1v)))),V0f))) <-> p(ap(ap(c_2Ebool_2ELET(A_27a,bool),V0f),V1v))))))))) # label(conj_thm_2Ecombin_2ELET__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 375 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27b) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f)) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 376 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2EC(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(A_27b,arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2EC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 377 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> f79(A_27b,A_27a,V1b,V0a) = ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1b))))))))) # label(ax_thm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 378 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27a)) -> (all V1f (mem(V1f,arr(A_27c,A_27b)) -> (all V2v (mem(V2v,A_27c) -> ap(ap(c_2Ebool_2ELET(A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,A_27b),V0P),V1f)),V2v) = ap(V0P,ap(ap(c_2Ebool_2ELET(A_27c,A_27b),V1f),V2v)))))))))))))) # label(conj_thm_2Ecombin_2EGEN__LET__RAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 379 (all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V2x ap(V0f,V2x) = ap(f80(A_27c,A_27a,V0f),V2x)))) # label(lameq_f80) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 380 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V1f2 (mem(V1f2,arr(A_27a,A_27b)) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (all V4c (mem(V4c,A_27b) -> (ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V3b),V0f1) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V4c),V1f2) -> V3b = V4c & (all V5v (mem(V5v,A_27b) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V1f2) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V0f1)))))))))))))))))) # label(conj_thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 381 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V2x ap(V0f,V2x) = ap(f84(A_27b,A_27c,A_27a,V0f),V2x)))) # label(lameq_f84) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 382 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ecombin_2EFAIL(A_27a,A_27b) = f68(A_27b,A_27a))))) # label(ax_thm_2Ecombin_2EFAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 383 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(ap(c_2Ebool_2Eliteral__case(A_27a,bool),V0f),V1v)) <-> p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2ES(A_27a,bool,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(bool,bool),bool),c_2Emin_2E_3D_3D_3E),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Emarker_2EAbbrev),ap(ap(c_2Ecombin_2EC(A_27a,A_27a,bool),c_2Emin_2E_3D(A_27a)),V1v)))),V0f)))))))))) # label(conj_thm_2Ecombin_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.11 384 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> V0x = ap(ap(c_2Ecombin_2EFAIL(A_27a,A_27b),V0x),V1y))))))))) # label(conj_thm_2Ecombin_2EFAIL__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 385 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2E_3A_3E(A_27a,A_27b),arr(A_27b,arr(arr(A_27b,A_27a),A_27a))))))) # label(mem_c_2Ecombin_2E_3A_3E) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 386 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EUPDATE(A_27a,A_27b),arr(A_27a,arr(A_27b,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))))) # label(mem_c_2Ecombin_2EUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 387 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (all V1e (mem(V1e,A_27a) -> (p(ap(ap(c_2Ecombin_2EMONOID(A_27a),V0f),V1e)) <-> p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27a),V0f),V1e)) & p(ap(ap(c_2Ecombin_2ELEFT__ID(A_27a,A_27a),V0f),V1e)) & p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))))))))) # label(ax_thm_2Ecombin_2EMONOID__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 388 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EMONOID(A_27a),arr(arr(A_27a,arr(A_27a,A_27a)),arr(A_27a,bool))))) # label(mem_c_2Ecombin_2EMONOID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 389 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ERIGHT__ID(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27a)),arr(A_27b,bool))))))) # label(mem_c_2Ecombin_2ERIGHT__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 390 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> f83(A_27c,A_27b,A_27a,V1g,V0f) = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),f82(A_27c,A_27a,V1g)))))))))))) # label(conj_thm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 391 (all A_27a all A_27c all A_27b all V0f ap(f74(A_27a,A_27c,A_27b),V0f) = f73(A_27a,A_27c,A_27b,V0f)) # label(lameq_f74) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 392 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2x ap(f69(A_27b,A_27c,A_27a,V0f,V1g),V2x) = ap(ap(V0f,V2x),ap(V1g,V2x))))))) # label(lameq_f69) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 393 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27b) -> (all V2y ap(f72(A_27b,A_27c,A_27a,V0f,V1x),V2y) = ap(ap(V0f,V2y),V1x)))))) # label(lameq_f72) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 394 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> c_2Ecombin_2ES(A_27a,A_27b,A_27c) = f71(A_27c,A_27a,A_27b))))))) # label(ax_thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 395 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1b (mem(V1b,A_27b) -> (all V2a (mem(V2a,A_27a) -> (V1b = ap(V0f,V2a) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V1b),V0f) = V0f))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY__IMP__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 396 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27a),V0f),c_2Ecombin_2EI(A_27a)) = V0f & V0f = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)),V0f))))))) # label(conj_thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 397 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> (all V1x (mem(V1x,A_27a) -> ap(ap(V0f,V1x),V1x) = ap(ap(c_2Ecombin_2EW(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 398 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2f f78(A_27b,A_27a,V1b,V0a,V2f) = ap(f79(A_27b,A_27a,V1b,V0a),V2f)))))) # label(lameq_f79) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 399 (all A_27c all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g ap(f70(A_27c,A_27a,A_27b,V0f),V1g) = f69(A_27b,A_27c,A_27a,V0f,V1g)))) # label(lameq_f70) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 400 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f76(A_27b,A_27a) = c_2Ecombin_2EW(A_27a,A_27b))))) # label(ax_thm_2Ecombin_2EW__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 401 (all A_27a all A_27c all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x f72(A_27b,A_27c,A_27a,V0f,V1x) = ap(f73(A_27a,A_27c,A_27b,V0f),V1x)))) # label(lameq_f73) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 402 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V1a),V3c)),V2b),ap(V0f,V3c)) = ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f),V3c))))))))))))) # label(conj_thm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 403 (all A_27c all A_27b all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V2x ap(V0f,ap(V1g,V2x)) = ap(f77(A_27c,A_27b,A_27a,V1g,V0f),V2x)))))) # label(lameq_f77) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 404 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27a)) -> (all V1f (mem(V1f,arr(A_27c,A_27b)) -> (all V2v (mem(V2v,A_27c) -> ap(V0P,ap(ap(c_2Ebool_2Eliteral__case(A_27c,A_27b),V1f),V2v)) = ap(ap(c_2Ebool_2Eliteral__case(A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,A_27b),V0P),V1f)),V2v))))))))))))) # label(conj_thm_2Ecombin_2EGEN__literal__case__RAND) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 405 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ECOMM(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),bool)))))) # label(mem_c_2Ecombin_2ECOMM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 406 (all A_27a (ne(A_27a) -> c_2Ecombin_2EI(A_27a) = ap(ap(c_2Ecombin_2ES(A_27a,arr(A_27a,A_27a),A_27a),c_2Ecombin_2EK(A_27a,arr(A_27a,A_27a))),c_2Ecombin_2EK(A_27a,A_27a)))) # label(ax_thm_2Ecombin_2EI__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 407 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3c ap(f78(A_27b,A_27a,V1b,V0a,V2f),V3c) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V0a),V3c)),V1b),ap(V2f,V3c))))))))) # label(lameq_f78) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 408 (all A_27c all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V2x ap(V1g,V2x) = ap(f82(A_27c,A_27a,V1g),V2x)))) # label(lameq_f82) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 409 (all A_27c all A_27a all A_27b all V0f ap(f71(A_27c,A_27a,A_27b),V0f) = f70(A_27c,A_27a,A_27b,V0f)) # label(lameq_f71) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 410 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Ecombin_2EI(A_27a),V0x))))) # label(conj_thm_2Ecombin_2EI__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 411 (all A_27b all A_27a all V0f ap(f76(A_27b,A_27a),V0f) = f75(A_27b,A_27a,V0f)) # label(lameq_f76) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 412 (all A_27c all A_27b all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V3x ap(f83(A_27c,A_27b,A_27a,V1g,V0f),V3x) = ap(V0f,ap(V1g,V3x))))))) # label(lameq_f83) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 413 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) <-> p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27a,A_27a),V0f),V0f))))))) # label(conj_thm_2Ecombin_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 414 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> ap(ap(c_2Ecombin_2E_3A_3E(A_27a,A_27b),V0x),V1f) = ap(V1f,V0x))))))))) # label(ax_thm_2Ecombin_2EAPP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 415 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (all V3c (mem(V3c,A_27b) -> (all V4d (mem(V4d,A_27b) -> (V2b != V1a -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f)) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f))))))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__COMMUTES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 416 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EK(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))))))) # label(mem_c_2Ecombin_2EK) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 417 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1y (mem(V1y,A_27c) -> ap(ap(c_2Ecombin_2EC(A_27a,A_27c,A_27b),f84(A_27b,A_27c,A_27a,V0f)),V1y) = f86(A_27c,A_27b,A_27a,V0f,V1y))))))))))) # label(conj_thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 418 (all A_27c all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1y (mem(V1y,A_27c) -> (all V3x ap(f86(A_27c,A_27b,A_27a,V0f,V1y),V3x) = ap(ap(V0f,V3x),V1y)))))) # label(lameq_f86) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 419 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Ecombin_2EI) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 420 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27a) -> ap(ap(ap(c_2Ecombin_2EC(A_27a,A_27b,A_27c),V0f),V1x),V2y) = ap(ap(V0f,V2y),V1x))))))))))))) # label(conj_thm_2Ecombin_2EC__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 421 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> (all V2x (mem(V2x,A_27c) -> ap(V0f,ap(V1g,V2x)) = ap(ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g),V2x))))))))))))) # label(conj_thm_2Ecombin_2Eo__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 422 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (ap(V0f,V1a) = V2b <-> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f) = V0f))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 423 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> ap(ap(c_2Ecombin_2Eo(A_27b,A_27c,A_27a),f80(A_27c,A_27a,V0f)),V1g) = f81(A_27a,A_27c,A_27b,V1g,V0f))))))))))) # label(conj_thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 424 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f68(A_27b,A_27a) = c_2Ecombin_2EK(A_27a,A_27b))))) # label(ax_thm_2Ecombin_2EK__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 425 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> (all V2h (mem(V2h,arr(A_27d,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27d,A_27b,A_27c),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)),V2h) = ap(ap(c_2Ecombin_2Eo(A_27d,A_27b,A_27a),V0f),ap(ap(c_2Ecombin_2Eo(A_27d,A_27a,A_27c),V1g),V2h)))))))))))))))) # label(conj_thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 426 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0a (mem(V0a,A_27a) -> (all V1x (mem(V1x,A_27b) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1x),V2f),V0a) = V1x)))))) & (all V3a (mem(V3a,A_27c) -> (all V4b (mem(V4b,A_27c) -> (all V5x (mem(V5x,A_27d) -> (all V6f (mem(V6f,arr(A_27c,A_27d)) -> (V4b != V3a -> ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V5x),V6f),V4b) = ap(V6f,V4b)))))))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 427 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27a))) -> (all V1g (mem(V1g,arr(A_27c,arr(A_27a,A_27a))) -> (p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27b,A_27c),V0f),V1g)) <-> (all V2x (mem(V2x,A_27c) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27b) -> ap(ap(V0f,ap(ap(V1g,V2x),V3y)),V4z) = ap(ap(V1g,V2x),ap(ap(V0f,V3y),V4z))))))))))))))))))) # label(ax_thm_2Ecombin_2EFCOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 428 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27c,A_27d)) -> (all V1f1 (mem(V1f1,A_27a) -> (all V2f2 (mem(V2f2,A_27b) -> (all V3a (mem(V3a,A_27c) -> (all V4b (mem(V4b,A_27d) -> (all V5c (mem(V5c,A_27d) -> (V5c != V4b -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V5c),V0f) != ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V4b),V0f)))))))))))))))))))))) # label(conj_thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 429 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g) = f77(A_27c,A_27b,A_27a,V1g,V0f))))))))))) # label(ax_thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 430 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)) = ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z)))))))))))) # label(ax_thm_2Ecombin_2EASSOC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 431 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (all V3c (mem(V3c,A_27b) -> (all V4d (mem(V4d,A_27b) -> (ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f) = V0f & V0f = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) & V2b != V1a | V2b = V1a & V3c = V4d <-> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f)))))))))))))))) # label(conj_thm_2Ecombin_2EUPD11__SAME__BASE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 432 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1v (mem(V1v,A_27b) -> (all V2x (mem(V2x,A_27c) -> ap(ap(c_2Ebool_2ELET(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v) = ap(ap(ap(c_2Ebool_2ELET(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x))))))))))))) # label(conj_thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 433 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1v (mem(V1v,A_27b) -> (all V2x (mem(V2x,A_27c) -> ap(ap(ap(c_2Ebool_2Eliteral__case(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x) = ap(ap(c_2Ebool_2Eliteral__case(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v))))))))))))) # label(conj_thm_2Ecombin_2EGEN__literal__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 434 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)) = ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z))))))) <-> p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))))))) # label(conj_thm_2Ecombin_2EASSOC__SYM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 435 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ELEFT__ID(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(A_27a,bool))))))) # label(mem_c_2Ecombin_2ELEFT__ID) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 436 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27b) -> (ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) <-> V2b = V3c))))))))))))) # label(conj_thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 437 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> ap(ap(c_2Ecombin_2ES(A_27a,A_27c,A_27b),f84(A_27b,A_27c,A_27a,V0f)),V1g) = f85(A_27c,A_27b,A_27a,V0f,V1g))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 438 (all A_27c all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V3x ap(ap(V0f,V3x),ap(V1g,V3x)) = ap(f85(A_27c,A_27b,A_27a,V0f,V1g),V3x)))))) # label(lameq_f85) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 439 (all A_27a all A_27c all A_27b all V1g (mem(V1g,arr(A_27b,A_27a)) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3x ap(f81(A_27a,A_27c,A_27b,V1g,V0f),V3x) = ap(V0f,ap(V1g,V3x))))))) # label(lameq_f81) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 440 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EFAIL(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))))))) # label(mem_c_2Ecombin_2EFAIL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 441 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1e (mem(V1e,A_27a) -> (p(ap(ap(c_2Ecombin_2ELEFT__ID(A_27a,A_27b),V0f),V1e)) <-> (all V2x (mem(V2x,A_27b) -> ap(ap(V0f,V1e),V2x) = V2x))))))))))) # label(ax_thm_2Ecombin_2ELEFT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 442 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2ES(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(arr(A_27a,A_27b),arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2ES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 443 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,A_27c),arr(A_27a,A_27b)))))))))) # label(mem_c_2Ecombin_2Eo) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 444 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2EFCOMM(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27a)),arr(arr(A_27c,arr(A_27a,A_27a)),bool))))))))) # label(mem_c_2Ecombin_2EFCOMM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 445 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EASSOC(A_27a),arr(arr(A_27a,arr(A_27a,A_27a)),bool)))) # label(mem_c_2Ecombin_2EASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 446 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1v (mem(V1v,A_27c) -> ap(c_2Ecombin_2EK(A_27c,A_27a),V1v) = ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),ap(c_2Ecombin_2EK(A_27c,A_27b),V1v)),V0f))))) & (all V2f (mem(V2f,arr(A_27d,A_27e)) -> (all V3v (mem(V3v,A_27d) -> ap(c_2Ecombin_2EK(A_27e,A_27f),ap(V2f,V3v)) = ap(ap(c_2Ecombin_2Eo(A_27f,A_27e,A_27d),V2f),ap(c_2Ecombin_2EK(A_27d,A_27f),V3v)))))))))))))))))) # label(conj_thm_2Ecombin_2EK__o__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 447 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> f85(A_27c,A_27b,A_27a,V0f,V1g) = ap(ap(c_2Ecombin_2ES(A_27a,A_27c,A_27b),V0f),f82(A_27c,A_27a,V1g)))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 448 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> f74(A_27a,A_27c,A_27b) = c_2Ecombin_2EC(A_27a,A_27b,A_27c))))))) # label(ax_thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 449 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(V0f,V2x),ap(V1g,V2x)) = ap(ap(ap(c_2Ecombin_2ES(A_27a,A_27b,A_27c),V0f),V1g),V2x))))))))))))) # label(conj_thm_2Ecombin_2ES__THM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 450 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27a))) -> (all V1e (mem(V1e,A_27b) -> (p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27b),V0f),V1e)) <-> (all V2x (mem(V2x,A_27a) -> V2x = ap(ap(V0f,V2x),V1e)))))))))))) # label(ax_thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 451 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EW(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),arr(A_27a,A_27b))))))) # label(mem_c_2Ecombin_2EW) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 452 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Enum_2EABS__num,ap(c_2Enum_2ESUC__REP,ap(c_2Enum_2EREP__num,V0m))) = ap(c_2Enum_2ESUC,V0m))) # label(ax_thm_2Enum_2ESUC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 453 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V0m) = ap(c_2Enum_2ESUC,V1n) -> V0m = V1n))))) # label(conj_thm_2Enum_2EINV__SUC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 454 (all V1r (mem(V1r,ind) -> (V1r = ap(c_2Enum_2EREP__num,ap(c_2Enum_2EABS__num,V1r)) <-> p(ap(c_2Enum_2EIS__NUM__REP,V1r))))) # label(ax_thm_2Enum_2Enum__ISO__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 455 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(c_2Enum_2EABS__num,ap(c_2Enum_2EREP__num,V0a)) = V0a)) # label(ax_thm_2Enum_2Enum__ISO__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 456 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != c_2Enum_2E0)) # label(conj_thm_2Enum_2ENOT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 457 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,V1n)) -> p(ap(V0P,ap(c_2Enum_2ESUC,V1n)))))) & p(ap(V0P,c_2Enum_2E0)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(V0P,V2n))))))) # label(conj_thm_2Enum_2EINDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 458 (all V0y (mem(V0y,ind) -> c_2Enum_2EZERO__REP != ap(c_2Enum_2ESUC__REP,V0y))) # label(ax_thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 459 (all V0m (mem(V0m,ind) -> (p(ap(c_2Enum_2EIS__NUM__REP,V0m)) <-> (all V1P (mem(V1P,arr(ind,bool)) -> (p(ap(V1P,c_2Enum_2EZERO__REP)) & (all V2n (mem(V2n,ind) -> (p(ap(V1P,V2n)) -> p(ap(V1P,ap(c_2Enum_2ESUC__REP,V2n)))))) -> p(ap(V1P,V0m)))))))) # label(ax_thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 460 (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ind,ty_2Enum_2Enum),c_2Enum_2EIS__NUM__REP),V0rep)) & mem(V0rep,arr(ty_2Enum_2Enum,ind)))) # label(ax_thm_2Enum_2Enum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 461 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(ap(c_2Eone_2Eone__CASE(A_27a),c_2Eone_2Eone),V0x))))) # label(conj_thm_2Eone_2Eone__case__thm) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 462 (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(bool,ty_2Eone_2Eone),i(bool)),V0rep)) & mem(V0rep,arr(ty_2Eone_2Eone,bool)))) # label(ax_thm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 463 (all A_27a (ne(A_27a) -> mem(c_2Eone_2Eone__CASE(A_27a),arr(ty_2Eone_2Eone,arr(A_27a,A_27a))))) # label(mem_c_2Eone_2Eone__CASE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 464 (all V0P (mem(V0P,arr(ty_2Eone_2Eone,bool)) -> ((all V1x (mem(V1x,ty_2Eone_2Eone) -> p(ap(V0P,V1x)))) <-> p(ap(V0P,c_2Eone_2Eone))))) # label(conj_thm_2Eone_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 465 (all A_27a all V0e (mem(V0e,A_27a) -> (all V1fn ap(ap(c_2Emin_2E_3D(A_27a),ap(V1fn,c_2Eone_2Eone)),V0e) = ap(f87(A_27a,V0e),V1fn)))) # label(lameq_f87) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 466 (all A_27a (ne(A_27a) -> (all V0u (mem(V0u,ty_2Eone_2Eone) -> (all V1x (mem(V1x,A_27a) -> V1x = ap(ap(c_2Eone_2Eone__CASE(A_27a),V0u),V1x))))))) # label(ax_thm_2Eone_2Eone__case__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 467 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (exists V1fn (mem(V1fn,arr(ty_2Eone_2Eone,A_27a)) & V0e = ap(V1fn,c_2Eone_2Eone))))))) # label(conj_thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 468 (all V0P (mem(V0P,arr(ty_2Eone_2Eone,bool)) -> (p(ap(V0P,c_2Eone_2Eone)) -> (all V1x (mem(V1x,ty_2Eone_2Eone) -> p(ap(V0P,V1x))))))) # label(conj_thm_2Eone_2Eone__induction) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 469 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Eone_2Eone)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Eone_2Eone)) -> V1g = V0f)))))) # label(conj_thm_2Eone_2Eone__axiom) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 470 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Eone_2Eone,A_27a)),f87(A_27a,V0e))))))) # label(conj_thm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 471 (all V0v (mem(V0v,ty_2Eone_2Eone) -> c_2Eone_2Eone = V0v)) # label(conj_thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 472 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EOUTL(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),A_27a)))))) # label(mem_c_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 473 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EISR(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))) # label(mem_c_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 474 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Esum_2EINR(A_27a,A_27b),V1y) != ap(c_2Esum_2EINL(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2Esum__distinct) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 475 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EINL(A_27a,A_27b),arr(A_27a,ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 476 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EISL(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))) # label(mem_c_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 477 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3Q_27 (mem(V3Q_27,arr(A_27b,bool)) -> (all V4s (mem(V4s,ty_2Esum_2Esum(A_27a,A_27b)) -> ((all V6y (mem(V6y,A_27b) -> (p(ap(V2Q,V6y)) -> p(ap(V3Q_27,V6y))))) & (all V5x (mem(V5x,A_27a) -> (p(ap(V0P,V5x)) -> p(ap(V1P_27,V5x))))) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V0P),V2Q),V4s)) -> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V1P_27),V3Q_27),V4s)))))))))))))))))) # label(conj_thm_2Esum_2ESUM__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 478 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (exists V0rep (mem(V0rep,arr(ty_2Esum_2Esum(A_27a,A_27b),arr(bool,arr(A_27a,arr(A_27b,bool))))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(bool,arr(A_27a,arr(A_27b,bool))),ty_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EIS__SUM__REP(A_27a,A_27b)),V0rep)))))))) # label(ax_thm_2Esum_2Esum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 479 (all A_27a all A_27b all A_27c all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2h ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(A_27a,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,ty_2Esum_2Esum(A_27a,A_27b)),V2h),c_2Esum_2EINL(A_27a,A_27b))),V0f)),ap(ap(c_2Emin_2E_3D(arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27b,A_27c,ty_2Esum_2Esum(A_27a,A_27b)),V2h),c_2Esum_2EINR(A_27a,A_27b))),V1g)) = ap(f96(A_27a,A_27b,A_27c,V0f,V1g),V2h)))))) # label(lameq_f96) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 480 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27c),A_27c)))))))))) # label(mem_c_2Esum_2Esum__CASE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 481 (all A_27a all A_27b all V1v1 (mem(V1v1,A_27a) -> (all V3b ap(f89(A_27a,A_27b,V1v1),V3b) = f88(A_27b,A_27a,V1v1,V3b)))) # label(lameq_f89) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 482 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1y (mem(V1y,A_27a) -> -p(ap(c_2Esum_2EISR(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V1y))))) & (all V0x (mem(V0x,A_27b) -> p(ap(c_2Esum_2EISR(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V0x))))))))) # label(ax_thm_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 483 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> ap(c_2Esum_2EOUTR(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V0x)) = V0x)))))) # label(ax_thm_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 484 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Esum_2EINL(A_27a,A_27b),V0x) != ap(c_2Esum_2EINR(A_27a,A_27b),V1y))))))))) # label(conj_thm_2Esum_2Esum__distinct1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 485 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2z (mem(V2z,ty_2Esum_2Esum(A_27a,A_27b)) -> ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,ty_2Esum_2Esum(A_27c,A_27d)),V2z),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Esum_2Esum(A_27c,A_27d),A_27c),c_2Esum_2EINL(A_27c,A_27d)),V0f)),ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Esum_2Esum(A_27c,A_27d),A_27d),c_2Esum_2EINR(A_27c,A_27d)),V1g)) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2z))))))))))))))) # label(conj_thm_2Esum_2ESUM__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 486 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> ap(c_2Esum_2EINR(A_27a,A_27b),V0e) = ap(c_2Esum_2EABS__sum(A_27a,A_27b),f95(A_27b,A_27a,V0e)))))))) # label(ax_thm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 487 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) <-> -p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2ENOT__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 488 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) -> ap(c_2Esum_2EINL(A_27a,A_27b),ap(c_2Esum_2EOUTL(A_27a,A_27b),V0x)) = V0x))))))) # label(conj_thm_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 489 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Esum_2EOUTL(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V0x)))))))) # label(ax_thm_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 490 (all A_27a all A_27b all V0e (mem(V0e,A_27a) -> (all V1b ap(f93(A_27a,A_27b,V0e),V1b) = f92(A_27b,A_27a,V0e,V1b)))) # label(lameq_f93) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 491 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V1s_27 (mem(V1s_27,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5Q_27 (mem(V5Q_27,arr(A_27b,bool)) -> ((all V6a (mem(V6a,A_27a) -> (V1s_27 = ap(c_2Esum_2EINL(A_27a,A_27b),V6a) -> (p(ap(V3P_27,V6a)) <-> p(ap(V2P,V6a)))))) & (all V7b (mem(V7b,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V7b) = V1s_27 -> (p(ap(V5Q_27,V7b)) <-> p(ap(V4Q,V7b)))))) & V1s_27 = V0s -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V2P),V4Q),V0s)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P_27),V5Q_27),V1s_27)))))))))))))))))))) # label(conj_thm_2Esum_2ESUM__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 492 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EOUTR(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),A_27b)))))) # label(mem_c_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 493 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Esum_2Esum(A_27a,A_27b)) -> V0a = ap(c_2Esum_2EABS__sum(A_27a,A_27b),ap(c_2Esum_2EREP__sum(A_27a,A_27b),V0a)))) & (all V1r (mem(V1r,arr(bool,arr(A_27a,arr(A_27b,bool)))) -> (ap(c_2Esum_2EREP__sum(A_27a,A_27b),ap(c_2Esum_2EABS__sum(A_27a,A_27b),V1r)) = V1r <-> p(ap(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),V1r))))))))) # label(ax_thm_2Esum_2Esum__ISO__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 494 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ss (mem(V0ss,ty_2Esum_2Esum(A_27a,A_27b)) -> (exists V1x (ap(c_2Esum_2EINL(A_27a,A_27b),V1x) = V0ss & mem(V1x,A_27a))) | (exists V2y (mem(V2y,A_27b) & ap(c_2Esum_2EINR(A_27a,A_27b),V2y) = V0ss)))))))) # label(conj_thm_2Esum_2Esum__CASES) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 495 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V1y = V0x <-> ap(c_2Esum_2EINL(A_27a,A_27b),V0x) = ap(c_2Esum_2EINL(A_27a,A_27b),V1y)))))))))) # label(conj_thm_2Esum_2EINL__11) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 496 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) -> V0x = ap(c_2Esum_2EINR(A_27a,A_27b),ap(c_2Esum_2EOUTR(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 497 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((exists V3y (p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V3y))) & mem(V3y,A_27b))) | (exists V2x (p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) & mem(V2x,A_27a))) <-> (exists V1s (mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)) & p(ap(V0P,V1s))))))))))) # label(conj_thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 498 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0sum (mem(V0sum,arr(arr(A_27a,ty_2Esum_2Esum(A_27a,A_27b)),arr(arr(A_27b,ty_2Esum_2Esum(A_27a,A_27b)),A_27c))) -> p(ap(c_2Ebool_2EDATATYPE(A_27c),ap(ap(V0sum,c_2Esum_2EINL(A_27a,A_27b)),c_2Esum_2EINR(A_27a,A_27b)))))))))))) # label(conj_thm_2Esum_2Edatatype__sum) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 499 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(bool,arr(A_27a,arr(A_27b,bool)))) -> ((exists V1v1 (mem(V1v1,A_27a) & (exists V2v2 (mem(V2v2,A_27b) & (V0f = f91(A_27b,A_27a,V2v2) | V0f = f89(A_27a,A_27b,V1v1)))))) <-> p(ap(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),V0f))))))))) # label(ax_thm_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 500 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27a) -> ap(c_2Esum_2EABS__sum(A_27a,A_27b),f93(A_27a,A_27b,V0e)) = ap(c_2Esum_2EINL(A_27a,A_27b),V0e))))))) # label(ax_thm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 501 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EREP__sum(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(bool,arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Esum_2EREP__sum) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 502 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EINR(A_27a,A_27b),arr(A_27b,ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 503 (all A0 (ne(A0) -> (all A1 (ne(A1) -> ne(ty_2Esum_2Esum(A0,A1)))))) # label(ne_ty_2Esum_2Esum) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 504 (all A_27b all A_27a all V0e (mem(V0e,A_27a) -> (all V1b (mem(V1b,bool) -> (all V2x k(A_27b,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2x),V0e)),V1b)) = ap(f92(A_27b,A_27a,V0e,V1b),V2x)))))) # label(lameq_f92) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 505 (all A_27b all A_27a all V1v1 (mem(V1v1,A_27a) -> (all V3b (mem(V3b,bool) -> (all V4x ap(f88(A_27b,A_27a,V1v1,V3b),V4x) = k(A_27b,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V4x),V1v1)),V3b))))))) # label(lameq_f88) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 506 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2a (mem(V2a,A_27a) -> ap(c_2Esum_2EINL(A_27c,A_27d),ap(V0f,V2a)) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2a)))))))) & (all V3f (mem(V3f,arr(A_27a,A_27c)) -> (all V4g (mem(V4g,arr(A_27b,A_27d)) -> (all V5b (mem(V5b,A_27b) -> ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5b)) = ap(c_2Esum_2EINR(A_27c,A_27d),ap(V4g,V5b)))))))))))))))) # label(ax_thm_2Esum_2ESUM__MAP__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 507 (all A_27b all A_27a all V0e (mem(V0e,A_27b) -> (all V1b k(A_27a,f94(A_27b,V0e,V1b)) = ap(f95(A_27b,A_27a,V0e),V1b)))) # label(lameq_f95) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 508 (all A_27b all V2v2 (mem(V2v2,A_27b) -> (all V6b (mem(V6b,bool) -> (all V8y ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V8y),V2v2)),ap(c_2Ebool_2E_7E,V6b)) = ap(f90(A_27b,V2v2,V6b),V8y)))))) # label(lameq_f90) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 509 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v1 (mem(V0v1,A_27a) -> (all V1v2 (mem(V1v2,A_27b) -> ap(c_2Esum_2EINR(A_27a,A_27b),V1v2) != ap(c_2Esum_2EINL(A_27a,A_27b),V0v1))))))))) # label(conj_thm_2Esum_2EINR__neq__INL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 510 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Esum_2EISL(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V0x))))) & (all V1y (mem(V1y,A_27b) -> -p(ap(c_2Esum_2EISL(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V1y))))))))) # label(ax_thm_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 511 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1x (mem(V1x,A_27a) -> (ap(c_2Esum_2EINL(A_27a,A_27b),V1x) = ap(c_2Esum_2EINL(A_27a,A_27b),V0y) <-> V0y = V1x))))) & (all V2y (mem(V2y,A_27b) -> (all V3x (mem(V3x,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V2y) = ap(c_2Esum_2EINR(A_27a,A_27b),V3x) <-> V3x = V2y))))))))) # label(conj_thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 512 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2ESUM__ALL(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))))) # label(mem_c_2Esum_2ESUM__ALL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 513 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> mem(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Esum_2Esum(A_27c,A_27d))))))))))))) # label(mem_c_2Esum_2E_2B_2B) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 514 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (-p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) <-> p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2ENOT__ISR__ISL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 515 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((all V2x (mem(V2x,A_27a) -> p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V2x))))) & (all V3y (mem(V3y,A_27b) -> p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V3y))))) <-> (all V1s (mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(V0P,V1s))))))))))) # label(conj_thm_2Esum_2EFORALL__SUM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 516 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2f1 (mem(V2f1,arr(A_27b,A_27c)) -> ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),ap(c_2Esum_2EINL(A_27a,A_27b),V0x)),V1f),V2f1) = ap(V1f,V0x))))))) & (all V3y (mem(V3y,A_27b) -> (all V4f (mem(V4f,arr(A_27a,A_27c)) -> (all V5f1 (mem(V5f1,arr(A_27b,A_27c)) -> ap(V5f1,V3y) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),ap(c_2Esum_2EINR(A_27a,A_27b),V3y)),V4f),V5f1))))))))))))) # label(ax_thm_2Esum_2Esum__case__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 517 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),arr(arr(bool,arr(A_27a,arr(A_27b,bool))),bool)))))) # label(mem_c_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 518 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EABS__sum(A_27a,A_27b),arr(arr(bool,arr(A_27a,arr(A_27b,bool))),ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EABS__sum) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 519 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all V0P (mem(V0P,bool) -> (all V7x (mem(V7x,A_27e) -> (all V8y (mem(V8y,A_27f) -> (all V9z (mem(V9z,A_27e) -> (ap(c_2Esum_2EINL(A_27e,A_27f),V9z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27e,A_27f)),V0P),ap(c_2Esum_2EINL(A_27e,A_27f),V7x)),ap(c_2Esum_2EINR(A_27e,A_27f),V8y)) <-> p(V0P) & V7x = V9z))))))) & (all V10x (mem(V10x,A_27g) -> (all V11y (mem(V11y,A_27h) -> (all V12z (mem(V12z,A_27h) -> (V12z = V11y & -p(V0P) <-> ap(c_2Esum_2EINR(A_27g,A_27h),V12z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27g,A_27h)),V0P),ap(c_2Esum_2EINL(A_27g,A_27h),V10x)),ap(c_2Esum_2EINR(A_27g,A_27h),V11y))))))))) & (all V4x (mem(V4x,A_27c) -> (all V5y (mem(V5y,A_27d) -> (all V6z (mem(V6z,A_27d) -> (-p(V0P) & V6z = V5y <-> ap(c_2Esum_2EINL(A_27d,A_27c),V6z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27d,A_27c)),V0P),ap(c_2Esum_2EINR(A_27d,A_27c),V4x)),ap(c_2Esum_2EINL(A_27d,A_27c),V5y))))))))) & (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (all V3z (mem(V3z,A_27a) -> (ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,A_27a)),V0P),ap(c_2Esum_2EINR(A_27b,A_27a),V1x)),ap(c_2Esum_2EINL(A_27b,A_27a),V2y)) = ap(c_2Esum_2EINR(A_27b,A_27a),V3z) <-> p(V0P) & V3z = V1x))))))))))))))))))))))))) # label(conj_thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 520 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (exists V2h ((all V4y (mem(V4y,A_27b) -> ap(V1g,V4y) = ap(V2h,ap(c_2Esum_2EINR(A_27a,A_27b),V4y)))) & (all V3x (mem(V3x,A_27a) -> ap(V2h,ap(c_2Esum_2EINL(A_27a,A_27b),V3x)) = ap(V0f,V3x))) & mem(V2h,arr(ty_2Esum_2Esum(A_27a,A_27b),A_27c)))))))))))))) # label(conj_thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 521 (all A_27b all V0e (mem(V0e,A_27b) -> (all V1b (mem(V1b,bool) -> (all V3y ap(f94(A_27b,V0e,V1b),V3y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V3y),V0e)),ap(c_2Ebool_2E_7E,V1b))))))) # label(lameq_f94) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 522 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27a,A_27b),c_2Ecombin_2EI(A_27a)),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(ty_2Esum_2Esum(A_27a,A_27b)))))) # label(conj_thm_2Esum_2ESUM__MAP__I) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 523 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((all V1x (mem(V1x,A_27a) -> p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V1x))))) & (all V2y (mem(V2y,A_27b) -> p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V2y))))) -> (all V3s (mem(V3s,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(V0P,V3s))))))))))) # label(conj_thm_2Esum_2Esum__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 524 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5y (mem(V5y,A_27b) -> (p(ap(V4Q,V5y)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P),V4Q),ap(c_2Esum_2EINR(A_27a,A_27b),V5y)))))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V0P),V1Q),ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) <-> p(ap(V0P,V2x))))))))))))) # label(ax_thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 525 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V0x) = ap(c_2Esum_2EINR(A_27a,A_27b),V1y) <-> V1y = V0x))))))))) # label(conj_thm_2Esum_2EINR__11) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 526 (all A_27b all A_27a all V2v2 (mem(V2v2,A_27b) -> (all V6b ap(f91(A_27b,A_27a,V2v2),V6b) = k(A_27a,f90(A_27b,V2v2,V6b))))) # label(lameq_f91) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 527 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27a,A_27c)) -> (all V1f1_27 (mem(V1f1_27,arr(A_27b,A_27c)) -> (all V2M (mem(V2M,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V3M_27 (mem(V3M_27,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V4f (mem(V4f,arr(A_27a,A_27c)) -> (all V5f1 (mem(V5f1,arr(A_27b,A_27c)) -> ((all V7y (mem(V7y,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V7y) = V3M_27 -> ap(V5f1,V7y) = ap(V1f1_27,V7y)))) & (all V6x (mem(V6x,A_27a) -> (V3M_27 = ap(c_2Esum_2EINL(A_27a,A_27b),V6x) -> ap(V0f_27,V6x) = ap(V4f,V6x)))) & V2M = V3M_27 -> ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V2M),V4f),V5f1) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V3M_27),V0f_27),V1f1_27)))))))))))))))))))) # label(conj_thm_2Esum_2Esum__case__cong) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 528 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) | p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)))))))) # label(conj_thm_2Esum_2EISL__OR__ISR) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 529 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2z (mem(V2z,ty_2Esum_2Esum(A_27a,A_27b)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27c,A_27d)),ap(c_2Esum_2EISL(A_27a,A_27b),V2z)),ap(c_2Esum_2EINL(A_27c,A_27d),ap(V0f,ap(c_2Esum_2EOUTL(A_27a,A_27b),V2z)))),ap(c_2Esum_2EINR(A_27c,A_27d),ap(V1g,ap(c_2Esum_2EOUTR(A_27a,A_27b),V2z)))) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2z))))))))))))))) # label(conj_thm_2Esum_2ESUM__MAP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 530 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Esum_2Esum(A_27a,A_27b),A_27c)),f96(A_27a,A_27b,A_27c,V0f,V1g))))))))))))) # label(conj_thm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 531 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2)),V2R3))))))))))) # label(conj_thm_2Erelation_2ERINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 532 (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all A_27k (ne(A_27k) -> (all V0R1 (mem(V0R1,arr(A_27h,arr(A_27k,bool))) -> (all V1R2 (mem(V1R2,arr(A_27g,arr(A_27h,bool))) -> (all V2x (mem(V2x,A_27g) -> (all V3z (mem(V3z,A_27k) -> (p(ap(ap(ap(ap(c_2Erelation_2EO(A_27g,A_27h,A_27k),V0R1),V1R2),V2x),V3z)) <-> (exists V4y (p(ap(ap(V0R1,V4y),V3z)) & p(ap(ap(V1R2,V2x),V4y)) & mem(V4y,A_27h)))))))))))))))))) # label(ax_thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 533 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ETC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 534 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 535 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <-> (exists V3y (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a))) | p(ap(ap(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 536 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ediag(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2Ediag) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 537 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__EQC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 538 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWFP(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,bool))))) # label(mem_c_2Erelation_2EWFP) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 539 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V2Q,V5y)) & p(ap(ap(V1R,V4x),V5y)) -> p(ap(V2Q,V4x))))))) & (all V3x (mem(V3x,A_27a) -> (p(ap(ap(V1R,V3x),V0b)) -> p(ap(V2Q,V3x))))) -> (all V6a (mem(V6a,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V6a),V0b)) -> p(ap(V2Q,V6a)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__ALT__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 540 (all A_27z (ne(A_27z) -> mem(c_2Erelation_2EINVOL(A_27z),arr(arr(A_27z,A_27z),bool)))) # label(mem_c_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 541 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESC(A_27a),V0R) = ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ESC__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 542 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etotal(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etotal) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 543 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1R),V4x),V5y)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 544 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Etransitive__RC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 545 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (p(ap(ap(V0R,V1x),V2y)) -> V1x != V2y)))))))))) # label(conj_thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 546 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) -> (exists V3y (mem(V3y,A_27a) & p(ap(ap(V0R,V1x),V3y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)))) | p(ap(ap(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 547 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERCOMPL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool)))))))) # label(mem_c_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 548 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V4x)) -> p(ap(V1P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWFP__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 549 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eirreflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eirreflexive) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 550 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ereflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ereflexive) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 551 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V2x) = ap(V1f,V3y)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 552 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 553 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__RTC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 554 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ESC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 555 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2EEQC__REFL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 556 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERC__RTC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 557 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ERTC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ERTC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 558 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool))))))))) # label(mem_c_2Erelation_2EINDUCTIVE__INVARIANT__ON) # label(axiom) # label(non_clause). [assumption]. 6.15/6.12 559 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> ((all V2P (mem(V2P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> ((all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V4y),V3x)) -> p(ap(V2P,V4y))))) -> p(ap(V2P,V3x))))) -> p(ap(V2P,V1a))))) <-> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1a))))))))) # label(ax_thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 560 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Ethe__fun(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(A_27a,A_27b))))))))) # label(mem_c_2Erelation_2Ethe__fun) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 561 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ((exists V3u (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & p(ap(ap(V0R,V1x),V3u)) & mem(V3u,A_27a))) | V1x = V2y <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 562 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (c_2Ecombin_2EI(A_27z) = ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f) <-> p(ap(c_2Erelation_2EINVOL(A_27z),V0f))))))) # label(ax_thm_2Erelation_2EINVOL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 563 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> p(ap(c_2Erelation_2Esymmetric(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Esymmetric__inv__image) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 564 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ESC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 565 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__inv__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 566 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> (all V1B (mem(V1B,arr(A_27a,bool)) -> ((exists V2w (p(ap(V1B,V2w)) & mem(V2w,A_27a))) -> (exists V3min (mem(V3min,A_27a) & p(ap(V1B,V3min)) & (all V4b (mem(V4b,A_27a) -> (p(ap(ap(V0R,V4b),V3min)) -> -p(ap(V1B,V4b))))))))))))))) # label(ax_thm_2Erelation_2EWF__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 567 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ERC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 568 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ETC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ETC) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 569 (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all A_27k (ne(A_27k) -> mem(c_2Erelation_2EO(A_27g,A_27h,A_27k),arr(arr(A_27h,arr(A_27k,bool)),arr(arr(A_27g,arr(A_27h,bool)),arr(A_27g,arr(A_27k,bool))))))))))) # label(mem_c_2Erelation_2EO) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 570 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) -> p(ap(ap(V1P,V4x),V6z))))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 571 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1D (mem(V1D,arr(A_27a,bool)) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3M (mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> ((all V4f (mem(V4f,arr(A_27a,A_27b)) -> (all V5x (mem(V5x,A_27a) -> (p(ap(V1D,V5x)) & (all V6y (mem(V6y,A_27a) -> (p(ap(V1D,V6y)) -> (p(ap(ap(V0R,V6y),V5x)) -> p(ap(ap(V2P,V6y),ap(V4f,V6y))))))) -> p(ap(ap(V2P,V5x),ap(ap(V3M,V4f),V5x)))))))) <-> p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V1D),V2P),V3M))))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 572 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2x ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),ap(ap(ap(c_2Erelation_2Ethe__fun(A_27a,A_27b),ap(c_2Erelation_2ETC(A_27a),V0R)),f103(A_27b,A_27a,V1M,V0R)),V2x)),V0R),V2x)),V2x) = ap(f104(A_27b,A_27a,V1M,V0R),V2x)))))) # label(lameq_f104) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 573 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R1),V1R2)) -> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R1))))))))) # label(conj_thm_2Erelation_2Eirreflexive__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 574 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 575 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> p(ap(c_2Erelation_2EWeakOrder(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))) # label(conj_thm_2Erelation_2ERSUBSET__WeakOrder) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 576 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2EEQC__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 577 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27a),V0R),c_2Emin_2E_3D(A_27a)) = ap(c_2Erelation_2ERC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ERC__OR__Id) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 578 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EPreOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 579 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (p(ap(ap(c_2Erelation_2ERUNIV(A_27a,A_27b),V0x),V1y)) <-> $T))))))))) # label(ax_thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 580 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Einv(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,arr(A_27a,bool)))))))) # label(mem_c_2Erelation_2Einv) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 581 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EWF(A_27a),c_2Erelation_2EEMPTY__REL(A_27a))))) # label(conj_thm_2Erelation_2EWF__EMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 582 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eantisymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eantisymmetric) # label(axiom) # label(non_clause). [assumption]. 6.15/6.13 583 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),V0R) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ETC__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 584 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Esymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Esymmetric) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 585 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V4y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4y),V5z)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V5z))))))))))))) # label(conj_thm_2Erelation_2ETC__RULES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 586 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> ap(c_2Erelation_2Ediag(A_27a),V0A) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2Ediag(A_27a),V0A)))))) # label(conj_thm_2Erelation_2Einv__diag) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 587 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etrichotomous__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 588 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERDOM(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))))))) # label(mem_c_2Erelation_2ERDOM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 589 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R),ap(c_2Erelation_2ERCOMPL(A_27a,A_27a),c_2Emin_2E_3D(A_27a))) = ap(c_2Erelation_2ESTRORD(A_27a),V0R))))) # label(conj_thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 590 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V3z)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2EEQC__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 591 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) & ap(c_2Erelation_2ERC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) & ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERC__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 592 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x = V2y | (exists V3u (mem(V3u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(V0R,V3u),V2y)))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 593 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 594 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Einv__image(A_27a,A_27b),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,A_27b),arr(A_27a,arr(A_27a,bool))))))))) # label(mem_c_2Erelation_2Einv__image) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 595 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etrichotomous(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 596 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERRANGE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,bool))))))) # label(mem_c_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 597 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESN(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ESN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 598 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (c_2Erelation_2EEMPTY__REL(A_27a) = V0R <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R),c_2Erelation_2EEMPTY__REL(A_27a)))) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),c_2Erelation_2EEMPTY__REL(A_27a)),V0R)))))) # label(conj_thm_2Erelation_2EREMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 599 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V3y) = ap(V1f,V2x)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 600 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> (all V1y (mem(V1y,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(V0R,V1y),V2z)) & p(ap(ap(V0R,V2z),V1y)) <-> V1y = V2z)))))))))) # label(conj_thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 601 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4y ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V3f),V0R),V4y)),V4y) = ap(f100(A_27b,A_27a,V1M,V0R,V3f),V4y)))))))) # label(lameq_f100) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 602 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2),V2x),V3y)) <-> p(ap(ap(V1R2,V2x),V3y)) & p(ap(ap(V0R1,V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 603 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ELinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 604 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x))))))) -> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EINDUCTION__WF__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 605 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y))))) <-> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x))))))))) # label(conj_thm_2Erelation_2EWFP__CASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 606 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EWeakOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 607 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(ap(ap(c_2Erelation_2ERRESTRICT(A_27a,A_27b),V0R),V1s),V2x),V3y)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(V0R,V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 608 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R))) <-> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 609 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERUNIV(A_27a,A_27b),arr(A_27a,arr(A_27b,bool))))))) # label(mem_c_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 610 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y)))))))) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) & p(ap(c_2Erelation_2Ereflexive(A_27b),V1Q)) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V6y)) -> p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))))))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 611 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> ((exists V2y (mem(V2y,A_27b) & p(ap(ap(V0R,V1x),V2y)))) <-> p(ap(ap(c_2Erelation_2ERDOM(A_27a,A_27b),V0R),V1x))))))))))) # label(ax_thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 612 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWF__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 613 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> ((all V1x (mem(V1x,A_27z) -> V1x = ap(V0f,ap(V0f,V1x)))) <-> p(ap(c_2Erelation_2EINVOL(A_27z),V0f))))))) # label(conj_thm_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 614 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ERTC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__RTC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 615 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eantisymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 616 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool)))))))) # label(mem_c_2Erelation_2EINDUCTIVE__INVARIANT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 617 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1R2),V0R1)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) -> V1R2 = V0R1))))))))) # label(conj_thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 618 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERTC(A_27a),V0R) = ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERTC__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.13 619 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V0R1) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2))))))))) # label(conj_thm_2Erelation_2ERUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 620 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__irreflexive) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 621 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> ap(c_2Erelation_2ESC(A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Esymmetric__SC__identity) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 622 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERC__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 623 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4y),V5z)) & p(ap(ap(V1P,V4y),V5z)) & p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1P,V3x),V5z))))))))) & (all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 624 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWCR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWCR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 625 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eequivalence(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eequivalence) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 626 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y)))))))) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5x),V6y)) -> p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))))))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 627 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V1x),V2y)) <-> p(ap(ap(V0R,V2y),V1x)) | p(ap(ap(V0R,V1x),V2y))))))))))) # label(ax_thm_2Erelation_2ESC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 628 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <-> p(ap(c_2Erelation_2EPreOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 629 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V5x),V6y)) & p(ap(ap(V1P,V5x),V6y)) -> p(ap(ap(V1P,V6y),V5x))))))) & (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (all V9z (mem(V9z,A_27a) -> (p(ap(ap(V1P,V7x),V8y)) & p(ap(ap(V1P,V8y),V9z)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V7x),V8y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V8y),V9z)) -> p(ap(ap(V1P,V7x),V9z))))))))) & (all V4x (mem(V4x,A_27a) -> p(ap(ap(V1P,V4x),V4x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V10x (mem(V10x,A_27a) -> (all V11y (mem(V11y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) -> p(ap(ap(V1P,V10x),V11y)))))))))))))) # label(conj_thm_2Erelation_2ESTRONG__EQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 630 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Esymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 631 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> (exists V4u (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V4u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3z),V4u)) & mem(V4u,A_27a)))))))))) <-> p(ap(c_2Erelation_2EWCR(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EWCR__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 632 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2EWF__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 633 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M)),V0R),V2x)),V2x) = ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M),V2x)))))))))))) # label(conj_thm_2Erelation_2EWFREC__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 634 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERTC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 635 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESC__SYMMETRIC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 636 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b)) <-> (all V3Q (mem(V3Q,arr(A_27a,bool)) -> ((all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(V3Q,V4y)) & p(ap(ap(V0R,V4y),V5z)) -> p(ap(V3Q,V5z))))))) & p(ap(V3Q,V1a)) -> p(ap(V3Q,V2b)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 637 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Eapprox(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(arr(A_27a,A_27b),bool))))))))) # label(mem_c_2Erelation_2Eapprox) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 638 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) -> ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Eequivalence__inv__identity) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 639 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) & ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) & ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R))))) # label(conj_thm_2Erelation_2EEQC__MOVES__IN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 640 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1R (mem(V1R,arr(A_27b,arr(A_27a,bool))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Erelation_2ERRANGE(A_27b,A_27a),V1R))) <-> (exists V2x (mem(V2x,A_27b) & p(ap(ap(V1R,V2x),V0y))))))))))))) # label(conj_thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 641 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> -p(ap(ap(V0R,V1x),V1x)))) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 642 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> (exists V3u (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & mem(V3u,A_27a)))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__RTC__TWICE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 643 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESTRORD(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 644 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2ERTC__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 645 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERTC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 646 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2ESN(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(ax_thm_2Erelation_2ESN__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 647 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ECR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ECR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 648 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ETC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 649 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ediamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ediamond) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 650 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> ($F <-> p(ap(ap(c_2Erelation_2EEMPTY__REL(A_27a),V0x),V1y))))))))) # label(ax_thm_2Erelation_2EEMPTY__REL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 651 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Eequivalence(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EEQC__EQUIVALENCE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 652 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2S1 (mem(V2S1,arr(A_27c,arr(A_27a,bool))) -> (all V3S2 (mem(V3S2,arr(A_27c,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27c,A_27a),V2S1),V3S2)) -> p(ap(ap(c_2Erelation_2ERSUBSET(A_27c,A_27b),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V0R1),V2S1)),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V1R2),V3S2)))))))))))))))))) # label(conj_thm_2Erelation_2EO__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 653 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2f ap(c_2Ebool_2E_21(A_27a),f105(A_27b,A_27a,V0R,V1M,V2f)) = ap(f106(A_27b,A_27a,V1M,V0R),V2f)))))) # label(lameq_f106) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 654 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(ap(V0R,V1x),V1x))))))))) # label(ax_thm_2Erelation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 655 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V3y ap(f99(A_27b,A_27a,V0f,V2x,V1R),V3y) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(V1R,V3y),V2x)),ap(V0f,V3y)),c_2Ebool_2EARB(A_27b))))))))) # label(lameq_f99) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 656 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> V0R = ap(c_2Erelation_2Einv(A_27b,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)))))))) # label(conj_thm_2Erelation_2Einv__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 657 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R1 (mem(V1R1,arr(A_27a,arr(A_27b,bool))) -> (all V2R2 (mem(V2R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R1),V2R2)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V2R2))) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R1)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RUNION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 658 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 659 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V0R,V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(V1P,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 660 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1R_27 (mem(V1R_27,arr(A_27c,arr(A_27a,bool))) -> ap(c_2Erelation_2Einv(A_27c,A_27b),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V0R),V1R_27)) = ap(ap(c_2Erelation_2EO(A_27b,A_27a,A_27c),ap(c_2Erelation_2Einv(A_27c,A_27a),V1R_27)),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)))))))))))) # label(conj_thm_2Erelation_2Einv__O) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 661 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 662 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__EQC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 663 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0R1 (mem(V0R1,arr(A_27c,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27d,arr(A_27c,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27d,bool))) -> ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),V0R1),ap(ap(c_2Erelation_2EO(A_27a,A_27d,A_27c),V1R2),V2R3)) = ap(ap(c_2Erelation_2EO(A_27a,A_27d,A_27b),ap(ap(c_2Erelation_2EO(A_27d,A_27c,A_27b),V0R1),V1R2)),V2R3))))))))))))))) # label(conj_thm_2Erelation_2EO__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.14 664 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERUNION(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 665 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) | p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 666 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ETC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 667 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <-> (all V1x (mem(V1x,A_27z) -> ap(V0f,ap(V0f,V1x)) = ap(V0f,V1x)))))))) # label(conj_thm_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 668 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2EWF__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 669 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> p(ap(ap(V0R,V1x),V2y)) | p(ap(ap(V0R,V2y),V1x))))))))))) # label(ax_thm_2Erelation_2Etotal__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 670 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 671 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> ((exists V3y (mem(V3y,A_27a) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)))) | p(ap(ap(V0R,V1x),V2z)) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 672 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) & p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 673 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 674 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R))))) # label(conj_thm_2Erelation_2Einv__EQC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 675 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,arr(A_27a,arr(A_27b,bool))) -> (all V1z (mem(V1z,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1z),V0y)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0y),V1z)) <-> V1z = V0y))))))))) # label(conj_thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 676 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Erelation_2Ethe__fun(A_27a,A_27b),V0R),V1M),V2x) = ap(c_2Emin_2E_40(arr(A_27a,A_27b)),f101(A_27a,A_27b,V2x,V0R,V1M)))))))))))) # label(ax_thm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 677 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) <-> p(ap(c_2Erelation_2EWeakOrder(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 678 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V1P,V3x),V4y)) & p(ap(ap(V0R,V4y),V5z)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3x),V4y)) -> p(ap(ap(V1P,V3x),V5z))))))))) & (all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 679 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V0R1))))))))) # label(conj_thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 680 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V3y),V2x)) -> p(ap(V0P,V3y))))) & p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V2x)) -> p(ap(V0P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V4x)) -> p(ap(V0P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWFP__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 681 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2b (mem(V2b,A_27a) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V1Q,V4y)) & p(ap(ap(V0R,V3x),V4y)) -> p(ap(V1Q,V3x))))))) & p(ap(V1Q,V2b)) -> (all V5x (mem(V5x,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V2b)) -> p(ap(V1Q,V5x)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 682 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERRESTRICT(A_27a,A_27b),V1R),V2s)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 683 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) & p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 684 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESTRORD__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 685 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ediamond__TC__diamond) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 686 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (p(ap(ap(ap(c_2Erelation_2ERCOMPL(A_27a,A_27b),V0R),V1x),V2y)) <-> -p(ap(ap(V0R,V1x),V2y))))))))))))) # label(ax_thm_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 687 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 688 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWeakOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 689 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V0R,V5y),V6z)) -> p(ap(ap(V1P,V4x),V6z))))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) -> p(ap(ap(V1P,V7x),V8y)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 690 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) -> p(ap(ap(V1P,V7x),V8y)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 691 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27b),V0R),c_2Emin_2E_3D(A_27a)) = V0R)))))) # label(conj_thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 692 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__RTC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 693 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2x f97(A_27b,A_27a,V0R,V2x,V1f) = ap(f98(A_27b,A_27a,V0R,V1f),V2x)))))) # label(lameq_f98) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 694 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 695 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1P,V2x),V3y)) -> p(ap(ap(V0R,V2x),V3y))))))) -> p(ap(c_2Erelation_2EWF(A_27a),V1P))))))))) # label(conj_thm_2Erelation_2EWF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 696 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) & p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 697 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__SINGLE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 698 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EEQC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 699 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1y (mem(V1y,A_27b) -> (p(ap(ap(c_2Erelation_2ERRANGE(A_27a,A_27b),V0R),V1y)) <-> (exists V2x (p(ap(ap(V0R,V2x),V1y)) & mem(V2x,A_27a)))))))))))) # label(ax_thm_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 700 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))) & (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eestablish__CR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 701 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) & V2y != V1x -> (exists V3z (mem(V3z,A_27a) & V1x != V3z & p(ap(ap(V0R,V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2ETC__implies__one__step) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 702 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27b) -> -p(ap(ap(V0R,V1x),V2y)))) <-> p(ap(ap(c_2Erelation_2Enf(A_27a,A_27b),V0R),V1x))))))))))) # label(ax_thm_2Erelation_2Enf__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 703 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> f98(A_27b,A_27a,V0R,V1f) = ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f))))))))) # label(ax_thm_2Erelation_2Einv__image__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 704 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ereflexive__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 705 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3x ap(ap(c_2Emin_2E_3D(A_27b),ap(V2f,V3x)),ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V0R),V3x)),V3x)) = ap(f105(A_27b,A_27a,V0R,V1M,V2f),V3x)))))))) # label(lameq_f105) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 706 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWF__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 707 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V1x))))))))))) # label(conj_thm_2Erelation_2EEQC__SYM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 708 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1a),V2b)) <-> (all V3P (mem(V3P,arr(A_27a,arr(A_27a,bool))) -> ((all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> (p(ap(ap(V3P,V7y),V8z)) & p(ap(ap(V3P,V6x),V7y)) -> p(ap(ap(V3P,V6x),V8z))))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V3P,V4x),V5y))))))) -> p(ap(ap(V3P,V1a),V2b)))))))))))))) # label(ax_thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 709 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V2y),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(V0R,V1x),V3z))))))))) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 710 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) <-> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(V0R1,V2x),V3y)) -> p(ap(ap(V1R2,V2x),V3y)))))))))))))))) # label(ax_thm_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 711 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R1)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))) & (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V1R2)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))))))))) # label(conj_thm_2Erelation_2Eantisymmetric__RINTER) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 712 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <-> (exists V3y (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a)))))))))))) # label(conj_thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 713 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eirrefl__trans__implies__antisym) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 714 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2)),V2R3))))))))))) # label(conj_thm_2Erelation_2ERUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 715 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EEQC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2EEQC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 716 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2D (mem(V2D,arr(A_27a,bool)) -> (all V3P (mem(V3P,arr(A_27a,arr(A_27b,bool))) -> (all V4M (mem(V4M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V5x (mem(V5x,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V1R)) & p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V1R),V2D),V3P),V4M)) & p(ap(V2D,V5x)) & V0f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V4M) -> p(ap(ap(V3P,V5x),ap(V0f,V5x)))))))))))))))))))) # label(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 717 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ESC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__SC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 718 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2Ediag(A_27a),V0A),V1x),V2y)) <-> V2y = V1x & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0A))))))))))) # label(ax_thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 719 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EStrongLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 720 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERRESTRICT(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERRESTRICT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 721 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) -> V2y != V1x)))))))))) # label(conj_thm_2Erelation_2EWF__noloops) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 722 (all A_27a (ne(A_27a) -> c_2Emin_2E_3D(A_27a) = ap(c_2Erelation_2Einv(A_27a,A_27a),c_2Emin_2E_3D(A_27a)))) # label(conj_thm_2Erelation_2Einv__Id) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 723 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EWFREC(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,A_27b)))))))) # label(mem_c_2Erelation_2EWFREC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 724 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) -> (all V3x (mem(V3x,A_27a) -> p(ap(ap(V1P,V3x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V3x)))))))))))))))) # label(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 725 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <-> p(ap(c_2Erelation_2Eequivalence(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Eequivalence__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 726 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2EEXTEND__RTC__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 727 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__Weak) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 728 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__EQC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 729 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) | V1x = V2y))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 730 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2a (mem(V2a,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V3y),V4z)) & p(ap(V1Q,V3y)) -> p(ap(V1Q,V4z))))))) & p(ap(V1Q,V2a)) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2a),V5z)) -> p(ap(V1Q,V5z)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 731 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) & p(ap(ap(V1P,V4y),V5z)) -> p(ap(ap(V1P,V3x),V5z))))))))) & (all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 732 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EStrongOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 733 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V3f ap(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f) = ap(f101(A_27a,A_27b,V2x,V0R,V1M),V3f)))))))) # label(lameq_f101) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 734 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(V0R1,V2x),V3y)) | p(ap(ap(V1R2,V2x),V3y)) <-> p(ap(ap(ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2),V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 735 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4v ap(f102(A_27b,A_27a,V1M,V0R,V3f),V4v) = ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V3f),V0R),V4v)),V4v)))))))) # label(lameq_f102) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 736 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V2x) = ap(V1f,V3y)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ESC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 737 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V2Q,V4x)) & p(ap(ap(V1R,V4x),V5y)) -> p(ap(V2Q,V5y))))))) & (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V0a),V3y)) -> p(ap(V2Q,V3y))))) -> (all V6b (mem(V6b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V0a),V6b)) -> p(ap(V2Q,V6b)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__ALT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 738 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> ((all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4x (mem(V4x,A_27a) -> ((all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V5y),V4x)) -> p(ap(ap(V1P,V5y),ap(V3f,V5y)))))) -> p(ap(ap(V1P,V4x),ap(ap(V2M,V3f),V4x)))))))) <-> p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 739 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V3y),V4z)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z))))))))))))) # label(conj_thm_2Erelation_2ERTC__RULES__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 740 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__EQC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 741 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V3D (mem(V3D,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(V3D,V4x)) & p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V3D),V1P),V2M)) -> p(ap(ap(V1P,V4x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V4x)))))))))))))))))) # label(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 742 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERINTER(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 743 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ediamond__RC__diamond) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 744 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1R_27 (mem(V1R_27,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1R_27,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V1R_27),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2EEQC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 745 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V4x),V5y)) & p(ap(V0P,V4x)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 746 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Etotal(A_27a),V0R)) -> p(ap(c_2Erelation_2Etotal(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Etotal__inv__image) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 747 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),c_2Emin_2E_3D(A_27a)),V0R)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 748 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> ((all V3Q (mem(V3Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V3Q,V5y)) & p(ap(ap(V0R,V4x),V5y)) -> p(ap(V3Q,V4x))))))) & p(ap(V3Q,V2b)) -> p(ap(V3Q,V1a))))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 749 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 750 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__STRORD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 751 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0M (mem(V0M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V0M) = V2f -> (p(ap(c_2Erelation_2EWF(A_27a),V1R)) -> (all V3x (mem(V3x,A_27a) -> ap(ap(V0M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V1R),V3x)),V3x) = ap(V2f,V3x))))))))))))))) # label(conj_thm_2Erelation_2EWFREC__COROLLARY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 752 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V1x),V3z)) -> (exists V4u (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V3z),V4u)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2y),V4u)) & mem(V4u,A_27a))))))))))))))) # label(ax_thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 753 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 754 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2EOrder(A_27g),V0Z)) <-> p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) & p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 755 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ESTRORD(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__STRORD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 756 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EINVOL(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2Einv(A_27a,A_27a))))) # label(conj_thm_2Erelation_2Einv__INVOL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.15 757 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> p(ap(ap(V0R,V2b),V1a)) | p(ap(ap(V0R,V1a),V2b)))))) & p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWeakLinearOrder__dichotomy) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 758 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3z)))))))))))))) # label(conj_thm_2Erelation_2ERTC__RTC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 759 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ESC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 760 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (all V9z (mem(V9z,A_27a) -> (p(ap(ap(V1P,V7x),V8y)) & p(ap(ap(V1P,V8y),V9z)) -> p(ap(ap(V1P,V7x),V9z))))))))) & (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(V1P,V5x),V6y)) -> p(ap(ap(V1P,V6y),V5x))))))) & (all V4x (mem(V4x,A_27a) -> p(ap(ap(V1P,V4x),V4x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V10x (mem(V10x,A_27a) -> (all V11y (mem(V11y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) -> p(ap(ap(V1P,V10x),V11y)))))))))))))) # label(conj_thm_2Erelation_2EEQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 761 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) & p(ap(c_2Erelation_2EOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2ELinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 762 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> f104(A_27b,A_27a,V1M,V0R) = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M))))))))) # label(ax_thm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 763 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etransitive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etransitive) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 764 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ercdiamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ercdiamond) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 765 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Esymmetric__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 766 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <-> V0f = ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f)))))) # label(ax_thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 767 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))) <-> p(ap(ap(ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f),V2x),V3y))))))))))))))) # label(conj_thm_2Erelation_2Einv__image__thm) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 768 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Etransitive__TC__identity) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 769 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V1P,V3x),V4y)) & p(ap(ap(V0R,V4y),V5z)) -> p(ap(ap(V1P,V3x),V5z))))))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 770 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) -> (all V1a (mem(V1a,A_27z) -> (all V2b (mem(V2b,A_27z) -> (V2b = ap(V0f,V1a) <-> ap(V0f,V2b) = V1a)))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 771 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ERC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 772 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V3y ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)) = ap(f97(A_27b,A_27a,V0R,V2x,V1f),V3y)))))))) # label(lameq_f97) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 773 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWF(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 774 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R))) <-> (exists V2y (p(ap(ap(V1R,V0x),V2y)) & mem(V2y,A_27b)))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 775 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 776 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Enf(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))))))) # label(mem_c_2Erelation_2Enf) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 777 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) -> (exists V3y (mem(V3y,A_27a) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)))) | p(ap(ap(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 778 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V1R2)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))))))))) # label(conj_thm_2Erelation_2Etransitive__RINTER) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 779 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) -> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EStrongOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 780 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) -> (all V1a (mem(V1a,A_27z) -> (all V2b (mem(V2b,A_27z) -> (V2b = V1a <-> ap(V0f,V1a) = ap(V0f,V2b))))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 781 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) & p(ap(ap(V0R,V1x),V2y)) -> V1x = V2y)))))))))) # label(ax_thm_2Erelation_2Eantisymmetric__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 782 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EEMPTY__REL(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Erelation_2EEMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 783 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> f99(A_27b,A_27a,V0f,V2x,V1R) = ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V2x))))))))))) # label(ax_thm_2Erelation_2ERESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 784 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2ECR(A_27a),V0R)) <-> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)))))))) # label(ax_thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 785 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y))))) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x))))))))) # label(conj_thm_2Erelation_2EWFP__RULES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 786 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) <-> p(ap(ap(V0R,V1x),V2y))))))) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Esymmetric__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 787 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 788 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) <-> V2y = V1x | p(ap(ap(V0R,V1x),V2y))))))))))) # label(ax_thm_2Erelation_2ERC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 789 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f f102(A_27b,A_27a,V1M,V0R,V3f) = ap(f103(A_27b,A_27a,V1M,V0R),V3f)))))) # label(lameq_f103) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 790 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x))))))))) # label(conj_thm_2Erelation_2EWF__EQ__WFP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 791 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 792 (all A_27z (ne(A_27z) -> mem(c_2Erelation_2EIDEM(A_27z),arr(arr(A_27z,A_27z),bool)))) # label(mem_c_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 793 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2u (mem(V2u,A_27a) -> (all V3v (mem(V3v,A_27b) -> (p(ap(ap(ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V0R),V1x),V2u),V3v)) <-> p(ap(ap(V0R,V2u),V3v)) & V2u != V1x))))))))))))) # label(ax_thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 794 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ETC__RTC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 795 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) & ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ETC__RC__EQNS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 796 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1R),V4x),V5y)) & p(ap(V0P,V4x)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 797 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2k (mem(V2k,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V1R),V2k)))) <-> V0x != V2k & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 798 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 799 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> V0R = ap(ap(c_2Erelation_2EO(A_27a,A_27b,A_27b),c_2Emin_2E_3D(A_27b)),V0R))))))) # label(conj_thm_2Erelation_2EId__O) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 800 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) & ap(c_2Erelation_2ESC(A_27a),V0R) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__SC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 801 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ERC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ERC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 802 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> p(ap(c_2Erelation_2Eantisymmetric(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))) # label(conj_thm_2Erelation_2ERSUBSET__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 803 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <-> p(ap(c_2Erelation_2Etrichotomous(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Etrichotomous__STRORD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 804 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) <-> p(ap(c_2Erelation_2EStrongOrder(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 805 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eantisymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 806 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERESTRICT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,A_27b))))))))) # label(mem_c_2Erelation_2ERESTRICT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 807 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),c_2Erelation_2ERUNIV(A_27a,A_27b)),V0R)) <-> c_2Erelation_2ERUNIV(A_27a,A_27b) = V0R) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R),c_2Erelation_2ERUNIV(A_27a,A_27b))))))))) # label(conj_thm_2Erelation_2ERUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 808 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWCR(A_27a),V0R)) & p(ap(c_2Erelation_2ESN(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ENewmans__lemma) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 809 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V1R,V2y),V3z)) -> ap(V0f,V2y) = ap(ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V3z),V2y)))))))))))))) # label(conj_thm_2Erelation_2ERESTRICT__LEMMA) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 810 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__RC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 811 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V3y) = ap(V1f,V2x)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 812 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <-> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> p(ap(ap(V0R,V1a),V2b)) | p(ap(ap(V0R,V2b),V1a)) | V1a = V2b))))))))) # label(ax_thm_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 813 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ereflexive__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 814 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) <-> p(ap(ap(ap(c_2Erelation_2Einv(A_27a,A_27b),V0R),V1x),V2y))))))))))))) # label(ax_thm_2Erelation_2Einv__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 815 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) <-> ap(V0R,V2y) = ap(V0R,V1x)))))) <-> p(ap(c_2Erelation_2Eequivalence(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 816 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> V0R = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) & ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)) & ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R))))) # label(conj_thm_2Erelation_2Einv__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 817 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> p(ap(c_2Ebool_2E_3F_21(arr(A_27a,A_27b)),f106(A_27b,A_27a,V1M,V0R)))))))))))) # label(conj_thm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 818 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b)) <-> (all V3P (mem(V3P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> p(ap(ap(V3P,V4x),V4x)))) & (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (all V7z (mem(V7z,A_27a) -> (p(ap(ap(V3P,V6y),V7z)) & p(ap(ap(V0R,V5x),V6y)) -> p(ap(ap(V3P,V5x),V7z))))))))) -> p(ap(ap(V3P,V1a),V2b)))))))))))))) # label(ax_thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 819 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V4z)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z))))))))) & (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 820 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 821 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27a),V0R),V0R)),V0R)) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__O__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 822 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ETC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 823 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3M (mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V1R),V2P),V3M)) & p(ap(c_2Erelation_2EWF(A_27a),V1R)) & ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V3M) = V0f -> p(ap(ap(V2P,V4x),ap(V0f,V4x)))))))))))))))))) # label(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 824 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ercdiamond__diamond) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 825 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2EEQC__R) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 826 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERSUBSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),bool))))))) # label(mem_c_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 827 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (p(ap(c_2Erelation_2EWF(A_27b),V0R)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2EWF__inv__image) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 828 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> (exists V4u (p(ap(ap(V0R,V3z),V4u)) & p(ap(ap(V0R,V2y),V4u)) & mem(V4u,A_27a))))))))))))))) # label(ax_thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 829 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESTRORD(A_27a),V0R),V1a),V2b)) <-> V2b != V1a & p(ap(ap(V0R,V1a),V2b))))))))))) # label(ax_thm_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 830 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Esymmetric__inv__identity) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 831 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> p(ap(c_2Erelation_2Ereflexive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Ereflexive__inv__image) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 832 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2x (mem(V2x,A_27a) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (V3f = ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),f100(A_27b,A_27a,V1M,V0R,V3f)),V0R),V2x) <-> p(ap(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f))))))))))))))) # label(ax_thm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 833 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Etransitive__inv__image) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 834 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWeakLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 835 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTREL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Eoption_2Eoption(A_27a),arr(ty_2Eoption_2Eoption(A_27b),bool)))))))) # label(mem_c_2Eoption_2EOPTREL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 836 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0o1 (mem(V0o1,ty_2Eoption_2Eoption(A_27a)) -> (all V1o2 (mem(V1o2,ty_2Eoption_2Eoption(A_27a)) -> (all V2f1 (mem(V2f1,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V3f2 (mem(V3f2,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (V0o1 = V1o2 & (all V4x (mem(V4x,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V4x) = V1o2 -> ap(V2f1,V4x) = ap(V3f2,V4x)))) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V1o2),V3f2) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0o1),V2f1)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__BIND__cong) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 837 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27b)) -> (all V2y (mem(V2y,A_27b) -> (ap(c_2Eoption_2ESOME(A_27b),V2y) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27b,A_27a),V0m1),V1m2) <-> (exists V3x (ap(c_2Eoption_2ESOME(A_27b),V2y) = V1m2 & ap(c_2Eoption_2ESOME(A_27a),V3x) = V0m1 & mem(V3x,A_27a)))) & (c_2Eoption_2ENONE(A_27b) = V1m2 | c_2Eoption_2ENONE(A_27a) = V0m1 <-> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27b,A_27a),V0m1),V1m2)))))))))))) # label(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 838 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0opt1 (mem(V0opt1,ty_2Eoption_2Eoption(A_27a)) -> (all V1opt2 (mem(V1opt2,ty_2Eoption_2Eoption(A_27a)) -> (all V2f1 (mem(V2f1,arr(A_27a,A_27b)) -> (all V3f2 (mem(V3f2,arr(A_27a,A_27b)) -> (V0opt1 = V1opt2 & (all V4x (mem(V4x,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V4x) = V1opt2 -> ap(V2f1,V4x) = ap(V3f2,V4x)))) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f1),V0opt1) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V3f2),V1opt2)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__CONG) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 839 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x) <-> c_2Eoption_2ENONE(A_27a) = V1x))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 840 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27b)),V1x),c_2Eoption_2ENONE(A_27b)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ESOME(A_27b)),V0f)))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 841 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,ap(c_2Eoption_2ESOME(A_27a),V2x)))))) & ((all V3x (mem(V3x,A_27a) -> -p(ap(V0P,V3x)))) -> p(ap(V1Q,c_2Eoption_2ENONE(A_27a)))) -> p(ap(V1Q,ap(c_2Eoption_2Esome(A_27a),V0P)))))))))) # label(conj_thm_2Eoption_2Esome__intro) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 842 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> V0x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)))))) # label(conj_thm_2Eoption_2Eoption__case__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 843 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (p(ap(c_2Eoption_2EIS__SOME(A_27b),ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0x),V1g))) -> p(ap(c_2Eoption_2EIS__SOME(A_27a),V0x))))))))))) # label(conj_thm_2Eoption_2EIS__SOME__BIND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 844 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((all V1opt (mem(V1opt,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V1opt)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V2x))))) & p(ap(V0P,c_2Eoption_2ENONE(A_27a)))))))) # label(conj_thm_2Eoption_2EFORALL__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 845 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27d,ty_2Eoption_2Eoption(A_27c))) -> (all V1g (mem(V1g,arr(A_27b,ty_2Eoption_2Eoption(A_27d))) -> (all V2h (mem(V2h,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27b,A_27a),ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27d,A_27b),V0f),V1g)),V2h) = ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27d,A_27a),V0f),ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27d,A_27b,A_27a),V1g),V2h)))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 846 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1X (mem(V1X,ty_2Eoption_2Eoption(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (-p(V0P) & V1X = ap(c_2Eoption_2ESOME(A_27a),V2x) <-> ap(c_2Eoption_2ESOME(A_27a),V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),V1X)) & (V1X = ap(c_2Eoption_2ESOME(A_27a),V2x) & p(V0P) <-> ap(c_2Eoption_2ESOME(A_27a),V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),V1X),c_2Eoption_2ENONE(A_27a))) & (ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),V1X) = c_2Eoption_2ENONE(A_27a) <-> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V1X)) -> p(V0P))) & (ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),V1X),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27a) <-> (p(V0P) -> p(ap(c_2Eoption_2EIS__NONE(A_27a),V1X)))))))))))) # label(conj_thm_2Eoption_2EIF__NONE__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 847 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),V0x)) <-> V0x = c_2Eoption_2ENONE(A_27a)))))) # label(conj_thm_2Eoption_2EIS__NONE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 848 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x1 (mem(V0x1,ty_2Eoption_2Eoption(A_27a)) -> (all V1x2 (mem(V1x2,ty_2Eoption_2Eoption(A_27a)) -> (all V2y1 (mem(V2y1,ty_2Eoption_2Eoption(A_27b)) -> (all V3y2 (mem(V3y2,ty_2Eoption_2Eoption(A_27b)) -> (all V4f1 (mem(V4f1,arr(A_27a,arr(A_27b,A_27c))) -> (all V5f2 (mem(V5f2,arr(A_27a,arr(A_27b,A_27c))) -> ((all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (ap(c_2Eoption_2ESOME(A_27a),V6x) = V1x2 & V3y2 = ap(c_2Eoption_2ESOME(A_27b),V7y) -> ap(ap(V4f1,V6x),V7y) = ap(ap(V5f2,V6x),V7y)))))) & V3y2 = V2y1 & V0x1 = V1x2 -> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V5f2),V1x2),V3y2) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V4f1),V0x1),V2y1)))))))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__cong) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 849 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0g (mem(V0g,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V1f (mem(V1f,arr(A_27c,ty_2Eoption_2Eoption(A_27b))) -> (all V2m (mem(V2m,A_27c) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),ap(V1f,V2m)),V0g) = ap(ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27a,A_27b,A_27c),V0g),V1f),V2m))))))))))))) # label(ax_thm_2Eoption_2EOPTION__MCOMP__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 850 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V0opt)) <-> (exists V1x (mem(V1x,A_27a) & V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x)))))))) # label(conj_thm_2Eoption_2EIS__SOME__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 851 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27c) -> c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),c_2Eoption_2ENONE(A_27c)) & ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),ap(c_2Eoption_2ESOME(A_27c),V2y)) = c_2Eoption_2ENONE(A_27a) & c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),c_2Eoption_2ENONE(A_27c)) & ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),ap(c_2Eoption_2ESOME(A_27c),V2y)) = ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,V1x),V2y)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 852 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v_27 (mem(V0v_27,A_27b) -> (all V1f_27 (mem(V1f_27,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,ty_2Eoption_2Eoption(A_27a)) -> (all V3M_27 (mem(V3M_27,ty_2Eoption_2Eoption(A_27a)) -> (all V4v (mem(V4v,A_27b) -> (all V5f (mem(V5f,arr(A_27a,A_27b)) -> ((all V6x (mem(V6x,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V6x) = V3M_27 -> ap(V1f_27,V6x) = ap(V5f,V6x)))) & (c_2Eoption_2ENONE(A_27a) = V3M_27 -> V4v = V0v_27) & V3M_27 = V2M -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V2M),V4v),V5f) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V3M_27),V0v_27),V1f_27)))))))))))))))))) # label(conj_thm_2Eoption_2Eoption__case__cong) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 853 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27b)) -> (V1x = c_2Eoption_2ENONE(A_27b) <-> ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x) = c_2Eoption_2ENONE(A_27a)) & (c_2Eoption_2ENONE(A_27b) = V1x <-> c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x)))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 854 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Eoption_2Eoption(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V2y (mem(V2y,A_27b) -> (ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0p),V1f) = c_2Eoption_2ENONE(A_27b) <-> (exists V3x (c_2Eoption_2ENONE(A_27b) = ap(V1f,V3x) & V0p = ap(c_2Eoption_2ESOME(A_27a),V3x) & mem(V3x,A_27a))) | V0p = c_2Eoption_2ENONE(A_27a)) & ((exists V4x (mem(V4x,A_27a) & ap(V1f,V4x) = ap(c_2Eoption_2ESOME(A_27b),V2y) & V0p = ap(c_2Eoption_2ESOME(A_27a),V4x))) <-> ap(c_2Eoption_2ESOME(A_27b),V2y) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0p),V1f)))))))))))) # label(conj_thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 855 (all A_27a (ne(A_27a) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),V0m1),c_2Eoption_2ENONE(A_27a)) = V0m1)))) # label(conj_thm_2Eoption_2EOPTION__CHOICE__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 856 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,ty_2Eoption_2Eoption(arr(A_27a,A_27b))) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,A_27a),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,arr(A_27a,A_27b)),ap(c_2Eoption_2ESOME(arr(arr(A_27a,A_27b),A_27b)),f107(A_27b,A_27a,V1x))),V0f))))))))) # label(conj_thm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 857 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x))) <-> $F))) & (p(ap(c_2Eoption_2EIS__NONE(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $T))) # label(ax_thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 858 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27c,ty_2Eoption_2Eoption(A_27d))) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> V1f = ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27b,A_27b,A_27a),c_2Eoption_2ESOME(A_27b)),V1f) & V0g = ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27d,A_27c,A_27c),V0g),c_2Eoption_2ESOME(A_27c)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 859 (all A_27a (ne(A_27a) -> (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),ty_2Eoption_2Eoption(A_27a)),k(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),c_2Ebool_2ET)),V0rep)) & mem(V0rep,arr(ty_2Eoption_2Eoption(A_27a),ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone))))))) # label(ax_thm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.16 860 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)))))))) # label(mem_c_2Eoption_2EOPTION__MAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 861 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1o1 (mem(V1o1,ty_2Eoption_2Eoption(A_27a)) -> (all V2o2 (mem(V2o2,ty_2Eoption_2Eoption(A_27b)) -> (ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1o1),V2o2) = c_2Eoption_2ENONE(A_27c) <-> c_2Eoption_2ENONE(A_27b) = V2o2 | c_2Eoption_2ENONE(A_27a) = V1o1))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 862 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),arr(ty_2Eoption_2Eoption(arr(A_27b,A_27a)),arr(ty_2Eoption_2Eoption(A_27b),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 863 (all A_27a all V0y (mem(V0y,A_27a) -> (all V2x ap(ap(c_2Emin_2E_3D(A_27a),V0y),V2x) = ap(f110(A_27a,V0y),V2x)))) # label(lameq_f110) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 864 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Eoption_2Eoption__REP(A_27a),V0a)) = V0a)) & (all V1r (mem(V1r,ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone)) -> (ap(c_2Eoption_2Eoption__REP(A_27a),ap(c_2Eoption_2Eoption__ABS(A_27a),V1r)) = V1r <-> p(ap(k(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),c_2Ebool_2ET),V1r))))))) # label(ax_thm_2Eoption_2Eoption__REP__ABS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 865 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (p(ap(V0P,c_2Eoption_2ENONE(A_27a))) & (all V1a (mem(V1a,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V1a))))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V2x))))))))) # label(conj_thm_2Eoption_2Eoption__Induct) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 866 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27b)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),V0m1),ap(c_2Ecombin_2EK(ty_2Eoption_2Eoption(A_27a),A_27b),V1m2)) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),V0m1),V1m2))))))))) # label(ax_thm_2Eoption_2EOPTION__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 867 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27b)) -> (c_2Eoption_2ENONE(A_27a) = V1x & c_2Eoption_2ENONE(A_27b) = V2y | (exists V3x0 (mem(V3x0,A_27a) & (exists V4y0 (V1x = ap(c_2Eoption_2ESOME(A_27a),V3x0) & p(ap(ap(V0R,V3x0),V4y0)) & ap(c_2Eoption_2ESOME(A_27b),V4y0) = V2y & mem(V4y0,A_27b))))) <-> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0R),V1x),V2y))))))))))))) # label(ax_thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 868 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Eoption_2EOPTION__MCOMP(A_27a,A_27b,A_27c),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(arr(A_27c,ty_2Eoption_2Eoption(A_27b)),arr(A_27c,ty_2Eoption_2Eoption(A_27a))))))))))) # label(mem_c_2Eoption_2EOPTION__MCOMP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 869 (all A_27a (ne(A_27a) -> (all V0m2 (mem(V0m2,ty_2Eoption_2Eoption(A_27a)) -> V0m2 = ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),c_2Eoption_2ENONE(A_27a)),V0m2))) & (all V1x (mem(V1x,A_27a) -> (all V2m2 (mem(V2m2,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2ESOME(A_27a),V1x) = ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V1x)),V2m2))))))) # label(ax_thm_2Eoption_2EOPTION__CHOICE__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 870 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Esum_2EINL(A_27a,ty_2Eone_2Eone),V0x)) = ap(c_2Eoption_2ESOME(A_27a),V0x))))) # label(ax_thm_2Eoption_2ESOME__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 871 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y) <-> V1y = V0x))))))) # label(conj_thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 872 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> p(ap(ap(V0R,V1x),V1x)))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),V2x),V2x))))))))) # label(conj_thm_2Eoption_2EOPTREL__refl) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 873 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2opt (mem(V2opt,ty_2Eoption_2Eoption(A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1P_27,V3x))))) -> (p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V0P),V2opt)) -> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V1P_27),V2opt)))))))))))) # label(conj_thm_2Eoption_2EOPTION__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 874 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__ALL(A_27a),arr(arr(A_27a,bool),arr(ty_2Eoption_2Eoption(A_27a),bool))))) # label(mem_c_2Eoption_2EOPTION__ALL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 875 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Eoption__ABS(A_27a),arr(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2Eoption__ABS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 876 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))))) & (p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $F))) # label(ax_thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 877 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27b)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27c)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(A_27b),V1x)),ap(c_2Eoption_2EIS__SOME(A_27c),V2y))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,ap(c_2Eoption_2ETHE(A_27b),V1x)),ap(c_2Eoption_2ETHE(A_27c),V2y)))),c_2Eoption_2ENONE(A_27a)) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),V1x),V2y))))))))))))) # label(ax_thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 878 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V2x (mem(V2x,A_27a) -> (all V3v (mem(V3v,A_27b) -> (all V4f (mem(V4f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V2x)),V3v),V4f) = ap(V4f,V2x))))))) & (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> V0v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V0v),V1f))))))))) # label(ax_thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 879 (all A_27a all V0y (mem(V0y,A_27a) -> (all V1x ap(ap(c_2Emin_2E_3D(A_27a),V1x),V0y) = ap(f109(A_27a,V0y),V1x)))) # label(lameq_f109) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 880 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x = V2y & p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2ESOME(A_27a),V2y)) & (V2y = V1x & -p(V0P) <-> ap(c_2Eoption_2ESOME(A_27a),V2y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x))) & (p(V0P) <-> c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x))) & (-p(V0P) <-> c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a))))))))))) # label(conj_thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 881 (all A_27a (ne(A_27a) -> (all V0Q (mem(V0Q,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(V0Q,ap(c_2Eoption_2Esome(A_27a),V1P))) -> (all V3x (mem(V3x,A_27a) -> -p(ap(V1P,V3x)))) & p(ap(V0Q,c_2Eoption_2ENONE(A_27a))) | (exists V2x (mem(V2x,A_27a) & p(ap(V0Q,ap(c_2Eoption_2ESOME(A_27a),V2x))) & p(ap(V1P,V2x))))))))))) # label(conj_thm_2Eoption_2Esome__elim) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 882 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> V0opt = c_2Eoption_2ENONE(A_27a) | (exists V1x (mem(V1x,A_27a) & ap(c_2Eoption_2ESOME(A_27a),V1x) = V0opt)))))) # label(conj_thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 883 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(c_2Eoption_2ESOME(A_27b),ap(V0f,V1x)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)))))) & (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27b))))))) # label(ax_thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 884 (all A_27a (ne(A_27a) -> c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Esum_2EINR(A_27a,ty_2Eone_2Eone),c_2Eone_2Eone)))) # label(ax_thm_2Eoption_2ENONE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 885 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27b)) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27b),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,arr(A_27b,A_27c)),V0f),V1x)),V2y) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1x),V2y))))))))))))) # label(conj_thm_2Eoption_2EOPTION__APPLY__MAP2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 886 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Eoption_2ENONE(A_27a) != ap(c_2Eoption_2ESOME(A_27a),V0x))))) # label(conj_thm_2Eoption_2ENOT__NONE__SOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 887 (all A_27a (ne(A_27a) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27a)) -> (c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),V0m1),V1m2) <-> c_2Eoption_2ENONE(A_27a) = V1m2 & c_2Eoption_2ENONE(A_27a) = V0m1))))))) # label(conj_thm_2Eoption_2EOPTION__CHOICE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 888 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (p(ap(V0P,c_2Eoption_2ENONE(A_27a))) | (exists V2x (mem(V2x,A_27a) & p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V2x))))) <-> (exists V1opt (mem(V1opt,ty_2Eoption_2Eoption(A_27a)) & p(ap(V0P,V1opt))))))))) # label(conj_thm_2Eoption_2EEXISTS__OPTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 889 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),c_2Eoption_2ENONE(A_27b)),V0f) = c_2Eoption_2ENONE(A_27a))) & (all V1x (mem(V1x,A_27b) -> (all V2f (mem(V2f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27b),V1x)),V2f) = ap(V2f,V1x))))))))) # label(ax_thm_2Eoption_2EOPTION__BIND__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 890 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0option (mem(V0option,arr(ty_2Eoption_2Eoption(A_27a),arr(arr(A_27a,ty_2Eoption_2Eoption(A_27a)),A_27b))) -> p(ap(c_2Ebool_2EDATATYPE(A_27b),ap(ap(V0option,c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)))))))))) # label(conj_thm_2Eoption_2Edatatype__option) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 891 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> (all V1nc (mem(V1nc,A_27b) -> (all V2sc (mem(V2sc,arr(A_27a,A_27b)) -> (all V3v (mem(V3v,A_27b) -> (V3v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V0opt),V1nc),V2sc) <-> (exists V4x (mem(V4x,A_27a) & V3v = ap(V2sc,V4x) & V0opt = ap(c_2Eoption_2ESOME(A_27a),V4x))) | V3v = V1nc & V0opt = c_2Eoption_2ENONE(A_27a)))))))))))))) # label(conj_thm_2Eoption_2Eoption__case__eq) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 892 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> V0x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0x),V0x),c_2Eoption_2ESOME(A_27a)))))) # label(conj_thm_2Eoption_2Eoption__case__SOME__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 893 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V0P),c_2Eoption_2ENONE(A_27a))) <-> $T))) & (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(V1P,V2x)) <-> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V1P),ap(c_2Eoption_2ESOME(A_27a),V2x)))))))))) # label(ax_thm_2Eoption_2EOPTION__ALL__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 894 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__IGNORE__BIND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 895 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (-p(ap(c_2Eoption_2EIS__SOME(A_27a),V0x)) <-> c_2Eoption_2ENONE(A_27a) = V0x))))) # label(conj_thm_2Eoption_2ENOT__IS__SOME__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 896 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V0x) != c_2Eoption_2ENONE(A_27a))))) # label(conj_thm_2Eoption_2ENOT__SOME__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 897 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> c_2Eoption_2ENONE(A_27a) = V0opt | (exists V1x (ap(c_2Eoption_2ESOME(A_27a),V1x) = V0opt & mem(V1x,A_27a))))))) # label(conj_thm_2Eoption_2Eoption__CASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 898 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__NONE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__NONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 899 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__BIND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 900 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 901 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__SOME(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__SOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 902 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2e (mem(V2e,ty_2Eoption_2Eoption(A_27a)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (V4y = V3x <-> ap(c_2Eoption_2ESOME(A_27a),V3x) = ap(c_2Eoption_2ESOME(A_27a),V4y)))))) & (all V5x (mem(V5x,A_27a) -> V5x = ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V5x)))) & (all V6x (mem(V6x,A_27a) -> c_2Eoption_2ENONE(A_27a) != ap(c_2Eoption_2ESOME(A_27a),V6x))) & (all V7x (mem(V7x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V7x) != c_2Eoption_2ENONE(A_27a))) & (p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $F) & (all V9x (mem(V9x,ty_2Eoption_2Eoption(A_27a)) -> (c_2Eoption_2ENONE(A_27a) = V9x <-> p(ap(c_2Eoption_2EIS__NONE(A_27a),V9x))))) & (all V14x (mem(V14x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),V14x)) -> V0e = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V14x),V0e),V1f)))) & (all V25x (mem(V25x,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V25x)) = V25x)) & ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) = c_2Eoption_2ENONE(A_27a) & (all V24f (mem(V24f,arr(A_27a,A_27b)) -> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V24f),c_2Eoption_2ENONE(A_27a)))) & (all V22f (mem(V22f,arr(A_27a,A_27b)) -> (all V23x (mem(V23x,A_27a) -> ap(c_2Eoption_2ESOME(A_27b),ap(V22f,V23x)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V22f),ap(c_2Eoption_2ESOME(A_27a),V23x)))))) & (all V19x (mem(V19x,A_27a) -> (all V20v (mem(V20v,A_27b) -> (all V21f (mem(V21f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V19x)),V20v),V21f) = ap(V21f,V19x))))))) & (all V17v (mem(V17v,A_27b) -> (all V18f (mem(V18f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V17v),V18f) = V17v)))) & (all V16x (mem(V16x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V16x)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V16x),V2e),c_2Eoption_2ESOME(A_27a)) = V16x))) & (all V15x (mem(V15x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V15x)) -> ap(V1f,ap(c_2Eoption_2ETHE(A_27a),V15x)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V15x),V0e),V1f)))) & (all V13x (mem(V13x,ty_2Eoption_2Eoption(A_27a)) -> V13x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V13x),V13x),c_2Eoption_2ESOME(A_27a)))) & (all V12x (mem(V12x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V12x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)) = V12x)) & (all V11x (mem(V11x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V11x)) -> V11x = ap(c_2Eoption_2ESOME(A_27a),ap(c_2Eoption_2ETHE(A_27a),V11x))))) & (all V10x (mem(V10x,ty_2Eoption_2Eoption(A_27a)) -> (V10x = c_2Eoption_2ENONE(A_27a) <-> -p(ap(c_2Eoption_2EIS__SOME(A_27a),V10x))))) & (all V8x (mem(V8x,A_27a) -> ($T <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V8x)))))))))))))))) # label(conj_thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 903 (all V0b (mem(V0b,bool) -> (p(V0b) <-> ap(c_2Eoption_2EOPTION__GUARD,V0b) = ap(c_2Eoption_2ESOME(ty_2Eone_2Eone),c_2Eone_2Eone)) & (-p(V0b) <-> c_2Eoption_2ENONE(ty_2Eone_2Eone) = ap(c_2Eoption_2EOPTION__GUARD,V0b)))) # label(conj_thm_2Eoption_2EOPTION__GUARD__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 904 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a))) -> (all V1y (mem(V1y,A_27a) -> (ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1y)) = V0x <-> ap(c_2Eoption_2EOPTION__JOIN(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y)))))))) # label(conj_thm_2Eoption_2EOPTION__JOIN__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 905 (all A_27a (ne(A_27a) -> c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2Esome(A_27a),k(A_27a,c_2Ebool_2EF)))) # label(conj_thm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 906 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V0x)) = V0x)) & ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) = c_2Eoption_2ENONE(A_27a))) # label(ax_thm_2Eoption_2EOPTION__JOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 907 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Eoption_2Eoption(A_27b),arr(ty_2Eoption_2Eoption(A_27c),ty_2Eoption_2Eoption(A_27a))))))))))) # label(mem_c_2Eoption_2EOPTION__MAP2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 908 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Esome(A_27a),arr(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2Esome) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 909 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(A_27a),f49(A_27a,V0P))),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Emin_2E_40(A_27a),f108(A_27a,V0P)))),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2Esome(A_27a),V0P))))) # label(ax_thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 910 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,A_27b) -> ((exists V3z (ap(c_2Eoption_2ESOME(A_27a),V3z) = V1x & V2y = ap(V0f,V3z) & mem(V3z,A_27a))) <-> ap(c_2Eoption_2ESOME(A_27b),V2y) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x)))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 911 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)) = V0x)))) # label(ax_thm_2Eoption_2ETHE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 912 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27b)) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),c_2Eoption_2ENONE(arr(A_27b,A_27a))),V0x) = c_2Eoption_2ENONE(A_27a))) & (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27b)) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),ap(c_2Eoption_2ESOME(arr(A_27b,A_27a)),V1f)),V2x) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V1f),V2x))))))))) # label(ax_thm_2Eoption_2EOPTION__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 913 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ETHE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),A_27a)))) # label(mem_c_2Eoption_2ETHE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 914 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27b),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x))) <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),V1x))))))))))) # label(conj_thm_2Eoption_2EIS__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 915 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,A_27b) -> ap(c_2Eoption_2ESOME(A_27a),ap(V0f,V1x)) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),ap(c_2Eoption_2ESOME(arr(A_27b,A_27a)),V0f)),ap(c_2Eoption_2ESOME(A_27b),V1x)))))))))) # label(conj_thm_2Eoption_2ESOME__SOME__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 916 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2Eoption__CASE(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),A_27b)))))))) # label(mem_c_2Eoption_2Eoption__CASE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 917 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((all V1a (mem(V1a,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V1a))))) & p(ap(V0P,c_2Eoption_2ENONE(A_27a))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V2x))))))))) # label(conj_thm_2Eoption_2Eoption__induction) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 918 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> ap(c_2Eoption_2Esome(A_27a),f110(A_27a,V0y)) = ap(c_2Eoption_2ESOME(A_27a),V0y) & ap(c_2Eoption_2ESOME(A_27a),V0y) = ap(c_2Eoption_2Esome(A_27a),f109(A_27a,V0y)))))) # label(conj_thm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 919 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__CHOICE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)))))) # label(mem_c_2Eoption_2EOPTION__CHOICE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 920 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)))) # label(mem_c_2Eoption_2ENONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 921 (all A_27b all A_27a all V1x (mem(V1x,A_27a) -> (all V2f ap(V2f,V1x) = ap(f107(A_27b,A_27a,V1x),V2f)))) # label(lameq_f107) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 922 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> (all V1opt_27 (mem(V1opt_27,ty_2Eoption_2Eoption(A_27a)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (V0opt = V1opt_27 & (all V4x (mem(V4x,A_27a) -> (V1opt_27 = ap(c_2Eoption_2ESOME(A_27a),V4x) -> (p(ap(V2P,V4x)) <-> p(ap(V3P_27,V4x)))))) -> (p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V3P_27),V1opt_27)) <-> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V2P),V0opt)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 923 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> (all V3y (mem(V3y,ty_2Eoption_2Eoption(A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (p(ap(ap(V0P,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0P),V2x),V3y)) -> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V1Q),V2x),V3y)))))))))))))))) # label(conj_thm_2Eoption_2EOPTREL__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 924 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Eoption__REP(A_27a),arr(ty_2Eoption_2Eoption(A_27a),ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone))))) # label(mem_c_2Eoption_2Eoption__REP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 925 (all V0b (mem(V0b,bool) -> ap(c_2Eoption_2EOPTION__GUARD,V0b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Eone_2Eone)),V0b),ap(c_2Eoption_2ESOME(ty_2Eone_2Eone),c_2Eone_2Eone)),c_2Eoption_2ENONE(ty_2Eone_2Eone)))) # label(conj_thm_2Eoption_2EOPTION__GUARD__COND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 926 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,ty_2Eoption_2Eoption(arr(A_27b,A_27c))) -> (all V1g (mem(V1g,ty_2Eoption_2Eoption(arr(A_27a,A_27b))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27b),V0f),ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,A_27a),V1g),V2x)) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27a),ap(ap(c_2Eoption_2EOPTION__APPLY(arr(A_27a,A_27c),arr(A_27a,A_27b)),ap(ap(c_2Eoption_2EOPTION__APPLY(arr(arr(A_27a,A_27b),arr(A_27a,A_27c)),arr(A_27b,A_27c)),ap(c_2Eoption_2ESOME(arr(arr(A_27b,A_27c),arr(arr(A_27a,A_27b),arr(A_27a,A_27c)))),c_2Ecombin_2Eo(A_27a,A_27c,A_27b))),V0f)),V1g)),V2x))))))))))))) # label(conj_thm_2Eoption_2EOPTION__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 927 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (exists V2fn (V0e = ap(V2fn,c_2Eoption_2ENONE(A_27a)) & (all V3x (mem(V3x,A_27a) -> ap(V1f,V3x) = ap(V2fn,ap(c_2Eoption_2ESOME(A_27a),V3x)))) & mem(V2fn,arr(ty_2Eoption_2Eoption(A_27a),A_27b)))))))))))) # label(conj_thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 928 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1o1 (mem(V1o1,ty_2Eoption_2Eoption(A_27a)) -> (all V2o2 (mem(V2o2,ty_2Eoption_2Eoption(A_27b)) -> (all V3v (mem(V3v,A_27c) -> ((exists V4x1 (mem(V4x1,A_27a) & (exists V5x2 (mem(V5x2,A_27b) & V3v = ap(ap(V0f,V4x1),V5x2) & ap(c_2Eoption_2ESOME(A_27b),V5x2) = V2o2 & ap(c_2Eoption_2ESOME(A_27a),V4x1) = V1o1)))) <-> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1o1),V2o2) = ap(c_2Eoption_2ESOME(A_27c),V3v)))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__SOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 929 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(f108(A_27a,V0P),V2x) = ap(V0P,V2x)))) # label(lameq_f108) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 930 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (all V1e (mem(V1e,A_27b) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Eoption_2EIS__SOME(A_27a),V0x)),ap(V2f,ap(c_2Eoption_2ETHE(A_27a),V0x))),V1e) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V0x),V1e),V2f))))))))))) # label(conj_thm_2Eoption_2Eoption__case__compute) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 931 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g)),V2x) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27c,A_27b),V0f),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27c),V1g),V2x)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 932 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2ESOME) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 933 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0m (mem(V0m,ty_2Eoption_2Eoption(A_27a)) -> (all V1v (mem(V1v,A_27c) -> ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),c_2Eoption_2ENONE(A_27b)),V0m) = c_2Eoption_2ENONE(A_27a) & ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27c),ap(c_2Eoption_2ESOME(A_27c),V1v)),V0m) = V0m)))))))))) # label(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__thm) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 934 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__JOIN(A_27a),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2EOPTION__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 935 (all A_27a all A_27b all V4a (mem(V4a,A_27a) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (all V5b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V4a),V2x)),ap(ap(c_2Emin_2E_3D(A_27b),V5b),V3y)) = ap(f111(A_27a,A_27b,V4a,V2x,V3y),V5b)))))))) # label(lameq_f111) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 936 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V1p (mem(V1p,arr(A_27a,arr(A_27b,bool))) -> (all V3y ap(ap(c_2Emin_2E_3D(arr(A_27a,arr(A_27b,bool))),V1p),f112(A_27b,A_27a,V2x,V3y)) = ap(f113(A_27a,A_27b,V2x,V1p),V3y)))))) # label(lameq_f113) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 937 (all A_27a all A_27b all V2a (mem(V2a,A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V3b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2a),V0x)),ap(ap(c_2Emin_2E_3D(A_27b),V3b),V1y)) = ap(f121(A_27a,A_27b,V2a,V0x,V1y),V3b)))))))) # label(lameq_f121) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 938 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (all V2R3 (mem(V2R3,arr(A_27b,arr(A_27b,bool))) -> (all V3R4 (mem(V3R4,arr(A_27b,arr(A_27b,bool))) -> (all V4x (mem(V4x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V5y (mem(V5y,ty_2Epair_2Eprod(A_27a,A_27b)) -> ((all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(V0R1,V6x),V7y)) -> p(ap(ap(V1R2,V6x),V7y))))))) & (all V8x (mem(V8x,A_27b) -> (all V9y (mem(V9y,A_27b) -> (p(ap(ap(V2R3,V8x),V9y)) -> p(ap(ap(V3R4,V8x),V9y))))))) -> (p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V2R3),V4x),V5y)) -> p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V1R2),V3R4),V4x),V5y)))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 939 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> mem(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27d))))))))))))) # label(mem_c_2Epair_2E_23_23) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 940 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0pair (mem(V0pair,arr(arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),A_27c)) -> p(ap(c_2Ebool_2EDATATYPE(A_27c),ap(V0pair,c_2Epair_2E_2C(A_27a,A_27b)))))))))))) # label(conj_thm_2Epair_2Edatatype__pair) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 941 (all A_27b all A_27c all A_27a all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V2p1 ap(f126(A_27b,A_27c,A_27a,V0P),V2p1) = f125(A_27a,A_27c,A_27b,V2p1,V0P)))) # label(lameq_f126) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 942 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27c) -> (all V2f (mem(V2f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(V2f,V0x),V1y) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V0x),V1y)),V2f))))))))))))) # label(conj_thm_2Epair_2Epair__case__thm) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 943 (all A_27d all A_27c all A_27a all A_27b all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V5x (mem(V5x,A_27a) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V6y ap(V0P,ap(ap(V2N,V5x),V6y)) = ap(f132(A_27d,A_27c,A_27a,A_27b,V2N,V5x,V0P),V6y)))))))) # label(lameq_f132) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 944 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1v (mem(V1v,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1v)),ap(c_2Epair_2ESND(A_27a,A_27b),V1v)) = ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),V1v))))))))))) # label(conj_thm_2Epair_2EUNCURRY__VAR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 945 (all A0 (ne(A0) -> (all A1 (ne(A1) -> ne(ty_2Epair_2Eprod(A0,A1)))))) # label(ne_ty_2Epair_2Eprod) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 946 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27b),V1R2)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) -> p(ap(c_2Erelation_2Etransitive(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Etransitive__LEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 947 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(c_2Erelation_2EWF(A_27b),V1Q)) -> p(ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R),V1Q)))))))))))) # label(conj_thm_2Epair_2EWF__LEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 948 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27d,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27d))) -> ap(ap(c_2Ecombin_2ES(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27c),V0f),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),V1g)) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2ES(A_27a,arr(A_27b,A_27d),arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(arr(A_27b,A_27d),arr(A_27b,A_27c)),arr(A_27b,arr(A_27d,A_27c))),c_2Ecombin_2ES(A_27b,A_27d,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,arr(A_27d,A_27c)),arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),ap(c_2Ecombin_2Eo(A_27b,arr(A_27d,A_27c),ty_2Epair_2Eprod(A_27a,A_27b)),V0f)),c_2Epair_2E_2C(A_27a,A_27b)))),V1g)))))))))))))) # label(conj_thm_2Epair_2ES__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 949 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_3F(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f129(A_27b,A_27a,V0P)))) <-> (exists V2x (p(ap(c_2Ebool_2E_3F(A_27b),ap(V0P,V2x))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 950 (all A_27a2 all A_27c all A_27b all A_27a1 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V2b (mem(V2b,A_27b) -> (all V5x f136(A_27b,A_27a1,A_27c,A_27a2,V1N,V5x,V2b) = ap(f137(A_27a2,A_27c,A_27b,A_27a1,V1N,V2b),V5x)))))) # label(lameq_f137) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 951 (all A_27b all A_27a all V1p (mem(V1p,arr(A_27a,arr(A_27b,bool))) -> (all V2x ap(f114(A_27b,A_27a,V1p),V2x) = ap(c_2Ebool_2E_3F(A_27b),f113(A_27a,A_27b,V2x,V1p))))) # label(lameq_f114) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 952 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (all V4c (mem(V4c,A_27a) -> (all V5d (mem(V5d,A_27b) -> (p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4c),V5d))) <-> p(ap(ap(V0R1,V2a),V4c)) | V2a = V4c & p(ap(ap(V1R2,V3b),V5d))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__DEF__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 953 (all A_27b all A_27a all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (all V5a ap(f117(A_27b,A_27a,V3x,V4y),V5a) = f116(A_27a,A_27b,V5a,V3x,V4y)))))) # label(lameq_f117) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 954 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27c,A_27a))) -> (all V2v (mem(V2v,A_27a) -> (V2v = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V0p),V1f) <-> (exists V3x ((exists V4y (mem(V4y,A_27c) & ap(ap(V1f,V3x),V4y) = V2v & ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V3x),V4y) = V0p)) & mem(V3x,A_27b)))))))))))))))) # label(conj_thm_2Epair_2Epair__case__eq) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 955 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1p_27 (mem(V1p_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5Q_27 (mem(V5Q_27,arr(A_27b,bool)) -> ((all V8x (mem(V8x,A_27a) -> (all V9y (mem(V9y,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8x),V9y) = V1p_27 -> (p(ap(V5Q_27,V9y)) <-> p(ap(V4Q,V9y)))))))) & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (V1p_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y) -> (p(ap(V2P,V6x)) <-> p(ap(V3P_27,V6x)))))))) & V0p = V1p_27 -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V3P_27),V5Q_27),V1p_27)) <-> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V2P),V4Q),V0p)))))))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 956 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> ap(ap(ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f),V1x),V2y) = ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)))))))))))))) # label(ax_thm_2Epair_2ECURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 957 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> V0x = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2EFST(A_27a,A_27b),V0x)),ap(c_2Epair_2ESND(A_27a,A_27b),V0x)))))))) # label(ax_thm_2Epair_2EPAIR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 958 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f)) = V0f)))))))) # label(conj_thm_2Epair_2EUNCURRY__CURRY__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 959 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EFST(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27a)))))) # label(mem_c_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 960 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27d)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27c) -> ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27c,A_27b,A_27d),V0f),V1g),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V3y)) = ap(ap(c_2Epair_2E_2C(A_27b,A_27d),ap(V0f,V2x)),ap(V1g,V3y)))))))))))))))))) # label(conj_thm_2Epair_2EPAIR__MAP__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 961 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1q (mem(V1q,ty_2Epair_2Eprod(A_27a,A_27b)) -> (V1q = V0p <-> ap(c_2Epair_2EFST(A_27a,A_27b),V0p) = ap(c_2Epair_2EFST(A_27a,A_27b),V1q) & ap(c_2Epair_2ESND(A_27a,A_27b),V0p) = ap(c_2Epair_2ESND(A_27a,A_27b),V1q)))))))))) # label(conj_thm_2Epair_2EPAIR__FST__SND__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 962 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ELEX(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))))))) # label(mem_c_2Epair_2ELEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 963 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V0p),V1f) = ap(ap(V1f,ap(c_2Epair_2EFST(A_27b,A_27c),V0p)),ap(c_2Epair_2ESND(A_27b,A_27c),V0p)))))))))))) # label(ax_thm_2Epair_2Epair__CASE__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 964 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0f))) <-> p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,arr(A_27b,bool)),c_2Ebool_2E_21(A_27b)),V0f)))))))))) # label(conj_thm_2Epair_2EFORALL__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 965 (all A_27c all A_27a all A_27b all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1p ap(f124(A_27c,A_27a,A_27b,V0P),V1p) = ap(V0P,V1p)))) # label(lameq_f124) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 966 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(V0f,V1x),V2y))))))))))))) # label(conj_thm_2Epair_2EUNCURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 967 (all A_27c all A_27b all A_27a1 all A_27a2 all V3x (mem(V3x,A_27a1) -> (all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V4y ap(ap(V1N,V3x),V4y) = ap(f134(A_27c,A_27b,A_27a1,A_27a2,V3x,V1N),V4y)))))) # label(lameq_f134) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 968 (all A_27c all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V4y ap(ap(V2N,V3x),V4y) = ap(f130(A_27c,A_27a,A_27b,V3x,V2N),V4y)))))) # label(lameq_f130) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 969 (all A_27b all A_27c all A_27a all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V3x f130(A_27c,A_27a,A_27b,V3x,V2N) = ap(f131(A_27b,A_27c,A_27a,V2N),V3x)))) # label(lameq_f131) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 970 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2p (mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2p) = ap(ap(c_2Epair_2E_2C(A_27c,A_27d),ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V2p))),ap(V1g,ap(c_2Epair_2ESND(A_27a,A_27b),V2p))))))))))))))))) # label(ax_thm_2Epair_2EPAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 971 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27d,A_27c)))) -> (all V1x (mem(V1x,A_27d) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2EC(A_27a,A_27d,arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27d,arr(A_27b,A_27c)),arr(A_27b,arr(A_27d,A_27c))),c_2Ecombin_2EC(A_27b,A_27d,A_27c)),V0f)),V1x)) = ap(ap(c_2Ecombin_2EC(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27d,A_27c)),V0f)),V1x))))))))))))) # label(conj_thm_2Epair_2EC__UNCURRY__L) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 972 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V1M (mem(V1M,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> ap(V0P,ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),f131(A_27b,A_27c,A_27a,V2N))),V1M)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27b),A_27d),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),f133(A_27b,A_27c,A_27d,A_27a,V2N,V0P))),V1M))))))))))))))) # label(conj_thm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 973 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c))))))))) # label(mem_c_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 974 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R1)) | p(ap(c_2Erelation_2Ereflexive(A_27b),V1R2)) <-> p(ap(c_2Erelation_2Ereflexive(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Ereflexive__LEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 975 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((exists V1p (p(ap(V0P,V1p)) & mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)))) <-> (exists V2p__1 ((exists V3p__2 (mem(V3p__2,A_27b) & p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2))))) & mem(V2p__1,A_27a)))))))))) # label(conj_thm_2Epair_2EEXISTS__PROD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 976 (all A_27a all A_27b all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V3t ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f146(A_27b,A_27a,V2s,V0R1,V3t,V1R2)) = ap(f147(A_27a,A_27b,V1R2,V0R1,V2s),V3t)))))))) # label(lameq_f147) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 977 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> f123(A_27c,A_27a,A_27b,V0f) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f))))))))) # label(conj_thm_2Epair_2EELIM__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 978 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) & p(ap(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Epair_2ESND(A_27a,A_27b),V1p))))) <-> (exists V2p1 (mem(V2p1,A_27a) & (exists V3p2 (p(ap(ap(V0P,V2p1),V3p2)) & mem(V3p2,A_27b)))))))))))) # label(conj_thm_2Epair_2EELIM__PEXISTS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 979 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_3F(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f128(A_27b,A_27a,V0P)))) <-> (exists V1x (mem(V1x,A_27a) & (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 980 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (exists V1q (mem(V1q,A_27a) & (exists V2r (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1q),V2r) = V0x & mem(V2r,A_27b))))))))))) # label(conj_thm_2Epair_2EABS__PAIR__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 981 (all A_27b all A_27c all A_27a all V2p (mem(V2p,ty_2Epair_2Eprod(arr(A_27a,A_27b),arr(A_27a,A_27c))) -> (all V3a ap(ap(c_2Epair_2E_2C(A_27b,A_27c),ap(ap(c_2Epair_2EFST(arr(A_27a,A_27b),arr(A_27a,A_27c)),V2p),V3a)),ap(ap(c_2Epair_2ESND(arr(A_27a,A_27b),arr(A_27a,A_27c)),V2p),V3a)) = ap(f139(A_27b,A_27c,A_27a,V2p),V3a)))) # label(lameq_f139) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 982 (all A_27a all A_27c all A_27b all V2p1 (mem(V2p1,A_27a) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V3p2 ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p1),V3p2)) = ap(f125(A_27a,A_27c,A_27b,V2p1,V0P),V3p2)))))) # label(lameq_f125) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 983 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V3x f127(A_27a,A_27b,V3x,V0P) = ap(f128(A_27b,A_27a,V0P),V3x)))) # label(lameq_f128) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 984 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (exists V0rep (mem(V0rep,arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27a,arr(A_27b,bool)))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(A_27a,arr(A_27b,bool)),ty_2Epair_2Eprod(A_27a,A_27b)),f115(A_27b,A_27a)),V0rep)))))))) # label(ax_thm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 985 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) <-> V2a = V0x & V1y = V3b))))))))))))) # label(conj_thm_2Epair_2EPAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 986 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2p (mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V1Q),V2p)) <-> p(ap(V1Q,ap(c_2Epair_2ESND(A_27a,A_27b),V2p))) & p(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V2p)))))))))))))) # label(ax_thm_2Epair_2EPROD__ALL__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 987 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f144(A_27b,A_27a,V0R1,V1R2)) = ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2))))))))) # label(ax_thm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 988 (all A_27a all A_27b all V5a (mem(V5a,A_27a) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (all V6b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V5a),V3x)),ap(ap(c_2Emin_2E_3D(A_27b),V6b),V4y)) = ap(f116(A_27a,A_27b,V5a,V3x,V4y),V6b)))))))) # label(lameq_f116) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 989 (all A_27a2 all A_27b all A_27c all A_27a1 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V3x ap(f135(A_27a2,A_27b,A_27c,A_27a1,V1N),V3x) = f134(A_27c,A_27b,A_27a1,A_27a2,V3x,V1N)))) # label(lameq_f135) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 990 (all A_27b all A_27a1 all A_27c all A_27a2 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V5x (mem(V5x,A_27a1) -> (all V2b (mem(V2b,A_27b) -> (all V6y ap(ap(ap(V1N,V5x),V6y),V2b) = ap(f136(A_27b,A_27a1,A_27c,A_27a2,V1N,V5x,V2b),V6y)))))))) # label(lameq_f136) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 991 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x ap(V0P,V1x) = ap(f129(A_27b,A_27a,V0P),V1x)))) # label(lameq_f129) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 992 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ESWAP(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27b,A_27a),ty_2Epair_2Eprod(A_27a,A_27b))))))) # label(mem_c_2Epair_2ESWAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 993 (all A_27b all A_27a all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V4u f141(A_27a,A_27b,V3t,V1R2,V4u,V0R1,V2s) = ap(f142(A_27b,A_27a,V3t,V1R2,V0R1,V2s),V4u)))))))))) # label(lameq_f142) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 994 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Epair_2Eprod(A_27b,A_27a)) -> ap(c_2Epair_2ESWAP(A_27a,A_27b),V0a) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2ESND(A_27b,A_27a),V0a)),ap(c_2Epair_2EFST(A_27b,A_27a),V0a)))))))) # label(ax_thm_2Epair_2ESWAP__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 995 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Epair_2ESND(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V1y)))))))) # label(conj_thm_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 996 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))))))) # label(mem_c_2Epair_2E_2C) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 997 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> ap(c_2Epair_2ESND(A_27c,A_27d),ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V1f),V2g),V0p)) = ap(V2g,ap(c_2Epair_2ESND(A_27a,A_27b),V0p)))))))))))))))) # label(conj_thm_2Epair_2ESND__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 998 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((all V2p__1 (mem(V2p__1,A_27a) -> (all V3p__2 (mem(V3p__2,A_27b) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2))))))) <-> (all V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(V0P,V1p))))))))))) # label(conj_thm_2Epair_2EFORALL__PROD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.17 999 (all A_27a all A_27b all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V3t ap(f143(A_27a,A_27b,V2s,V0R1,V1R2),V3t) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f142(A_27b,A_27a,V3t,V1R2,V0R1,V2s))))))))) # label(lameq_f143) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1000 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((all V1p__1 (mem(V1p__1,A_27a) -> (all V2p__2 (mem(V2p__2,A_27b) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1p__1),V2p__2))))))) -> (all V3p (mem(V3p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(V0P,V3p))))))))))) # label(conj_thm_2Epair_2Epair__induction) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1001 (all A_27c all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1x)),ap(c_2Epair_2ESND(A_27a,A_27b),V1x)) = ap(f123(A_27c,A_27a,A_27b,V0f),V1x)))) # label(lameq_f123) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1002 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27c))) -> (ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V1g) <-> V1g = V0f))))))))))) # label(conj_thm_2Epair_2EUNCURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1003 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27d,A_27c)) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27d))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,A_27c),arr(A_27b,A_27d)),ap(c_2Ecombin_2Eo(A_27b,A_27c,A_27d),V0f)),V1g)) = ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27d),V0f),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),V1g)))))))))))))) # label(conj_thm_2Epair_2Eo__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1004 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27a)) -> (all V1y (mem(V1y,A_27a) -> (ap(c_2Epair_2ESND(A_27b,A_27a),V0p) = V1y <-> (exists V2x (mem(V2x,A_27b) & V0p = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V1y)))))))))))) # label(conj_thm_2Epair_2ESND__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1005 (all A_27b all A_27a all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2s f143(A_27a,A_27b,V2s,V0R1,V1R2) = ap(f144(A_27b,A_27a,V0R1,V1R2),V2s)))))) # label(lameq_f144) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1006 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2EWF(A_27b),V1Q)) & p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ERPROD(A_27a,A_27b),V0R),V1Q)))))))))))) # label(conj_thm_2Epair_2EWF__RPROD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1007 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(V0P,V2x)) & p(ap(V1Q,V3y)) <-> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V1Q),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1008 (all A_27b all A_27a all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a f121(A_27a,A_27b,V2a,V0x,V1y) = ap(f122(A_27b,A_27a,V0x,V1y),V2a)))))) # label(lameq_f122) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1009 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> ap(c_2Epair_2EFST(A_27c,A_27d),ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V1f),V2g),V0p)) = ap(V1f,ap(c_2Epair_2EFST(A_27a,A_27b),V0p)))))))))))))))) # label(conj_thm_2Epair_2EFST__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1010 (all A_27b all A_27c all A_27d all A_27a all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V5x f132(A_27d,A_27c,A_27a,A_27b,V2N,V5x,V0P) = ap(f133(A_27b,A_27c,A_27d,A_27a,V2N,V0P),V5x)))))) # label(lameq_f133) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1011 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27b,arr(A_27c,A_27a))) -> (all V1M (mem(V1M,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V2M_27 (mem(V2M_27,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V3f (mem(V3f,arr(A_27b,arr(A_27c,A_27a))) -> ((all V4x (mem(V4x,A_27b) -> (all V5y (mem(V5y,A_27c) -> (V2M_27 = ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V4x),V5y) -> ap(ap(V0f_27,V4x),V5y) = ap(ap(V3f,V4x),V5y)))))) & V2M_27 = V1M -> ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V2M_27),V0f_27) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V1M),V3f)))))))))))))))) # label(conj_thm_2Epair_2Epair__case__cong) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1012 (all A_27b all A_27a all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V4u ap(f146(A_27b,A_27a,V2s,V0R1,V3t,V1R2),V4u) = f145(A_27a,A_27b,V2s,V0R1,V4u,V3t,V1R2)))))))))) # label(lameq_f146) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1013 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),arr(A_27a,arr(A_27b,A_27c)))))))))) # label(mem_c_2Epair_2ECURRY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1014 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> f124(A_27c,A_27a,A_27b,V0P) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),f126(A_27b,A_27c,A_27a,V0P)))))))))) # label(conj_thm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1015 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(c_2Epair_2EABS__prod(A_27a,A_27b),f122(A_27b,A_27a,V0x,V1y)))))))))) # label(ax_thm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1016 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R1)) & p(ap(c_2Erelation_2Esymmetric(A_27b),V1R2)) -> p(ap(c_2Erelation_2Esymmetric(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Esymmetric__LEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1017 (all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V2p (mem(V2p,arr(A_27a,arr(A_27b,bool))) -> (all V4y ap(ap(c_2Emin_2E_3D(arr(A_27a,arr(A_27b,bool))),V2p),f117(A_27b,A_27a,V3x,V4y)) = ap(f118(A_27a,A_27b,V3x,V2p),V4y)))))) # label(lameq_f118) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1018 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27b,bool))) -> (ap(c_2Epair_2EREP__prod(A_27a,A_27b),ap(c_2Epair_2EABS__prod(A_27a,A_27b),V1r)) = V1r <-> p(ap(f120(A_27b,A_27a),V1r))))) & (all V0a (mem(V0a,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(c_2Epair_2EABS__prod(A_27a,A_27b),ap(c_2Epair_2EREP__prod(A_27a,A_27b),V0a)) = V0a)))))) # label(ax_thm_2Epair_2EABS__REP__prod) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1019 (all A_27b all A_27c all A_27a all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (all V2p ap(f140(A_27b,A_27c,A_27a,V0P),V2p) = ap(V0P,f139(A_27b,A_27c,A_27a,V2p))))) # label(lameq_f140) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1020 (all A_27b all A_27a all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s ap(f148(A_27b,A_27a,V1R2,V0R1),V2s) = f147(A_27a,A_27b,V1R2,V0R1,V2s)))))) # label(lameq_f148) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1021 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27a,arr(A_27b,A_27c))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27c))) -> (all V2M_27 (mem(V2M_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V3M (mem(V3M,ty_2Epair_2Eprod(A_27a,A_27b)) -> (V2M_27 = V3M & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y) = V2M_27 -> ap(ap(V1f,V4x),V5y) = ap(ap(V0f_27,V4x),V5y)))))) -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f_27),V2M_27) = ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V1f),V3M)))))))))))))))) # label(conj_thm_2Epair_2EUNCURRY__CONG) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1022 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (exists V1fn (mem(V1fn,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> ap(ap(V0f,V2x),V3y) = ap(V1fn,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))))))))))))))) # label(conj_thm_2Epair_2Epair__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1023 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> ap(ap(c_2Epair_2ERPROD(A_27a,A_27b),V0R1),V1R2) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f148(A_27b,A_27a,V1R2,V0R1)))))))))) # label(ax_thm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1024 (all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V4y ap(f127(A_27a,A_27b,V3x,V0P),V4y) = ap(ap(V0P,V3x),V4y)))))) # label(lameq_f127) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1025 (all A_27b all A_27a all V2p (mem(V2p,arr(A_27a,arr(A_27b,bool))) -> (all V3x ap(c_2Ebool_2E_3F(A_27b),f118(A_27a,A_27b,V3x,V2p)) = ap(f119(A_27b,A_27a,V2p),V3x)))) # label(lameq_f119) # label(axiom) # label(non_clause). [assumption]. 6.17/6.18 1026 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> p(ap(ap(V0P,V1x),V2y)))))) <-> p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f128(A_27b,A_27a,V0P))))))))))) # label(conj_thm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1027 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f)) = V0f)))))))) # label(conj_thm_2Epair_2ECURRY__UNCURRY__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1028 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),arr(ty_2Epair_2Eprod(A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),A_27a))))))))) # label(mem_c_2Epair_2Epair__CASE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1029 (all A_27a all A_27b all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V4u (mem(V4u,A_27a) -> (all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V5v ap(f145(A_27a,A_27b,V2s,V0R1,V4u,V3t,V1R2),V5v) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R1,V2s),V4u)),ap(ap(V1R2,V3t),V5v))))))))))))) # label(lameq_f145) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1030 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EABS__prod(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),ty_2Epair_2Eprod(A_27a,A_27b))))))) # label(mem_c_2Epair_2EABS__prod) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1031 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EREP__prod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27a,arr(A_27b,bool)))))))) # label(mem_c_2Epair_2EREP__prod) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1032 (all A_27b all A_27a all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (all V4a ap(f112(A_27b,A_27a,V2x,V3y),V4a) = f111(A_27a,A_27b,V4a,V2x,V3y)))))) # label(lameq_f112) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1033 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2v1 (mem(V2v1,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V3v2 (mem(V3v2,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V4R1_27 (mem(V4R1_27,arr(A_27a,arr(A_27a,bool))) -> (all V5R2_27 (mem(V5R2_27,arr(A_27b,arr(A_27b,bool))) -> (all V6v1_27 (mem(V6v1_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V7v2_27 (mem(V7v2_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (V2v1 = V6v1_27 & V3v2 = V7v2_27 & (all V8a (mem(V8a,A_27a) -> (all V9b (mem(V9b,A_27b) -> (all V10c (mem(V10c,A_27a) -> (all V11d (mem(V11d,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10c),V11d) = V7v2_27 & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8a),V9b) = V6v1_27 -> (p(ap(ap(V4R1_27,V8a),V10c)) <-> p(ap(ap(V0R1,V8a),V10c)))))))))))) & (all V12a (mem(V12a,A_27a) -> (all V13b (mem(V13b,A_27b) -> (all V14c (mem(V14c,A_27a) -> (all V15d (mem(V15d,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V14c),V15d) = V7v2_27 & V12a = V14c & V6v1_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V12a),V13b) -> (p(ap(ap(V1R2,V13b),V15d)) <-> p(ap(ap(V5R2_27,V13b),V15d)))))))))))) -> (p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2),V2v1),V3v2)) <-> p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V4R1_27),V5R2_27),V6v1_27),V7v2_27)))))))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__CONG) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1034 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EPROD__ALL(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))))))) # label(mem_c_2Epair_2EPROD__ALL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1035 (all A_27b all A_27a all V2p ap(c_2Ebool_2E_3F(A_27a),f119(A_27b,A_27a,V2p)) = ap(f120(A_27b,A_27a),V2p)) # label(lameq_f120) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1036 (all A_27b all A_27a all V1p ap(f115(A_27b,A_27a),V1p) = ap(c_2Ebool_2E_3F(A_27a),f114(A_27b,A_27a,V1p))) # label(lameq_f115) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1037 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1g (mem(V1g,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (V0f = V1g <-> ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V1g) = ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f)))))))))))) # label(conj_thm_2Epair_2ECURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1038 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1v (mem(V1v,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),V1v) = ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1v)),ap(c_2Epair_2ESND(A_27a,A_27b),V1v)))))))))))) # label(ax_thm_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1039 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V2p1 (mem(V2p1,A_27a) -> (all V3p2 (mem(V3p2,A_27b) -> p(ap(ap(V0P,V2p1),V3p2)))))) <-> (all V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Epair_2ESND(A_27a,A_27b),V1p)))))))))))) # label(conj_thm_2Epair_2EELIM__PFORALL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1040 (all A_27a1 (ne(A_27a1) -> (all A_27a2 (ne(A_27a2) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0M (mem(V0M,ty_2Epair_2Eprod(A_27a1,A_27a2)) -> (all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V2b (mem(V2b,A_27b) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a1,A_27a2),A_27c),ap(c_2Epair_2EUNCURRY(A_27a1,A_27a2,A_27c),f137(A_27a2,A_27c,A_27b,A_27a1,V1N,V2b))),V0M) = ap(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a1,A_27a2),arr(A_27b,A_27c)),ap(c_2Epair_2EUNCURRY(A_27a1,A_27a2,arr(A_27b,A_27c)),f135(A_27a2,A_27b,A_27c,A_27a1,V1N))),V0M),V2b))))))))))))))) # label(conj_thm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1041 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3Q_27 (mem(V3Q_27,arr(A_27b,bool)) -> (all V4p (mem(V4p,ty_2Epair_2Eprod(A_27a,A_27b)) -> ((all V5x (mem(V5x,A_27a) -> (p(ap(V0P,V5x)) -> p(ap(V1P_27,V5x))))) & (all V6y (mem(V6y,A_27b) -> (p(ap(V2Q,V6y)) -> p(ap(V3Q_27,V6y))))) -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V2Q),V4p)) -> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V1P_27),V3Q_27),V4p)))))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1042 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (p(ap(c_2Ebool_2E_3F_21(ty_2Epair_2Eprod(arr(A_27a,A_27b),arr(A_27a,A_27c))),f140(A_27b,A_27c,A_27a,V0P))) <-> p(ap(c_2Ebool_2E_3F_21(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c))),f138(A_27c,A_27b,A_27a,V0P)))))))))))) # label(conj_thm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1043 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27b),V1R2)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R1)) -> p(ap(c_2Erelation_2Etotal(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Etotal__LEX) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1044 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Epair_2EFST(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V0x)))))))) # label(conj_thm_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1045 (all A_27a all A_27b all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V4u (mem(V4u,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V5v ap(ap(c_2Ebool_2E_5C_2F,ap(ap(V0R1,V2s),V4u)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2s),V4u)),ap(ap(V1R2,V3t),V5v))) = ap(f141(A_27a,A_27b,V3t,V1R2,V4u,V0R1,V2s),V5v)))))))))))) # label(lameq_f141) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1046 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V2x (mem(V2x,A_27a) -> p(ap(c_2Ebool_2E_21(A_27b),ap(V0P,V2x))))) <-> p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f129(A_27b,A_27a,V0P))))))))))) # label(conj_thm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1047 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (V2a = V0x & V3b = V1y <-> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b)))))))))))))) # label(conj_thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1048 (all A_27c all A_27b all A_27a all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (all V1f ap(V0P,V1f) = ap(f138(A_27c,A_27b,A_27a,V0P),V1f)))) # label(lameq_f138) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1049 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ((exists V2y (mem(V2y,A_27b) & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y) = V0p)) <-> ap(c_2Epair_2EFST(A_27a,A_27b),V0p) = V1x))))))))) # label(conj_thm_2Epair_2EFST__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1050 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (exists V1q ((exists V2r (mem(V2r,A_27b) & V0x = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1q),V2r))) & mem(V1q,A_27a))))))))) # label(conj_thm_2Epair_2Epair__CASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1051 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ESND(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27b)))))) # label(mem_c_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1052 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ERPROD(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))))))) # label(mem_c_2Epair_2ERPROD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1053 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27c) -> (all V2f (mem(V2f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V0x),V1y)),V2f) = ap(ap(V2f,V0x),V1y))))))))))))) # label(conj_thm_2Epair_2Epair__case__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1054 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> V0m != V1n))))) # label(conj_thm_2Eprim__rec_2ELESS__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1055 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y ap(f158(V0x),V1y) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1y),ap(c_2Enum_2ESUC,V0x))))) # label(lameq_f158) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1056 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> ap(ap(c_2Eprim__rec_2ESIMP__REC(arr(ty_2Enum_2Enum,A_27a)),k(ty_2Enum_2Enum,V0x)),f163(A_27a,V1f)) = ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f))))))) # label(ax_thm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1057 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),c_2Enum_2E0),V2n) = V0x)) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(V1f,ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),V3m),ap(c_2Eprim__rec_2EPRE,V4n))),V4n) = ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V3m)),V4n))))))))))) # label(conj_thm_2Eprim__rec_2EPRIM__REC__EQN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1058 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1059 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V3fun (mem(V3fun,arr(ty_2Enum_2Enum,A_27a)) -> (all V4n ap(ap(V1f,ap(V3fun,ap(c_2Eprim__rec_2EPRE,V4n))),V4n) = ap(f162(A_27a,V1f,V3fun),V4n)))))) # label(lameq_f162) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1060 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V0n)))) # label(conj_thm_2Eprim__rec_2ELESS__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1061 (all A_27a all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V3x ap(f155(A_27a,V0f),V3x) = f154(A_27a,V3x,V0f)))) # label(lameq_f155) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1062 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n))) -> (V0m != V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1063 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2EPRIM__REC(A_27a),arr(A_27a,arr(arr(A_27a,arr(ty_2Enum_2Enum,A_27a)),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1064 (all V2x ap(f151,V2x) = f150(V2x)) # label(lameq_f151) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1065 (all V4x ap(f153,V4x) = f152(V4x)) # label(lameq_f153) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1066 (all A_27a (ne(A_27a) -> c_2Eprim__rec_2Emeasure(A_27a) = ap(c_2Erelation_2Einv__image(A_27a,ty_2Enum_2Enum),c_2Eprim__rec_2E_3C))) # label(ax_thm_2Eprim__rec_2Emeasure__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1067 (all A_27a all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2fn1 ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),ap(V2fn1,c_2Enum_2E0)),V0e)),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f164(A_27a,V1f,V2fn1))) = ap(f165(A_27a,V0e,V1f),V2fn1)))))) # label(lameq_f165) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1068 (all A_27a all V5x (mem(V5x,A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V6y ap(f156(A_27a,V5x,V0f),V6y) = ap(ap(c_2Emin_2E_3D(A_27a),V6y),ap(V0f,V5x))))))) # label(lameq_f156) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1069 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,arr(A_27a,ty_2Enum_2Enum)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eprim__rec_2Emeasure(A_27a),V0m))))))) # label(conj_thm_2Eprim__rec_2EWF__measure) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1070 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (exists V3fun (mem(V3fun,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3fun),V0x),V1f),V2n)))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1071 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n ap(f149(V0m),V1n) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),ap(c_2Enum_2ESUC,V1n))))) # label(lameq_f149) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1072 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (exists V2fn (mem(V2fn,arr(ty_2Enum_2Enum,A_27a)) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(V1f,V3n),ap(V2fn,V3n)) = ap(V2fn,ap(c_2Enum_2ESUC,V3n)))) & V0e = ap(V2fn,c_2Enum_2E0))))))))) # label(conj_thm_2Eprim__rec_2Enum__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1073 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V3fun f162(A_27a,V1f,V3fun) = ap(f163(A_27a,V1f),V3fun)))) # label(lameq_f163) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1074 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> (exists V2P (mem(V2P,arr(ty_2Enum_2Enum,bool)) & -p(ap(V2P,V1n)) & p(ap(V2P,V0m)) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(V2P,ap(c_2Enum_2ESUC,V3n))) -> p(ap(V2P,V3n)))))))))))) # label(ax_thm_2Eprim__rec_2ELESS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1075 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != V0n)) # label(conj_thm_2Eprim__rec_2ESUC__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1076 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1077 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n <-> ap(c_2Enum_2ESUC,V1n) = ap(c_2Enum_2ESUC,V0m)))))) # label(conj_thm_2Eprim__rec_2EINV__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1078 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1079 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = V0m | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1080 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) | V0m = V1n))))) # label(conj_thm_2Eprim__rec_2ELESS__LEMMA1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1081 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V0m)))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V0m))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1082 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Enum_2Enum,A_27a)),f165(A_27a,V0e,V1f))))))))) # label(conj_thm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1083 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),V2m) = ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),V2m),ap(c_2Eprim__rec_2EPRE,V2m)))))))))) # label(ax_thm_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1084 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Enum_2E0)))) # label(conj_thm_2Eprim__rec_2ENOT__LESS__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1085 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2Emeasure(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Eprim__rec_2Emeasure) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1086 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Erelation_2ERTC(ty_2Enum_2Enum),f153),V0m),V1n)) <-> p(ap(ap(ap(c_2Erelation_2ETC(ty_2Enum_2Enum),f151),V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1087 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Emin_2E_40(ty_2Enum_2Enum),f149(V0m))) = ap(c_2Eprim__rec_2EPRE,V0m))) # label(ax_thm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.19 1088 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__LEMMA2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1089 (all A_27a all V3x (mem(V3x,A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V4y ap(f154(A_27a,V3x,V0f),V4y) = ap(ap(c_2Emin_2E_3D(A_27a),V4y),ap(V0f,V3x))))))) # label(lameq_f154) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1090 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (-(exists V1f ((all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(V0R,ap(V1f,ap(c_2Enum_2ESUC,V2n))),ap(V1f,V2n))))) & mem(V1f,arr(ty_2Enum_2Enum,A_27a)))) <-> p(ap(c_2Eprim__rec_2Ewellfounded(A_27a),V0R))))))) # label(ax_thm_2Eprim__rec_2Ewellfounded__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1091 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> p(ap(c_2Eprim__rec_2Ewellfounded(A_27a),V0R))))))) # label(conj_thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1092 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),arr(A_27a,arr(arr(A_27a,arr(ty_2Enum_2Enum,A_27a)),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a))))))) # label(mem_c_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1093 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2fn1 (mem(V2fn1,arr(ty_2Enum_2Enum,A_27a)) -> (all V3n ap(f164(A_27a,V1f,V2fn1),V3n) = ap(ap(c_2Emin_2E_3D(A_27a),ap(V2fn1,ap(c_2Enum_2ESUC,V3n))),ap(ap(V1f,ap(V2fn1,V3n)),V3n))))))) # label(lameq_f164) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1094 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1095 (all V4x (mem(V4x,ty_2Enum_2Enum) -> (all V5y ap(f152(V4x),V5y) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V5y),ap(c_2Enum_2ESUC,V4x))))) # label(lameq_f152) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1096 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2g1 (mem(V2g1,arr(ty_2Enum_2Enum,A_27a)) -> (all V3g2 (mem(V3g2,arr(ty_2Enum_2Enum,A_27a)) -> (all V4m1 (mem(V4m1,ty_2Enum_2Enum) -> (all V5m2 (mem(V5m2,ty_2Enum_2Enum) -> (p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3g2),V0x),V1f),V5m2)) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V2g1),V0x),V1f),V4m1)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V6n),V5m2)) & p(ap(ap(c_2Eprim__rec_2E_3C,V6n),V4m1)) -> ap(V3g2,V6n) = ap(V2g1,V6n))))))))))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1097 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ESUC__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1098 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1099 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(A_27a,arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,bool))))))) # label(mem_c_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1100 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f_27 (mem(V1f_27,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (exists V3g (ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f_27),V2n) = ap(V3g,V2n) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3g),V0x),V1f_27),ap(c_2Enum_2ESUC,V2n))) & mem(V3g,arr(ty_2Enum_2Enum,A_27a)))))))))))) # label(ax_thm_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1101 (all V0x ap(f159,V0x) = f158(V0x)) # label(lameq_f159) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1102 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2a (mem(V2a,A_27a) -> (p(ap(V0P,V2a)) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> (exists V4y (p(ap(V0P,V4y)) & p(ap(ap(V1R,V3x),V4y)) & mem(V4y,A_27a)))))) -> (exists V5f ((all V6n (mem(V6n,ty_2Enum_2Enum) -> p(ap(ap(V1R,ap(V5f,V6n)),ap(V5f,ap(c_2Enum_2ESUC,V6n)))) & p(ap(V0P,ap(V5f,V6n))))) & V2a = ap(V5f,c_2Enum_2E0) & mem(V5f,arr(ty_2Enum_2Enum,A_27a))))))))))))) # label(conj_thm_2Eprim__rec_2EDC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1103 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1104 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V2m)) = ap(ap(V1f,ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),V2m)),V2m))) & ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),c_2Enum_2E0) = V0x)))))) # label(conj_thm_2Eprim__rec_2EPRIM__REC__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1105 (all A_27a all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V0x (mem(V0x,A_27a) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3y (mem(V3y,A_27a) -> (all V4g ap(f160(A_27a,V1f,V0x,V2n,V3y),V4g) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V4g),V0x),V1f),ap(c_2Enum_2ESUC,V2n))),ap(ap(c_2Emin_2E_3D(A_27a),V3y),ap(V4g,V2n)))))))))))) # label(lameq_f160) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1106 (all A_27a all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V5x ap(f157(A_27a,V0f),V5x) = f156(A_27a,V5x,V0f)))) # label(lameq_f157) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1107 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1m (mem(V1m,A_27a) -> (all V2n (mem(V2n,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),f157(A_27a,V0f)),V1m),V2n)) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),f155(A_27a,V0f)),ap(V0f,V1m)),V2n))))))))))) # label(conj_thm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1108 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = V0m -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ENOT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1109 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Eprim__rec_2Emeasure(A_27a),V0f),V1x),V2y)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1x)),ap(V0f,V2y)))))))))))) # label(conj_thm_2Eprim__rec_2Emeasure__thm) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1110 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V0m) = V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2EEQ__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1111 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2Ewellfounded(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Eprim__rec_2Ewellfounded) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1112 (all A_27a all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V3y ap(f161(A_27a,V2n,V0x,V1f),V3y) = ap(c_2Ebool_2E_3F(arr(ty_2Enum_2Enum,A_27a)),f160(A_27a,V1f,V0x,V2n,V3y))))))))) # label(lameq_f161) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1113 (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y ap(f150(V2x),V3y) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3y),ap(c_2Enum_2ESUC,V2x))))) # label(lameq_f150) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1114 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f161(A_27a,V2n,V0x,V1f))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1115 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,ap(c_2Enum_2ESUC,V0m)) = V0m)) # label(conj_thm_2Eprim__rec_2EPRE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1116 (all A_27a (ne(A_27a) -> (all V0fun (mem(V0fun,arr(ty_2Enum_2Enum,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> ap(V0fun,ap(c_2Enum_2ESUC,V4m)) = ap(V2f,ap(V0fun,V4m))))) & V1x = ap(V0fun,c_2Enum_2E0) <-> p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V0fun),V1x),V2f),V3n))))))))))))) # label(ax_thm_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1117 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2ESIMP__REC(A_27a),arr(A_27a,arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1118 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> V0x = ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),c_2Enum_2E0) & (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(V1f,ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),V2m)) = ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V2m)))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1119 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V1x (p(ap(ap(c_2Eposet_2Ebottom(A_27a),V0p),V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Eposet_2Ecomplete__bottom) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1120 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1c (mem(V1c,arr(A_27a,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Elub(A_27a),V0p),V1c),V2x))))))))))) # label(conj_thm_2Eposet_2Ecomplete__up) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1121 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1c (mem(V1c,arr(A_27a,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V2x (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),V0p),V1c),V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eposet_2Ecomplete__down) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1122 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f166(A_27a,V0s,V2p)),V3x)) <-> p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x))))))))))))) # label(conj_thm_2Eposet_2Eglb__pred) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1123 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V3x)) & p(ap(ap(V1r,V3x),V4y)) & p(ap(V0s,V4y)) -> p(ap(ap(V1r,ap(V2f,V3x)),ap(V2f,V4y)))))))) <-> p(ap(ap(c_2Eposet_2Emonotonic(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f))))))))))) # label(ax_thm_2Eposet_2Emonotonic__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1124 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> (exists V1x (mem(V1x,A_27a) & p(ap(ap(c_2Eposet_2Etop(A_27a),V0p),V1x))))))))) # label(conj_thm_2Eposet_2Ecomplete__top) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1125 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Elub(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Elub) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1126 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Elfp(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Elfp) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1127 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> V0s = ap(c_2Eposet_2Ecarrier(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)))))))) # label(ax_thm_2Eposet_2Ecarrier__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1128 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V2x (p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski__lfp) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1129 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Egfp(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Egfp) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1130 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2c (mem(V2c,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V2c,V3x)) & p(ap(V2c,V4y)) & p(ap(V0s,V4y)) & p(ap(V0s,V3x)) -> p(ap(ap(V1r,V4y),V3x)) | p(ap(ap(V1r,V3x),V4y))))))) <-> p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2c))))))))))) # label(ax_thm_2Eposet_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1131 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> (exists V2x (p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x)) & mem(V2x,A_27a))) & (exists V3x (mem(V3x,A_27a) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V3x))))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1132 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3x (mem(V3x,A_27a) -> (ap(V2f,V3x) = V3x & (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(ap(V1r,V4y),ap(V2f,V4y))) -> p(ap(ap(V1r,V4y),V3x))))) & p(ap(V0s,V3x)) <-> p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f),V3x))))))))))))) # label(ax_thm_2Eposet_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1133 (all A_27b all A_27a all V4g (mem(V4g,arr(A_27a,A_27b)) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (all V5x ap(f167(A_27b,A_27a,V4g,V3f,V2r,V0t),V5x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V0t,V5x)),ap(ap(V2r,ap(V3f,V5x)),ap(V4g,V5x)))))))))))) # label(lameq_f167) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1134 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x)) <-> (all V5z (mem(V5z,A_27a) -> ((all V6y (mem(V6y,A_27a) -> (p(ap(V0s,V6y)) & p(ap(V2p,V6y)) -> p(ap(ap(V1r,V5z),V6y))))) & p(ap(V0s,V5z)) -> p(ap(ap(V1r,V5z),V3x))))) & (all V4y (mem(V4y,A_27a) -> (p(ap(V2p,V4y)) & p(ap(V0s,V4y)) -> p(ap(ap(V1r,V3x),V4y))))) & p(ap(V0s,V3x))))))))))))) # label(ax_thm_2Eposet_2Eglb__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1135 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V2x)) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V3x_27)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> V3x_27 = V2x))))))))))) # label(conj_thm_2Eposet_2Egfp__unique) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1136 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> ap(ap(c_2Epair_2E_2C(arr(arr(A_27a,A_27b),bool),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool))),ap(ap(c_2Eposet_2Efunction(A_27a,A_27b),V0t),V1s)),f169(A_27b,A_27a,V0t,V2r)) = ap(ap(c_2Eposet_2Epointwise__lift(A_27a,A_27b),V0t),ap(ap(c_2Epair_2E_2C(arr(A_27b,bool),arr(A_27b,arr(A_27b,bool))),V1s),V2r)))))))))))) # label(ax_thm_2Eposet_2Epointwise__lift__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1137 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,arr(A_27a,bool)) -> (all V1b (mem(V1b,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27b),V0a),V1b),V2f)) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(V0a,V3x)) -> p(ap(V1b,ap(V2f,V3x))))))))))))))))) # label(ax_thm_2Eposet_2Efunction__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1138 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V3f f168(A_27b,A_27a,V0t,V2r,V3f) = ap(f169(A_27b,A_27a,V0t,V2r),V3f)))))) # label(lameq_f169) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1139 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f166(A_27a,V0s,V2p)),V3x)) <-> p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x))))))))))))) # label(conj_thm_2Eposet_2Elub__pred) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1140 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> p(ap(c_2Eposet_2Ecomplete(arr(A_27b,A_27a)),ap(ap(c_2Eposet_2Epointwise__lift(A_27b,A_27a),V1t),V0p)))))))))))) # label(conj_thm_2Eposet_2Ecomplete__pointwise) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1141 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eposet(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),bool)))) # label(mem_c_2Eposet_2Eposet) # label(axiom) # label(non_clause). [assumption]. 6.17/6.20 1142 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3c (mem(V3c,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c),V4x)) & p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c)) -> p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f171(A_27a,V2f,V3c,V0s)),ap(V2f,V4x)))))))) <-> p(ap(ap(c_2Eposet_2Edown__continuous(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f))))))))))) # label(ax_thm_2Eposet_2Edown__continuous__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1143 (all A_27a all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V5y ap(f171(A_27a,V2f,V3c,V0s),V5y) = ap(c_2Ebool_2E_3F(A_27a),f170(A_27a,V0s,V3c,V2f,V5y))))))))) # label(lameq_f171) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1144 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V2x))))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski__gfp) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1145 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V3x_27)) & p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> V2x = V3x_27))))))))))) # label(conj_thm_2Eposet_2Elfp__unique) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1146 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(ap(c_2Eposet_2Econtinuous(A_27a),V0p),V1f)) <-> p(ap(ap(c_2Eposet_2Edown__continuous(A_27a),V0p),V1f)) & p(ap(ap(c_2Eposet_2Eup__continuous(A_27a),V0p),V1f))))))))) # label(ax_thm_2Eposet_2Econtinuous__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1147 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eglb(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Eglb) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1148 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Edown__continuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Edown__continuous) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1149 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ebottom(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Ebottom) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1150 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4g ap(c_2Ebool_2E_21(A_27a),f167(A_27b,A_27a,V4g,V3f,V2r,V0t)) = ap(f168(A_27b,A_27a,V0t,V2r,V3f),V4g)))))))) # label(lameq_f168) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1151 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Etop(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Etop) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1152 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(V0s,V2x)) & (all V3y (mem(V3y,A_27a) -> (p(ap(V0s,V3y)) -> p(ap(ap(V1r,V3y),V2x))))) <-> p(ap(ap(c_2Eposet_2Etop(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2x))))))))))) # label(ax_thm_2Eposet_2Etop__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1153 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) <-> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> (p(ap(V0s,V6x)) & p(ap(V0s,V8z)) & p(ap(ap(V1r,V7y),V8z)) & p(ap(ap(V1r,V6x),V7y)) & p(ap(V0s,V7y)) -> p(ap(ap(V1r,V6x),V8z))))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0s,V4x)) & p(ap(V0s,V5y)) & p(ap(ap(V1r,V5y),V4x)) & p(ap(ap(V1r,V4x),V5y)) -> V5y = V4x))))) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0s,V3x)) -> p(ap(ap(V1r,V3x),V3x))))) & (exists V2x (mem(V2x,A_27a) & p(ap(V0s,V2x))))))))))) # label(ax_thm_2Eposet_2Eposet__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1154 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> ((all V5z (mem(V5z,A_27a) -> (p(ap(V0s,V5z)) & (all V6y (mem(V6y,A_27a) -> (p(ap(V2p,V6y)) & p(ap(V0s,V6y)) -> p(ap(ap(V1r,V6y),V5z))))) -> p(ap(ap(V1r,V3x),V5z))))) & (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(V2p,V4y)) -> p(ap(ap(V1r,V4y),V3x))))) & p(ap(V0s,V3x)) <-> p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x))))))))))))) # label(ax_thm_2Eposet_2Elub__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1155 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) <-> (all V1c (mem(V1c,arr(A_27a,bool)) -> (exists V3x (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),V0p),V1c),V3x)) & mem(V3x,A_27a))) & (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Elub(A_27a),V0p),V1c),V2x))))))))))) # label(ax_thm_2Eposet_2Ecomplete__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1156 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V5y (mem(V5y,A_27a) -> (all V6z ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2E_2F_5C,ap(V0s,V6z)),ap(V3c,V6z))),ap(ap(c_2Emin_2E_3D(A_27a),V5y),ap(V2f,V6z))) = ap(f170(A_27a,V0s,V3c,V2f,V5y),V6z)))))))))) # label(lameq_f170) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1157 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Econtinuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Econtinuous) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1158 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eup__continuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Eup__continuous) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1159 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Erelation(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Erelation) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1160 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eposet_2Efunction(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Eposet_2Efunction) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1161 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) & p(ap(V0s,V2x)) -> p(ap(ap(V1r,V2x),V2x))))))))))) # label(conj_thm_2Eposet_2Eposet__refl) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1162 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Echain(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eposet_2Echain) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1163 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) -> (exists V2x (mem(V2x,A_27a) & p(ap(V0s,V2x))))))))))) # label(conj_thm_2Eposet_2Eposet__nonempty) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1164 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Eposet_2Ebottom(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2x)) <-> (all V3y (mem(V3y,A_27a) -> (p(ap(V0s,V3y)) -> p(ap(ap(V1r,V2x),V3y))))) & p(ap(V0s,V2x))))))))))) # label(ax_thm_2Eposet_2Ebottom__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1165 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ecarrier(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Ecarrier) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1166 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V4j ap(f166(A_27a,V0s,V2p),V4j) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0s,V4j)),ap(V2p,V4j))))))) # label(lameq_f166) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1167 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ecomplete(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),bool)))) # label(mem_c_2Eposet_2Ecomplete) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1168 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eposet_2Epointwise__lift(A_27a,A_27b),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(arr(A_27b,bool),arr(A_27b,arr(A_27b,bool))),ty_2Epair_2Eprod(arr(arr(A_27a,A_27b),bool),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))))))) # label(mem_c_2Eposet_2Epointwise__lift) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1169 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> V1r = ap(c_2Eposet_2Erelation(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)))))))) # label(ax_thm_2Eposet_2Erelation__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1170 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) & p(ap(V0s,V2x)) & p(ap(V0s,V3y)) & p(ap(ap(V1r,V3y),V2x)) & p(ap(ap(V1r,V2x),V3y)) -> V2x = V3y))))))))))) # label(conj_thm_2Eposet_2Eposet__antisym) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1171 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(V0s,V3x)) & (all V4y (mem(V4y,A_27a) -> (p(ap(ap(V1r,ap(V2f,V4y)),V4y)) & p(ap(V0s,V4y)) -> p(ap(ap(V1r,V3x),V4y))))) & ap(V2f,V3x) = V3x <-> p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f),V3x))))))))))))) # label(ax_thm_2Eposet_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1172 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (p(ap(ap(c_2Eposet_2Eup__continuous(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f)) <-> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c),V4x)) & p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c)) -> p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f171(A_27a,V2f,V3c,V0s)),ap(V2f,V4x))))))))))))))))) # label(ax_thm_2Eposet_2Eup__continuous__def) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1173 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(V0s,V2x)) & p(ap(V0s,V4z)) & p(ap(ap(V1r,V3y),V4z)) & p(ap(ap(V1r,V2x),V3y)) & p(ap(V0s,V3y)) & p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) -> p(ap(ap(V1r,V2x),V4z))))))))))))))) # label(conj_thm_2Eposet_2Eposet__trans) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1174 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Emonotonic(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Emonotonic) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1175 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (V0m = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V2p)),V1n) & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__STRONG__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1176 (all V0m (mem(V0m,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EMULT__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1177 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1178 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0m))))))))) # label(conj_thm_2Earithmetic_2EEXP2__LT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1179 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EMOD,V1j),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1j),V2k)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1180 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V2m)),ap(V0f,V3n))))))))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__TC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1181 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0z),V1y)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V2x),V1y))))))))) # label(conj_thm_2Earithmetic_2ELE__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1182 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V1m)),ap(c_2Eprim__rec_2EPRE,V0n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)))))))) # label(conj_thm_2Earithmetic_2EINV__PRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1183 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ap(ap(c_2Earithmetic_2EMOD,V3x),V2n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2n),V3x)),V2n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1184 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1185 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1186 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1q),V0p)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2D,V0p),V1q)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q))))))))) # label(conj_thm_2Earithmetic_2EEXP__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1187 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1188 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V0p)) -> (ap(ap(c_2Earithmetic_2E_2D,V0p),V1n) = ap(ap(c_2Earithmetic_2E_2D,V0p),V2m) <-> V2m = V1n)))))))) # label(conj_thm_2Earithmetic_2ESUB__CANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1189 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1190 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) | V0m = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1191 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELT__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1192 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,V2z) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))),V1y) <-> ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))) = V1y & ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))) = c_2Enum_2E0) & (ap(c_2Earithmetic_2ENUMERAL,V2z) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))),V1y) <-> V1y = ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))) & ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))) = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1193 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n))))))))) # label(conj_thm_2Earithmetic_2EINV__PRE__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1194 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) | (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0n = ap(ap(c_2Earithmetic_2E_2B,V2p),V1m))))))) # label(conj_thm_2Earithmetic_2ELESS__OR__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1195 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0n),V0n) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) # label(conj_thm_2Earithmetic_2ETIMES2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1196 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2EFACT,V0n))))) # label(conj_thm_2Earithmetic_2EFACT__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1197 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0)))))) # label(ax_thm_2Earithmetic_2EBIT2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1198 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) -> (V0x = ap(ap(c_2Earithmetic_2EMOD,V0x),V1y) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)))))))) # label(conj_thm_2Earithmetic_2EX__MOD__Y__EQ__X) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1199 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__OR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1200 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V2x)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z)))))))))) # label(conj_thm_2Earithmetic_2ELT__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1201 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,V0x),V2z))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x)))))))))) # label(conj_thm_2Earithmetic_2EDIV__LT__X) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1202 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1203 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1204 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (V0x = c_2Enum_2E0 | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1b)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,V1b),V0x)))))))) # label(conj_thm_2Earithmetic_2EX__LT__EXP__X__IFF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1205 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2ESUB__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1206 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(ap(c_2Earithmetic_2E_2B,V2y),V1z))),ap(ap(c_2Earithmetic_2E_2B,V2y),ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__PLUS__LE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1207 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1208 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1i)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i)))))))))) # label(conj_thm_2Earithmetic_2ELESS__MULT__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1209 (all V0b1 (mem(V0b1,ty_2Enum_2Enum) -> (all V1b2 (mem(V1b2,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EEXP,V0b1),V2x) = ap(ap(c_2Earithmetic_2EEXP,V1b2),V2x) <-> V2x = c_2Enum_2E0 | V0b1 = V1b2))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1210 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c))))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__SUB__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1211 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,V1n)) | p(ap(c_2Earithmetic_2EEVEN,V0m)) <-> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__MULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1212 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V0n) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2EABS__DIFF__EQS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1213 (all V0n1 (mem(V0n1,ty_2Enum_2Enum) -> (all V1n2 (mem(V1n2,ty_2Enum_2Enum) -> (all V2m1 (mem(V2m1,ty_2Enum_2Enum) -> (all V3m2 (mem(V3m2,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n1),V1n2)),ap(ap(c_2Earithmetic_2E_2B,V2m1),V3m2))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0n1),V2m1)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1n2),V3m2)))))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUMS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1214 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELEFT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1215 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n))) # label(ax_thm_2Earithmetic_2EADD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1216 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1m)),V2n))))) # label(ax_thm_2Earithmetic_2EADD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1217 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3z (mem(V3z,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) & p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V3z)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V3z))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1218 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) <-> c_2Enum_2E0 = V1n | ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0m))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1219 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V0n),V1x)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1220 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n)) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n)))) # label(conj_thm_2Earithmetic_2EONE__MOD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1221 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V0m),V1n))))) # label(ax_thm_2Earithmetic_2EMIN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1222 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) <-> V0a = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2Efindq__eq__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1223 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0m = ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1224 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V1x) != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y)))))) # label(conj_thm_2Earithmetic_2EMOD__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1225 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EADD__SYM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1226 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.21 1227 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) & V0m = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) & V0m = ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m))))) # label(conj_thm_2Earithmetic_2EMULT__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1228 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) | V0m = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2ELESS__0__CASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1229 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V0n),c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMODEQ__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1230 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V0n) = V1q))))) # label(conj_thm_2Earithmetic_2EMULT__DIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1231 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2ESUC__NOT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1232 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1233 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (exists V3n (p(ap(ap(c_2Eprim__rec_2E_3C,V2b),ap(V0f,V3n))) & mem(V3n,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1234 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1a),V2b))))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1235 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) <-> V1n = V0m))))))) # label(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1236 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1237 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ENRC__1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1238 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & V1n != ap(c_2Enum_2ESUC,V0m) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__NOT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1239 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1240 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0n)),ap(c_2Earithmetic_2EFACT,V0n)) = ap(c_2Earithmetic_2EFACT,ap(c_2Enum_2ESUC,V0n)))) # label(ax_thm_2Earithmetic_2EFACT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1241 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,V1x),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1242 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n)) | V1n = V0m <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n))))))) # label(ax_thm_2Earithmetic_2EGREATER__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1243 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> V1n = V0m | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(ax_thm_2Earithmetic_2ELESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1244 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1245 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Enum_2ESUC,V0n))) # label(conj_thm_2Earithmetic_2ESUC__ONE__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1246 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) -> (exists V2p (ap(ap(c_2Earithmetic_2E_2B,V2p),V1n) = V0m & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1247 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__RTC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1248 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1249 (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V1a ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f182(V1a,V0f)) = ap(f183(V0f),V1a)))) # label(lameq_f183) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1250 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2e (mem(V2e,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,V1x),V2e)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2e)),V0n)))))))) # label(conj_thm_2Earithmetic_2EEXP__MOD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1251 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V2m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V1n)) -> (ap(ap(c_2Earithmetic_2E_2D,V2m),V0p) = ap(ap(c_2Earithmetic_2E_2D,V1n),V0p) <-> V1n = V2m)))))))) # label(conj_thm_2Earithmetic_2ECANCEL__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1252 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = c_2Enum_2E0 | V1n = c_2Enum_2E0 <-> ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = V0m))))) # label(conj_thm_2Earithmetic_2ESUB__EQ__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1253 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1254 (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V2m ap(f182(V1a,V0f),V2m) = f181(V2m,V1a,V0f)))))) # label(lameq_f182) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1255 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2ERIGHT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1256 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n)))))))) # label(conj_thm_2Earithmetic_2EPRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1257 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__MULT2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1258 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,A_27a) -> (all V1g (mem(V1g,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0f),ap(V1g,ap(c_2Eprim__rec_2EPRE,V2n))) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2n),V0f),V1g))))))))) # label(conj_thm_2Earithmetic_2Enum__case__compute) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1259 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2Enat__elim____magic,V0n) = V0n)) # label(ax_thm_2Earithmetic_2Enat__elim____magic) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1260 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2EADD__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1261 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__NONZERO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1262 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V3d ap(f179(V0a,V1m),V3d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V3d)),V0a),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V3d))))))))) # label(lameq_f179) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1263 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EMULT__INCREASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1264 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,V0n),V0n) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2EDIV,V0n),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EDIVMOD__ID) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1265 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m) <-> V1i = V0m))))))) # label(conj_thm_2Earithmetic_2EMULT__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1266 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V1m = V0n <-> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m)))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1267 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1268 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q)) = ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2B,V0p),V1q)))))))) # label(conj_thm_2Earithmetic_2EEXP__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1269 (all V0c (mem(V0c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0c),V0c) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2ESUB__EQUAL__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1270 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) -> ((exists V3k (mem(V3k,ty_2Enum_2Enum) & (exists V4r (p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q)) & p(ap(V0P,V3k)) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r) = V1p & mem(V4r,ty_2Enum_2Enum))))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1p),V2q))))))))))) # label(conj_thm_2Earithmetic_2EDIV__P) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1271 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x)) | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0x),V1y)))))))) # label(conj_thm_2Earithmetic_2EONE__LT__MULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1272 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((all V2m (mem(V2m,ty_2Enum_2Enum) -> (V1n = ap(c_2Enum_2ESUC,V2m) -> p(ap(V0P,V2m))) & (V1n = c_2Enum_2E0 -> p(ap(V0P,c_2Enum_2E0))))) <-> p(ap(V0P,ap(c_2Eprim__rec_2EPRE,V1n)))))))) # label(conj_thm_2Earithmetic_2EPRE__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1273 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n)))))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n)))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1274 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z)),V1y)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z))))))))))) # label(conj_thm_2Earithmetic_2EX__LT__DIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1275 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD__INV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1276 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Earithmetic_2EMOD,V0m),V1n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__MOD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1277 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1x)))),V0n) = ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))) & ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x)))),V0n) = ap(ap(c_2Earithmetic_2EEXP,V0n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Earithmetic_2EEXP__SUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1278 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V0m)))) # label(conj_thm_2Earithmetic_2ELESS__EQ__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1279 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0m),ap(ap(c_2Earithmetic_2EMAX,V1n),V2p)) = ap(ap(c_2Earithmetic_2EMAX,ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2EMAX__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1280 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),V2k)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1j),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__PLUS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1281 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> c_2Enum_2E0 != ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m))))) # label(conj_thm_2Earithmetic_2ENOT__EXP__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1282 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> V0a = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0a),V1c)),V1c))))) # label(conj_thm_2Earithmetic_2EADD__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1283 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n != V0m <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__NUM__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1284 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,V0m),c_2Enum_2E0))) # label(ax_thm_2Earithmetic_2EEXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1285 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V1m),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(ap(c_2Earithmetic_2EEXP,V1m),V2n)))))) # label(ax_thm_2Earithmetic_2EEXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1286 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> (exists V2k (mem(V2k,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2D,V1n),V2k) = V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1287 (all V0k (mem(V0k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Enum_2ESUC,c_2Enum_2E0)) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2EMOD__ONE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1288 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Enum_2ESUC,V0m))) # label(conj_thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1289 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (ap(ap(c_2Earithmetic_2EMOD,V2b),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) <-> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1a)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V2b)),V0n))))))))) # label(conj_thm_2Earithmetic_2ESUC__MOD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1290 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (mem(V1n,ty_2Enum_2Enum) & p(ap(V0P,V1n)))) -> (exists V2n (p(ap(V0P,V2n)) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V2n)) -> -p(ap(V0P,V3m))))) & mem(V2n,ty_2Enum_2Enum)))))) # label(conj_thm_2Earithmetic_2EWOP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1291 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELE__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1292 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Enum_2ESUC,V1n)),V2x) = ap(V0f,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V1n),V2x)))))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1293 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1zc (mem(V1zc,A_27a) -> (all V2sc (mem(V2sc,arr(ty_2Enum_2Enum,A_27a)) -> (all V3v (mem(V3v,A_27a) -> (V0n = c_2Enum_2E0 & V3v = V1zc | (exists V4x (V0n = ap(c_2Enum_2ESUC,V4x) & ap(V2sc,V4x) = V3v & mem(V4x,ty_2Enum_2Enum))) <-> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V0n),V1zc),V2sc) = V3v))))))))))) # label(conj_thm_2Earithmetic_2Enum__case__eq) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1294 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V4y)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V4y),V5z)) -> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V5z))))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__I) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1295 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (V0x = ap(ap(c_2Earithmetic_2EDIV,V1y),V2z) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0x)),V2z))))))))))) # label(conj_thm_2Earithmetic_2EDIV__EQ__X) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1296 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c) = ap(ap(c_2Earithmetic_2E_2D,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c)))))))) # label(conj_thm_2Earithmetic_2ESUB__PLUS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1297 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> (exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y))))))))))))) # label(conj_thm_2Earithmetic_2ERTC__NRC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1298 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)),ap(ap(c_2Earithmetic_2E_2B,V0x),V1z))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__LE__SUM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1299 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 <-> p(ap(c_2Earithmetic_2EEVEN,V0x))))) # label(conj_thm_2Earithmetic_2EEVEN__MOD2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1300 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (V0x = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & V1y = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) <-> ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1301 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,V0m) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EPRE__SUB1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1302 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V0n)))),V0n)),ap(ap(c_2Earithmetic_2E_2A,V2a),V1m)))))))))) # label(conj_thm_2Earithmetic_2Efindq__divisor) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1303 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__OR) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1304 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0m)) & p(ap(c_2Earithmetic_2EODD,V1n)) <-> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EODD__MULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1305 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1306 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = c_2Enum_2E0 & c_2Enum_2E0 = V0m <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EADD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1307 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y)))))))) # label(conj_thm_2Earithmetic_2EONE__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1308 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) | c_2Enum_2E0 = V1y))))) # label(conj_thm_2Earithmetic_2EZERO__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1309 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMIN,c_2Enum_2E0),V0n) & ap(ap(c_2Earithmetic_2EMIN,V0n),c_2Enum_2E0) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2EMIN__0) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1310 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2ERIGHT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1311 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,c_2Enum_2E0))) = ap(c_2Earithmetic_2EBIT1,V0n))) # label(ax_thm_2Earithmetic_2EBIT1) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1312 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,V2m),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__SUB) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1313 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V2m (p(ap(V0P,ap(c_2Enum_2ESUC,V2m))) & mem(V2m,ty_2Enum_2Enum))) | p(ap(V0P,c_2Enum_2E0)) <-> (exists V1n (p(ap(V0P,V1n)) & mem(V1n,ty_2Enum_2Enum)))))) # label(conj_thm_2Earithmetic_2EEXISTS__NUM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1314 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ((exists V3q (mem(V3q,ty_2Enum_2Enum) & V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V0n)),V2r) & p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V0n)))) -> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V2r))))))) # label(conj_thm_2Earithmetic_2EMOD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1315 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1m),V2n))) <-> (all V3q (mem(V3q,ty_2Enum_2Enum) -> (all V4r (mem(V4r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) & V1m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r) -> p(ap(V0P,V3q))))))))))))))) # label(conj_thm_2Earithmetic_2EDIV__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1316 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> V0n = V1m))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1317 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ((exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V3n)),V1x),V2y)))) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ETC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1318 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1319 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),V0n) = V0n & V0n = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EABS__DIFF__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1320 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a))) -> (all V1g (mem(V1g,arr(ty_2Enum_2Enum,A_27a)) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) = ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))))) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) = ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))))) <-> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(V1g,ap(c_2Enum_2ESUC,V2n)) = ap(ap(V0f,V2n),ap(c_2Enum_2ESUC,V2n))))))))))) # label(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1321 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n))) <-> p(ap(c_2Earithmetic_2EODD,V1m)) | V0n = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EODD__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1322 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1323 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),V1m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n))))))) # label(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1324 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z)) <-> (exists V5y (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) & mem(V5y,A_27a)))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__EQN) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1325 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1326 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(c_2Earithmetic_2EODD,V0m)) -> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EODD__EXP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1327 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1d (mem(V1d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1d)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V0n),V1d)),V0n))))))) # label(conj_thm_2Earithmetic_2EDIV__LESS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1328 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (ap(c_2Enum_2ESUC,V0m) = V1n <-> V0m = ap(c_2Eprim__rec_2EPRE,V1n))))))) # label(conj_thm_2Earithmetic_2EPRE__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1329 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (-p(ap(c_2Earithmetic_2EODD,V0n)) <-> p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,V0n)))))) # label(ax_thm_2Earithmetic_2EODD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1330 $F <-> p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2EODD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1331 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f179(V0a,V1m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n))))))))) # label(conj_thm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1332 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(c_2Earithmetic_2EEVEN,V0m)) -> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__EXP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1333 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2ENRC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Enum_2Enum,arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1334 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> (exists V2p (ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = V1n & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1335 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1a),V2b)) | V0n = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1336 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__MULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1337 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2EMIN,V0m),ap(ap(c_2Earithmetic_2EMIN,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2EMIN__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1338 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (exists V2m (mem(V2m,ty_2Enum_2Enum) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)))))))))) # label(conj_thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1339 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> V0m = V1n | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) | p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__CASES) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1340 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m))))))))) # label(conj_thm_2Earithmetic_2EMAX__LE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1341 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> ((all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) -> p(ap(V0P,V2m))))) -> p(ap(V0P,V1n))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Earithmetic_2ECOMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1342 (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V4q ap(V0f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V1a),V4q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V3n),V4q))),V3n))) = ap(f180(V1a,V2m,V3n,V0f),V4q)))))))))) # label(lameq_f180) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1343 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -(p(ap(c_2Earithmetic_2EODD,V0n)) & p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__AND__ODD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1344 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-(p(ap(c_2Earithmetic_2EODD,V0m)) <-> p(ap(c_2Earithmetic_2EODD,V1n))) <-> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EODD__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1345 (all A_27a (ne(A_27a) -> (all V3R (mem(V3R,arr(A_27a,arr(A_27a,bool))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> ((exists V7z (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),V4n),V7z),V6y)) & p(ap(ap(V3R,V5x),V7z)) & mem(V7z,A_27a))) <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),ap(c_2Enum_2ESUC,V4n)),V5x),V6y))))))))))) & (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V2y = V1x <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y))))))))))) # label(ax_thm_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1346 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m != V1n <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__LT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1347 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))))))))) # label(conj_thm_2Earithmetic_2ELT__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1348 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))))) # label(conj_thm_2Earithmetic_2EODD__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1349 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V1x),ap(ap(c_2Earithmetic_2E_2A,V2y),V0z)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EEXP,V1x),V2y)),V0z))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1350 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EDIV,c_2Enum_2E0),V0n) = c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EZERO__DIV) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1351 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (V2n = V1m <-> ap(ap(c_2Earithmetic_2E_2A,V2n),ap(c_2Enum_2ESUC,V0p)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(c_2Enum_2ESUC,V0p))))))))) # label(conj_thm_2Earithmetic_2EMULT__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1352 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,V0n)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMOD__2) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1353 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1p)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1p),V0m)),V2n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1p),ap(ap(c_2Earithmetic_2E_2B,V0m),V2n))))))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1354 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V4x (p(ap(V0P,V4x)) & (all V5y (mem(V5y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V5y),V4x)) -> -p(ap(V0P,V5y))))) & mem(V4x,ty_2Enum_2Enum))) <-> (exists V1x (mem(V1x,ty_2Enum_2Enum) & p(ap(V0P,V1x)))) & (exists V2x (mem(V2x,ty_2Enum_2Enum) & (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V3y),V2x)) -> -p(ap(V0P,V3y)))))))))) # label(conj_thm_2Earithmetic_2EEXISTS__GREATEST) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1355 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))) <-> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2k) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V2k)),V0n))))))))) # label(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1356 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1357 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,c_2Enum_2E0),V0n)))) # label(conj_thm_2Earithmetic_2EZERO__MOD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1358 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (ap(c_2Eprim__rec_2EPRE,V0m) = ap(c_2Eprim__rec_2EPRE,V1n) <-> V1n = V0m)))))) # label(conj_thm_2Earithmetic_2EINV__PRE__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1359 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & c_2Enum_2E0 = V1n) & (V0m = c_2Enum_2E0 & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1360 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2Enum__CASE(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),A_27a)))))) # label(mem_c_2Earithmetic_2Enum__CASE) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1361 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMULT__COMM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1362 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__IMP__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1363 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1364 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1365 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Enum_2ESUC,V0m))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1366 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V1x)))))) # label(conj_thm_2Earithmetic_2EMODEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1367 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c)) -> ((exists V2n (mem(V2n,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c)) & p(ap(V0P,V2n)))) <-> (exists V3n (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) & p(ap(V0P,V3n)) & mem(V3n,ty_2Enum_2Enum))) | p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) # label(conj_thm_2Earithmetic_2EBOUNDED__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1368 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) -> p(ap(V0P,ap(c_2Enum_2ESUC,V2n)))))) & p(ap(V0P,c_2Enum_2E0)) <-> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(V0P,V1n))))))) # label(conj_thm_2Earithmetic_2EFORALL__NUM__THM) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1369 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1370 p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) <-> $T # label(ax_thm_2Earithmetic_2EEVEN_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1371 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,ap(c_2Enum_2ESUC,V0n))) <-> -p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(ax_thm_2Earithmetic_2EEVEN_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1372 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V1n),V0m) = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))))) # label(ax_thm_2Earithmetic_2EMAX__DEF) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1373 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0x),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),V0x))) # label(conj_thm_2Earithmetic_2EZERO__EXP) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1374 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) -> V0m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__ADD) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1375 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0p),V1m)),ap(c_2Enum_2ESUC,V0p))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1376 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n)) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V0n)),ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)) = V1k))))) # label(ax_thm_2Earithmetic_2EDIVISION) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1377 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) -> (exists V2m (ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2m)) = V0n & mem(V2m,ty_2Enum_2Enum)))) & (p(ap(c_2Earithmetic_2EEVEN,V0n)) -> (exists V1m (ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m) = V0n & mem(V1m,ty_2Enum_2Enum)))))) # label(conj_thm_2Earithmetic_2EEVEN__ODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1378 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V1n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.17/6.22 1379 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(V0R,ap(V1f,V2n)),ap(V1f,ap(c_2Enum_2ESUC,V2n)))))) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V4n)) -> p(ap(ap(V0R,ap(V1f,V3m)),ap(V1f,V4n))))))))))))))) # label(conj_thm_2Earithmetic_2Etransitive__monotone) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1380 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1c),V0b)) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1c)),V0b) = ap(ap(c_2Earithmetic_2E_2D,V2a),ap(ap(c_2Earithmetic_2E_2D,V0b),V1c))))))))) # label(conj_thm_2Earithmetic_2ESUB__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1381 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> (ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)) <-> ap(c_2Enum_2ESUC,V1x) != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y))))))) # label(conj_thm_2Earithmetic_2EMOD__SUC__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1382 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) <-> V1n = V0m))))))) # label(conj_thm_2Earithmetic_2EEQ__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1383 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1384 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EDIV,V2x),V0m)),V1n) = ap(ap(c_2Earithmetic_2EDIV,V2x),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2EDIV__DIV__DIV__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1385 (all A_27a (ne(A_27a) -> (all V0num (mem(V0num,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),A_27a))) -> p(ap(c_2Ebool_2EDATATYPE(A_27a),ap(ap(V0num,c_2Enum_2E0),c_2Enum_2ESUC))))))) # label(conj_thm_2Earithmetic_2Edatatype__num) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1386 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> -(all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,ap(c_2Enum_2ESUC,V1n))),ap(V0f,V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__STRICTLY__DECREASING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1387 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) | p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)))))))))) # label(conj_thm_2Earithmetic_2EMAX__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1388 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) | c_2Enum_2E0 = V0m) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) | V1n = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1389 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eprim__rec_2EPRE,V0m)),V1n) = ap(c_2Eprim__rec_2EPRE,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EPRE__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1390 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1k),V0n)),V0n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMOD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1391 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V2p)) | p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1392 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V0n),V1p)),ap(ap(c_2Earithmetic_2E_2A,V0n),V2q)) = ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2EMOD,V1p),V2q))))))))) # label(conj_thm_2Earithmetic_2EMOD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1393 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V1n & V0m = c_2Enum_2E0 <-> ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMAX__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1394 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V1k))))))) # label(conj_thm_2Earithmetic_2EDIV__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1395 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = c_2Enum_2E0 <-> V1n = c_2Enum_2E0 | c_2Enum_2E0 = V0m))))) # label(conj_thm_2Earithmetic_2EMIN__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1396 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V7d ap(f174(V3f,V5m,V4a),V7d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V5m),V7d)),V4a),ap(V3f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5m),V7d))))))))))) # label(lameq_f174) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1397 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1398 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Earithmetic_2EDIV,V0m),V1n) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1399 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n)) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)))) = ap(ap(c_2Earithmetic_2EMOD,V2m),V3n)))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CALC_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1400 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> ((exists V3a ((exists V4b (mem(V4b,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V4b),V0n)),V2m2) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3a),V0n)),V1m1))) & mem(V3a,ty_2Enum_2Enum))) <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))))))))) # label(ax_thm_2Earithmetic_2EMODEQ__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1401 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(c_2Enum_2ESUC,V1z))),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUC__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1402 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (all V3p (mem(V3p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1a),V3p)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2b),V3p)),V0n) <-> ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2b),V0n))))))))))) # label(conj_thm_2Earithmetic_2EADD__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1403 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2r),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0n),V2r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1404 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)),V1n))))))) # label(conj_thm_2Earithmetic_2EMOD__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1405 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EOR__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1406 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1e0 (mem(V1e0,ty_2Enum_2Enum) -> (all V2e1 (mem(V2e1,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1e0),V2e1)) -> ap(ap(c_2Earithmetic_2EMOD,V2e1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1e0),V0n))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__INTRO__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1407 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),V2p),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1408 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V1x))))))) # label(conj_thm_2Earithmetic_2EMODEQ__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1409 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0n),V0n) = V0n)) # label(conj_thm_2Earithmetic_2EMAX__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1410 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)),V1x))))))) # label(conj_thm_2Earithmetic_2EMOD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1411 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)))) # label(conj_thm_2Earithmetic_2EZERO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1412 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V2m),V0n)),V1q) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n)))))))) # label(conj_thm_2Earithmetic_2EDIV__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1413 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> ap(V0f,V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1414 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EADD__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1415 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ((exists V1m (mem(V1m,ty_2Enum_2Enum) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) = V0n)) <-> p(ap(c_2Earithmetic_2EODD,V0n))))) # label(conj_thm_2Earithmetic_2EODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1416 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) <-> -p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1417 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMULT__RIGHT__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1418 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V0n <-> -p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))))) # label(conj_thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1419 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0a)),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Earithmetic_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1420 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m)))))))) # label(conj_thm_2Earithmetic_2ELESS__SUC__NOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1421 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2EMAX,c_2Enum_2E0),V0n) & V0n = ap(ap(c_2Earithmetic_2EMAX,V0n),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EMAX__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1422 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) <-> p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))))))) # label(ax_thm_2Earithmetic_2EGREATER__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1423 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),V1y))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem) # label(axiom) # label(non_clause). [assumption]. 6.29/6.22 1424 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(V0P,ap(c_2Enum_2ESUC,V2n))))) & p(ap(V0P,c_2Enum_2E0)) <-> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(V0P,V1n))))))) # label(conj_thm_2Earithmetic_2EFORALL__NUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1425 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V0m = c_2Enum_2E0 | V1n = V2p <-> ap(ap(c_2Earithmetic_2E_2A,V2p),V0m) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))))))) # label(conj_thm_2Earithmetic_2EEQ__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1426 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1x),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2E_2B,V1x),ap(ap(c_2Earithmetic_2EDIV,V2r),V0n))))))))) # label(conj_thm_2Earithmetic_2EADD__DIV__ADD__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1427 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p))))))))) # label(conj_thm_2Earithmetic_2EMIN__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1428 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p)) | p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)))))))))) # label(conj_thm_2Earithmetic_2EMIN__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1429 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x0 (mem(V1x0,ty_2Enum_2Enum) -> (all V2x1 (mem(V2x1,ty_2Enum_2Enum) -> (all V3y0 (mem(V3y0,ty_2Enum_2Enum) -> (all V4y1 (mem(V4y1,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2A,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2A,V2x1),V4y1))))))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__MULT__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1430 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) & p(ap(ap(c_2Earithmetic_2E_3E,V0m),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1431 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__CASES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1432 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1433 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)),ap(ap(c_2Earithmetic_2E_2D,V1m),V0n)),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))) # label(ax_thm_2Earithmetic_2EABS__DIFF__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1434 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) & p(ap(V0P,V1m)) -> p(ap(V0P,ap(ap(c_2Earithmetic_2EMIN,V1m),V2n))) & p(ap(V0P,ap(ap(c_2Earithmetic_2EMAX,V1m),V2n)))))))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__PRED) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1435 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1x),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2y),V0n)))))))))) # label(conj_thm_2Earithmetic_2EDIV__LE__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1436 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> V1x = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1437 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2r),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1438 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1439 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1440 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (V2m = V1n <-> ap(ap(c_2Earithmetic_2EEXP,V0b),V2m) = ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1441 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2E_2D,V0m),c_2Enum_2E0) = V0m)) # label(conj_thm_2Earithmetic_2ESUB__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1442 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1443 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m)) # label(conj_thm_2Earithmetic_2EADD__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1444 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n ap(f172(V1m),V2n) = ap(ap(c_2Earithmetic_2E_2D,V1m),V2n)))) # label(lameq_f172) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1445 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) | c_2Enum_2E0 = V0n & V2m2 = V1m1 <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1446 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b))) <-> (all V3d (mem(V3d,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V1a),V3d) = V2b -> p(ap(V0P,c_2Enum_2E0))) & (V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d) -> p(ap(V0P,V3d)))))))))))) # label(conj_thm_2Earithmetic_2ESUB__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1447 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1448 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3q ap(f185(V0a,V1m,V2n),V3q) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V0a),V3q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V1m),ap(ap(c_2Earithmetic_2E_2A,V2n),V3q))),V2n)))))))))) # label(lameq_f185) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1449 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V1n)))))))))) # label(conj_thm_2Earithmetic_2EMULT__LESS__EQ__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1450 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),ap(c_2Enum_2ESUC,V0n)))))))) # label(conj_thm_2Earithmetic_2ELESS__EXP__SUC__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1451 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1452 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) <-> (p(ap(c_2Earithmetic_2EEVEN,V0m)) <-> p(ap(c_2Earithmetic_2EEVEN,V1n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1453 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V2n))) <-> c_2Enum_2E0 = V0b & c_2Enum_2E0 = V2n | ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0b | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) | V0b = c_2Enum_2E0 & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LE__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1454 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V0m)))))))))) # label(conj_thm_2Earithmetic_2ELE__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1455 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) -> c_2Enum_2E0 = V1n))))) # label(conj_thm_2Earithmetic_2EADD__INV__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1456 (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V6n ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6n),c_2Enum_2E0)),V4a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f174(V3f,V5m,V4a)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V6n))) = ap(f175(V5m,V3f,V4a),V6n)))))))) # label(lameq_f175) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1457 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m))) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V1m)),V0n))))))))) # label(conj_thm_2Earithmetic_2ELESS__SUB__ADD__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1458 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMULT__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1459 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n != V0m & -p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__CASES__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1460 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n)) -> V1k = ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)))))) # label(conj_thm_2Earithmetic_2ELESS__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1461 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) | V0m = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))) & (c_2Enum_2E0 = V0m | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1462 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V0m) != V1n & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__SUC__EQ__COR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1463 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELEFT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1464 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__ADD__SAME) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1465 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2EDIV,V0m),V1n))),ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)))))))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CORRECT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1466 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(ap(c_2Earithmetic_2EEXP,V1x),V0n)))))))) # label(conj_thm_2Earithmetic_2EX__LE__X__EXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1467 (all A_27a (ne(A_27a) -> (all V0v_27 (mem(V0v_27,A_27a) -> (all V1f_27 (mem(V1f_27,arr(ty_2Enum_2Enum,A_27a)) -> (all V2M (mem(V2M,ty_2Enum_2Enum) -> (all V3M_27 (mem(V3M_27,ty_2Enum_2Enum) -> (all V4v (mem(V4v,A_27a) -> (all V5f (mem(V5f,arr(ty_2Enum_2Enum,A_27a)) -> ((all V6n (mem(V6n,ty_2Enum_2Enum) -> (V3M_27 = ap(c_2Enum_2ESUC,V6n) -> ap(V5f,V6n) = ap(V1f_27,V6n)))) & (c_2Enum_2E0 = V3M_27 -> V4v = V0v_27) & V3M_27 = V2M -> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V3M_27),V0v_27),V1f_27) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2M),V4v),V5f)))))))))))))))) # label(conj_thm_2Earithmetic_2Enum__case__cong) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1468 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V3n ap(f181(V2m,V1a,V0f),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1a),V2m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f180(V1a,V2m,V3n,V0f)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n))))))))))))) # label(lameq_f181) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1469 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V2p = ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) <-> V0m = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1470 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2k)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2k))),V1n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V0m),V1n)),V2k)))))))) # label(conj_thm_2Earithmetic_2EDIV__MOD__MOD__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1471 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0p),V1q)))))))) # label(conj_thm_2Earithmetic_2EONE__LT__MULT__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1472 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V1n)),V1n)))) <-> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> p(ap(ap(V0P,V2n),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) # label(conj_thm_2Earithmetic_2ESUC__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1473 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),ap(c_2Enum_2ESUC,c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1474 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1n)),V0m) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2ESUC__ADD__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1475 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (exists V1n (ap(c_2Enum_2ESUC,V1n) = V0m & mem(V1n,ty_2Enum_2Enum))) | c_2Enum_2E0 = V0m)) # label(conj_thm_2Earithmetic_2Enum__CASES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1476 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EMULT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1477 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x0 (mem(V1x0,ty_2Enum_2Enum) -> (all V2x1 (mem(V2x1,ty_2Enum_2Enum) -> (all V3y0 (mem(V3y0,ty_2Enum_2Enum) -> (all V4y1 (mem(V4y1,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2B,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2B,V2x1),V4y1))))))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__PLUS__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1478 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EEQ__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1479 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V2p = V1n <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EEQ__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1480 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)))))) # label(conj_thm_2Earithmetic_2EADD__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1481 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) -> (ap(ap(c_2Earithmetic_2E_2D,V2p),V1n) = V0m <-> V2p = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2EADD__EQ__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1482 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3e (mem(V3e,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EEXP,V1x),V3e)),ap(ap(c_2Earithmetic_2EEXP,V2y),V3e)))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__EXP__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1483 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V2y = V1x <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ENRC__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1484 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) | V1n = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1485 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V2z)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1y),V2z)))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1486 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1487 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1488 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1p),V2q))) <-> (exists V3k (mem(V3k,ty_2Enum_2Enum) & (exists V4r (mem(V4r,ty_2Enum_2Enum) & p(ap(V0P,V4r)) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q)) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r) = V1p)))))))))))) # label(conj_thm_2Earithmetic_2EMOD__P) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1489 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1r (mem(V1r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n)) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n) = V2q))))))) # label(conj_thm_2Earithmetic_2EDIV__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1490 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) <-> c_2Enum_2E0 = V0m | V2p = V1n))))))) # label(conj_thm_2Earithmetic_2EEQ__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1491 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V1m),V2n))) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2n))))) # label(ax_thm_2Earithmetic_2ESUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1492 (all V0m (mem(V0m,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m))) # label(ax_thm_2Earithmetic_2ESUB_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1493 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__EXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1494 (all V0m1 (mem(V0m1,ty_2Enum_2Enum) -> (all V1m2 (mem(V1m2,ty_2Enum_2Enum) -> (V0m1 = V1m2 <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,c_2Enum_2E0),V0m1),V1m2))))))) # label(conj_thm_2Earithmetic_2EMODEQ__0__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1495 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> -p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__GREATER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1496 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (all V3q (mem(V3q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3q)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V2p),V3q)))))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1497 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1q))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1q)))))))) # label(conj_thm_2Earithmetic_2EDOUBLE__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1498 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0)) <-> V0n = c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2ELE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1499 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V2n) = V1m | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Enum_2ESUC,V2n)))))))) # label(conj_thm_2Earithmetic_2ELE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1500 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n & ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Earithmetic_2EEXP__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1501 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ((exists V2d (mem(V2d,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,V2d),V0n) = V1k)) <-> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = c_2Enum_2E0)))))) # label(conj_thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1502 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V1x))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1503 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2ELESS__CASES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1504 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,V0x) = V0x)) # label(ax_thm_2Earithmetic_2ENUMERAL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1505 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))))) # label(conj_thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1506 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2)) <-> ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1507 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1r (mem(V1r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n)) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n) = V1r))))))) # label(conj_thm_2Earithmetic_2EMOD__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1508 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f)) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (exists V2n (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(V0f,V2n))) & mem(V2n,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2EONE__ONE__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1509 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1x),ap(ap(c_2Earithmetic_2EEXP,V0b),V1x)))))))) # label(conj_thm_2Earithmetic_2EX__LT__EXP__X) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1510 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) <-> -p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EODD__EVEN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1511 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(c_2Earithmetic_2EEVEN,V1m)) <-> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1512 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V1m),V0n) | c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V2p),V0n) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V1m),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2p),V0n)))))))))) # label(conj_thm_2Earithmetic_2EADD__DIV__RWT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1513 (all V3f ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),f177(V3f)) = ap(f178,V3f)) # label(lameq_f178) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1514 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = c_2Enum_2E0 <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) & c_2Enum_2E0 = V0n))))) # label(conj_thm_2Earithmetic_2EEXP__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1515 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) -> (V2z = ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) <-> ap(ap(c_2Earithmetic_2EDIV,V2z),V0x) = V1y & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V2z),V0x))))))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1516 (all A_27a (ne(A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),V3n),ap(V2f,V4x)) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),ap(c_2Enum_2ESUC,V3n)),V4x))))))) & (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> V1x = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x))))))) # label(ax_thm_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1517 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)),V0n)))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1518 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f)) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (exists V2a ((all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V3x)),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),V2a))))) & mem(V2a,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1519 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1520 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,V0n)) <-> (exists V1m (mem(V1m,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m) = V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1521 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = c_2Enum_2E0 | c_2Enum_2E0 = V0m <-> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1522 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))),V0m)))))) # label(conj_thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1523 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1524 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3j (mem(V3j,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2i)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3j)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2i),V3j)))))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__MULT2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1525 (all V0k (mem(V0k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2EMOD__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1526 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m)) # label(conj_thm_2Earithmetic_2EMULT__LEFT__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1527 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2A,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2EMULT__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1528 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m)) # label(conj_thm_2Earithmetic_2ESUC__SUB1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1529 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V0n),V0n) = V0n)) # label(conj_thm_2Earithmetic_2EMIN__IDEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1530 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> V0m = ap(c_2Enum_2ESUC,ap(c_2Eprim__rec_2EPRE,V0m))))) # label(conj_thm_2Earithmetic_2ESUC__PRE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1531 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p)) = ap(ap(c_2Earithmetic_2E_2A,V3m),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p)) <-> V2n = V3m))))))))) # label(conj_thm_2Earithmetic_2EMULT__EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1532 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V0m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V1n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1533 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1534 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) & ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) & V0m = ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) & V0m = ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m))))) # label(conj_thm_2Earithmetic_2EADD__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1535 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2D,V1n),V2p) = V0m <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = V1n | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1536 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),c_2Enum_2E0)))) # label(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1537 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1538 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z))))))))))) # label(conj_thm_2Earithmetic_2EX__LE__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1539 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1m ((ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n | ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m) = V0n) & mem(V1m,ty_2Enum_2Enum))))) # label(conj_thm_2Earithmetic_2EODD__OR__EVEN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1540 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eprim__rec_2Emeasure(A_27a),V0f))))))) # label(conj_thm_2Earithmetic_2Etransitive__measure) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1541 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1x),V0z)),ap(ap(c_2Earithmetic_2EEXP,V2y),V0z)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2E_2A,V1x),V2y)),V0z))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1542 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ((all V3q (mem(V3q,ty_2Enum_2Enum) -> (all V4r (mem(V4r,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r) = V1m & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) -> p(ap(V0P,V4r))))))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1m),V2n))))))))))) # label(conj_thm_2Earithmetic_2EMOD__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1543 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m)))))))))) # label(conj_thm_2Earithmetic_2ELE__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1544 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z)) -> (exists V5y (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y)) & mem(V5y,A_27a)))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__E) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1545 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m)))))))))) # label(conj_thm_2Earithmetic_2ELT__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1546 (all V0q (mem(V0q,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Enum_2ESUC,c_2Enum_2E0)) = V0q)) # label(conj_thm_2Earithmetic_2EDIV__ONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1547 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V1n),V0m) = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EMAX__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1548 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1549 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((exists V2p (V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) & mem(V2p,ty_2Enum_2Enum))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1550 (all V0k (mem(V0k,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (exists V2r ((exists V3q (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V1n)),V2r) = V0k & p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V1n)) & mem(V3q,ty_2Enum_2Enum))) & mem(V2r,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2EDA) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1551 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V1n)),V2x),V3y)) <-> (exists V4z (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V4z)) & p(ap(ap(V0R,V4z),V3y)) & mem(V4z,A_27a)))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1552 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2E_2B,V1y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Earithmetic_2ELE__LT1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1553 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2ENOT__LEQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1554 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) <-> V0n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) | V1m = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EEXP__EQ__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1555 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(c_2Enum_2ESUC,V1x)),ap(c_2Enum_2ESUC,V2y)))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__SUC__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1556 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c)) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) -> p(ap(V0P,V3n))))) <-> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c)) -> p(ap(V0P,V2n))))))))))) # label(conj_thm_2Earithmetic_2EBOUNDED__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1557 (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0c),V1b)) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2E_2D,V1b),V0c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1b)),V0c)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1558 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x)))))))))) # label(conj_thm_2Earithmetic_2EDIV__LE__X) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1559 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1560 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1561 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m <-> c_2Enum_2E0 = V1n))))) # label(conj_thm_2Earithmetic_2EADD__INV__0__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1562 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__LESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1563 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)))) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2x),V1k)),V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)),V1k)))))))) # label(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1564 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V1m),V1m) != ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V0n)))))) # label(conj_thm_2Earithmetic_2ENOT__ODD__EQ__EVEN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1565 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2B,V1n),ap(ap(c_2Earithmetic_2E_2B,V2p),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1566 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(c_2Earithmetic_2EMIN,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMIN__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1567 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1568 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,V0n),V1m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n))))))) # label(conj_thm_2Earithmetic_2EGREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1569 (all A_27a (ne(A_27a) -> (all V0v (mem(V0v,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),c_2Enum_2E0),V0v),V1f) = V0v)))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3v (mem(V3v,A_27a) -> (all V4f (mem(V4f,arr(ty_2Enum_2Enum,A_27a)) -> ap(V4f,V2n) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),ap(c_2Enum_2ESUC,V2n)),V3v),V4f))))))))) # label(ax_thm_2Earithmetic_2Enum__case__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1570 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0n),V1m) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)))))) # label(conj_thm_2Earithmetic_2ESUB__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1571 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) <-> -p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__LESS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1572 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1573 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> ((exists V3r (V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V3r) & p(ap(ap(c_2Eprim__rec_2E_3C,V3r),V0n)) & mem(V3r,ty_2Enum_2Enum))) -> V2q = ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)))))))) # label(conj_thm_2Earithmetic_2EDIV__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1574 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(ap(c_2Earithmetic_2E_2B,V2m),V3n)),V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V2m),ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V3n),V1x)))))))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1575 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EEVEN,V0n)) | p(ap(c_2Earithmetic_2EODD,V0n)))) # label(conj_thm_2Earithmetic_2EEVEN__OR__ODD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1576 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n)) -> ap(ap(c_2Earithmetic_2EDIV,V0r),V1n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1577 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1578 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EDIV2,V0n) = ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) # label(ax_thm_2Earithmetic_2EDIV2__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1579 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1580 (all V0f ap(f184,V0f) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f183(V0f))) # label(lameq_f184) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1581 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Enum_2Enum),f176(V3f,V4a)) = ap(f177(V3f),V4a)))) # label(lameq_f177) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1582 (all V0q (mem(V0q,ty_2Enum_2Enum) -> V0q = ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EDIV__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1583 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n <-> ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1584 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) & p(ap(V0P,V1x)) & (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2B,V3y),V2n))) -> p(ap(V0P,V3y))))) -> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1x),V2n)))))))))) # label(conj_thm_2Earithmetic_2EMOD__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1585 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0a),V1m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f185(V0a,V1m,V2n)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n)))))) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))))))))) # label(conj_thm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1586 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Earithmetic_2EONE__MOD__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1587 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = c_2Enum_2E0 & V1n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) | c_2Enum_2E0 = V1n & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0m <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EADD__EQ__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1588 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n)))))) # label(conj_thm_2Earithmetic_2EMOD__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1589 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1590 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V2x),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))),V1n) = ap(ap(c_2Earithmetic_2EMOD,V2x),V1n)))))))) # label(conj_thm_2Earithmetic_2EMOD__MULT__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1591 (all V1m ap(f173,V1m) = f172(V1m)) # label(lameq_f173) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1592 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2EFUNPOW(A_27a),arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))))) # label(mem_c_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1593 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (-p(ap(c_2Earithmetic_2EODD,V0n)) <-> p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__ODD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1594 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0n))) # label(ax_thm_2Earithmetic_2EMULT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1595 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1m),V2n)),V2n) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V1m)),V2n))))) # label(ax_thm_2Earithmetic_2EMULT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1596 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> (exists V3n (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y)) & mem(V3n,ty_2Enum_2Enum)))))))))))) # label(conj_thm_2Earithmetic_2ERTC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1597 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V5m f175(V5m,V3f,V4a) = ap(f176(V3f,V4a),V5m)))))) # label(lameq_f176) # label(axiom) # label(non_clause). [assumption]. 6.29/6.23 1598 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27a,bool))) -> (all V1G (mem(V1G,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3s (mem(V3s,A_27a) -> (-p(ap(V1G,V3s)) -> p(ap(ap(V0P,V3s),V3s))))) & (all V4s1 (mem(V4s1,A_27a) -> (all V5s2 (mem(V5s2,A_27a) -> (p(ap(ap(V0P,ap(V2f,V4s1)),V5s2)) & p(ap(V1G,V4s1)) -> p(ap(ap(V0P,V4s1),V5s2))))))) -> (all V6s1 (mem(V6s1,A_27a) -> (all V7s2 (mem(V7s2,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V7s2) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V1G),V2f),V6s1) -> p(ap(ap(V0P,V6s1),V7s2)))))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__IND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1599 (all V0p (mem(V0p,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0p,V1n)) & mem(V1n,ty_2Enum_2Enum))) -> p(ap(V0p,ap(c_2Ewhile_2ELEAST,V0p))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Ewhile_2ELEAST,V0p))) -> -p(ap(V0p,V2n)))))))) # label(conj_thm_2Ewhile_2ELEAST__EXISTS__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1600 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(V0G,V2s)),ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),ap(V1f,V2s))),ap(c_2Eoption_2ESOME(A_27a),V2s)))))))))) # label(conj_thm_2Ewhile_2EOWHILE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1601 (all V0Q (mem(V0Q,arr(ty_2Enum_2Enum,bool)) -> (all V1P (mem(V1P,arr(ty_2Enum_2Enum,bool)) -> ((exists V2n (p(ap(V1P,V2n)) & mem(V2n,ty_2Enum_2Enum))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(V1P,V3n)) & (all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> -p(ap(V1P,V4m))))) -> p(ap(V0Q,V3n))))) -> p(ap(V0Q,ap(c_2Ewhile_2ELEAST,V1P)))))))) # label(conj_thm_2Ewhile_2ELEAST__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1602 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3s_27 (mem(V3s_27,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V3s_27) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) -> -p(ap(V0G,V3s_27))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__ENDCOND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1603 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(V0P,V1x)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewhile_2ELEAST,V0P)),V1x)) & p(ap(V0P,ap(c_2Ewhile_2ELEAST,V0P)))))))) # label(conj_thm_2Ewhile_2EFULL__LEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1604 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(V0P,V1x)) -> p(ap(V0P,ap(c_2Ewhile_2ELEAST,V0P)))))))) # label(conj_thm_2Ewhile_2ELEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1605 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V2n ap(f189(V0x),V2n) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0x),V2n)))) # label(lameq_f189) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1606 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),bool)) -> (((all V2n (mem(V2n,ty_2Enum_2Enum) -> -p(ap(V0P,V2n)))) -> p(ap(V1Q,c_2Eoption_2ENONE(ty_2Enum_2Enum)))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> -p(ap(V0P,V4m))))) & p(ap(V0P,V3n)) -> p(ap(V1Q,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V3n)))))) -> p(ap(V1Q,ap(c_2Ewhile_2EOLEAST,V0P)))))))) # label(conj_thm_2Ewhile_2EOLEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1607 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Ewhile_2EHOARE__SPEC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1608 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V3C (mem(V3C,arr(A_27a,A_27a)) -> ((all V4s (mem(V4s,A_27a) -> (p(ap(V2B,V4s)) -> p(ap(ap(V1R,ap(V3C,V4s)),V4s))))) & p(ap(c_2Erelation_2EWF(A_27a),V1R)) -> (p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27a),f186(A_27a,V0P,V2B)),V3C),V0P)) -> p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27a),V0P),ap(ap(c_2Ewhile_2EWHILE(A_27a),V2B),V3C)),f187(A_27a,V0P,V2B))))))))))))))) # label(conj_thm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1609 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1n) = ap(c_2Ewhile_2EOLEAST,V0P) <-> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) -> -p(ap(V0P,V2m))))) & p(ap(V0P,V1n))))))) # label(conj_thm_2Ewhile_2EOLEAST__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1610 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) <-> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V3n),V2s)))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1611 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (ap(c_2Ewhile_2EOLEAST,V0P) = c_2Eoption_2ENONE(ty_2Enum_2Enum) <-> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -p(ap(V0P,V1n))))))) # label(conj_thm_2Ewhile_2EOLEAST__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1612 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V2n ap(V0P,V2n) = ap(f191(V0P),V2n)))) # label(lameq_f191) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1613 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V5s ap(f186(A_27a,V0P,V2B),V5s) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V5s)),ap(V2B,V5s))))))) # label(lameq_f186) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1614 (all V0p (mem(V0p,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0p,V1n)) & mem(V1n,ty_2Enum_2Enum))) <-> p(ap(V0p,ap(c_2Ewhile_2ELEAST,V0p))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Ewhile_2ELEAST,V0p))) -> -p(ap(V0p,V2n)))))))) # label(conj_thm_2Ewhile_2ELEAST__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1615 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Ewhile_2ELEAST,f188(V0x)) = V0x & ap(c_2Ewhile_2ELEAST,f189(V0x)) = V0x)) # label(conj_thm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1616 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1g (mem(V1g,arr(A_27a,A_27a)) -> (exists V2f ((all V3x (mem(V3x,A_27a) -> ap(V2f,V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(V0P,V3x)),V3x),ap(V2f,ap(V1g,V3x))))) & mem(V2f,arr(A_27a,A_27a)))))))))) # label(conj_thm_2Ewhile_2EITERATION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1617 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f192(A_27a,V0G,V1f,V2s))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),ap(c_2Ewhile_2ELEAST,f193(A_27a,V0G,V1f,V2s))),V2s))),c_2Eoption_2ENONE(A_27a)) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s))))))))) # label(ax_thm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1618 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Enum_2Enum)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f190(V0P))),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),ap(c_2Ewhile_2ELEAST,f191(V0P)))),c_2Eoption_2ENONE(ty_2Enum_2Enum)) = ap(c_2Ewhile_2EOLEAST,V0P))) # label(ax_thm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1619 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1G (mem(V1G,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3s (mem(V3s,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(V0P,V4x)) & p(ap(V1G,V4x)) -> p(ap(V0P,ap(V2f,V4x)))))) & p(ap(V0P,V3s)) -> (all V5s_27 (mem(V5s_27,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V5s_27) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V1G),V2f),V3s) -> p(ap(V0P,V5s_27)))))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__INV__IND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1620 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V6s ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V6s)),ap(c_2Ebool_2E_7E,ap(V2B,V6s))) = ap(f187(A_27a,V0P,V2B),V6s)))))) # label(lameq_f187) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1621 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x) = ap(c_2Ewhile_2EOLEAST,f188(V0x)) & ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x) = ap(c_2Ewhile_2EOLEAST,f189(V0x)) & ap(c_2Ewhile_2EOLEAST,k(ty_2Enum_2Enum,c_2Ebool_2EF)) = c_2Eoption_2ENONE(ty_2Enum_2Enum) & ap(c_2Ewhile_2EOLEAST,k(ty_2Enum_2Enum,c_2Ebool_2ET)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),c_2Enum_2E0))) # label(conj_thm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1622 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n ap(V0P,V1n) = ap(f190(V0P),V1n)))) # label(lameq_f190) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1623 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),V0x) = ap(f188(V0x),V1n)))) # label(lameq_f188) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1624 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1g (mem(V1g,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(V0P,V2x)),ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0P),V1g),ap(V1g,V2x))),V2x) = ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0P),V1g),V2x))))))))) # label(ax_thm_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1625 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3s_27 (mem(V3s_27,A_27a) -> (ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) = ap(c_2Eoption_2ESOME(A_27a),V3s_27) -> V3s_27 = ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0G),V1f),V2s)))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__WHILE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1626 (all A_27a all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V4n ap(f193(A_27a,V0G,V1f,V2s),V4n) = ap(c_2Ebool_2E_7E,ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V4n),V2s)))))))))) # label(lameq_f193) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1627 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1C (mem(V1C,arr(A_27a,A_27b)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27b),V0P),V1C),V2Q)) <-> (all V3s (mem(V3s,A_27a) -> (p(ap(V0P,V3s)) -> p(ap(V2Q,ap(V1C,V3s))))))))))))))))) # label(ax_thm_2Ewhile_2EHOARE__SPEC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1628 (all A_27a (ne(A_27a) -> mem(c_2Ewhile_2EWHILE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,A_27a),arr(A_27a,A_27a)))))) # label(mem_c_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1629 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ap(c_2Ewhile_2ELEAST,V0P) = ap(ap(ap(c_2Ewhile_2EWHILE(ty_2Enum_2Enum),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,bool,bool),c_2Ebool_2E_7E),V0P)),c_2Enum_2ESUC),c_2Enum_2E0))) # label(ax_thm_2Ewhile_2ELEAST__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1630 (all A_27a (ne(A_27a) -> (all V0B (mem(V0B,arr(A_27a,bool)) -> (all V1C (mem(V1C,arr(A_27a,A_27a)) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> ((all V3s (mem(V3s,A_27a) -> (p(ap(V0B,V3s)) -> p(ap(ap(V2R,ap(V1C,V3s)),V3s))))) & p(ap(c_2Erelation_2EWF(A_27a),V2R)) -> (all V4P (mem(V4P,arr(A_27a,bool)) -> ((all V5s (mem(V5s,A_27a) -> ((p(ap(V0B,V5s)) -> p(ap(V4P,ap(V1C,V5s)))) -> p(ap(V4P,V5s))))) -> (all V6v (mem(V6v,A_27a) -> p(ap(V4P,V6v)))))))))))))))) # label(conj_thm_2Ewhile_2EWHILE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1631 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1m),ap(c_2Ewhile_2ELEAST,V0P))) -> -p(ap(V0P,V1m))))))) # label(conj_thm_2Ewhile_2ELESS__LEAST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1632 (all A_27a (ne(A_27a) -> mem(c_2Ewhile_2EOWHILE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))))) # label(mem_c_2Ewhile_2EOWHILE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1633 (all A_27a all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3n ap(c_2Ebool_2E_7E,ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V3n),V2s))) = ap(f192(A_27a,V0G,V1f,V2s),V3n)))))))) # label(lameq_f192) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1634 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V5m ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f205(V1x,V2y,V5m)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V2y))) = ap(f206(V1x,V2y),V5m)))))) # label(lameq_f206) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1635 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V0n),V1m))),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__sub) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1636 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V5m ap(f194(V3n),V5m) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V3n),V5m))))) # label(lameq_f194) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1637 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1b (mem(V1b,bool) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> V2n = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),c_2Earithmetic_2EZERO) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) & ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) & ap(c_2Earithmetic_2EBIT1,V2n) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),c_2Earithmetic_2EZERO) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(c_2Enumeral_2EiDUB,V2n) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),c_2Earithmetic_2EZERO) & c_2Earithmetic_2EZERO = ap(ap(ap(c_2Enumeral_2EiSUB,V1b),c_2Earithmetic_2EZERO),V0x))))))))) # label(conj_thm_2Enumeral_2EiSUB__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1638 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1639 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V1n)))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1640 (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,V2n) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2n)))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1641 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Enumeral_2EiiSUC,V0n))) # label(ax_thm_2Enumeral_2EiiSUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1642 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V4m ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V4m)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V4m)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V2y)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT1,V2y))) = ap(f204(V1x,V2y),V4m)))))) # label(lameq_f204) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1643 (all A_27a (ne(A_27a) -> mem(c_2Enumeral_2EiBIT__cases(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),arr(arr(ty_2Enum_2Enum,A_27a),A_27a))))))) # label(mem_c_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1644 (all V0acc (mem(V0acc,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,c_2Earithmetic_2EZERO),V0acc) = ap(c_2Earithmetic_2EBIT2,V0acc) & ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT2,V1n)),V0acc) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),ap(c_2Earithmetic_2EBIT1,V0acc)) & ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2EBIT1,V0acc)) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),V0acc))))) # label(conj_thm_2Enumeral_2Enumeral__texp__help) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1645 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiZ,V0x) = V0x)) # label(ax_thm_2Enumeral_2EiZ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1646 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,V0n),V1a) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Enumeral_2Etexp__help__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1647 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Earithmetic_2EZERO)) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) -> p(ap(V0P,ap(c_2Earithmetic_2EBIT2,V2n)))))) & (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,V1n)) -> p(ap(V0P,ap(c_2Earithmetic_2EBIT1,V1n)))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Enumeral_2Ebit__induction) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1648 (all V0acc (mem(V0acc,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,c_2Enum_2E0),V0acc) = ap(c_2Earithmetic_2EBIT2,V0acc))) # label(ax_thm_2Enumeral_2Etexp__help__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1649 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2acc (mem(V2acc,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,V1n),ap(c_2Earithmetic_2EBIT1,V2acc)) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Enum_2ESUC,V1n)),V2acc))))) # label(ax_thm_2Enumeral_2Etexp__help__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1650 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),c_2Enum_2E0) & ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))) & ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))),c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2ETWO__EXP__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1651 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f204(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) & ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f206(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f203(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V2y))) & ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) & c_2Earithmetic_2EZERO = ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) & c_2Earithmetic_2EZERO = ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n))))))) # label(conj_thm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1652 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3n ap(f203(V1x,V2y),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V3n)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V3n)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V1x)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)))))))) # label(lameq_f203) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1653 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,V0n)))) # label(conj_thm_2Enumeral_2Enumeral__suc_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1654 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,V1n)) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V1n)))) # label(conj_thm_2Enumeral_2Enumeral__suc_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1655 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,c_2Enum_2E0),V0x) = V0x & V0x = ap(ap(c_2Earithmetic_2EMAX,V0x),c_2Enum_2E0) & ap(ap(c_2Earithmetic_2EMAX,ap(c_2Earithmetic_2ENUMERAL,V0x)),ap(c_2Earithmetic_2ENUMERAL,V1y)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)),V1y),V0x)))))) # label(conj_thm_2Enumeral_2Enumeral__MAX) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1656 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V15m ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V10n),V15m)) = ap(f201(V10n),V15m)))) # label(lameq_f201) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1657 (all A_27a (ne(A_27a) -> (all V0zf (mem(V0zf,A_27a) -> (all V1b1f (mem(V1b1f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V2b2f (mem(V2b2f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (exists V3f (mem(V3f,arr(ty_2Enum_2Enum,A_27a)) & ap(V3f,c_2Earithmetic_2EZERO) = V0zf & (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(ap(V2b2f,V5n),ap(V3f,V5n)) = ap(V3f,ap(c_2Earithmetic_2EBIT2,V5n)))) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(V1b1f,V4n),ap(V3f,V4n)) = ap(V3f,ap(c_2Earithmetic_2EBIT1,V4n)))))))))))))) # label(conj_thm_2Enumeral_2Ebit__initiality) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1658 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiDUB,V0x) = ap(ap(c_2Earithmetic_2E_2B,V0x),V0x))) # label(ax_thm_2Enumeral_2EiDUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1659 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4m (mem(V4m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V3n),ap(c_2Earithmetic_2EBIT2,V4m)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enumeral_2EiSQR,V3n)),ap(c_2Enumeral_2EiSQR,ap(ap(c_2Earithmetic_2EEXP,V3n),V4m))))))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1660 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V1n),ap(c_2Earithmetic_2EBIT1,V2m)) = ap(ap(c_2Earithmetic_2E_2A,V1n),ap(c_2Enumeral_2EiSQR,ap(ap(c_2Earithmetic_2EEXP,V1n),V2m))))))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1661 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V0n),c_2Earithmetic_2EZERO) = ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1662 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(ap(c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),V0x))) # label(ax_thm_2Enumeral_2Eonecount__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1663 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT2,V3n)),V4x) = c_2Earithmetic_2EZERO)))) # label(ax_thm_2Enumeral_2Eonecount__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1664 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Eonecount,V1n),ap(c_2Enum_2ESUC,V2x)) = ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT1,V1n)),V2x))))) # label(ax_thm_2Enumeral_2Eonecount__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1665 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0x),V0x) = ap(c_2Enumeral_2EiSQR,V0x))) # label(ax_thm_2Enumeral_2EiSQR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1666 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1667 (all V1n (mem(V1n,ty_2Enum_2Enum) -> V1n = ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1668 (all V5n (mem(V5n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1669 (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7m (mem(V7m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1670 (all V8n (mem(V8n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n) = c_2Enum_2E0)) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1671 (all V9n (mem(V9n,ty_2Enum_2Enum) -> V9n = ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1672 (all V12n (mem(V12n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1673 (all V15n (mem(V15n,ty_2Enum_2Enum) -> (all V16m (mem(V16m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1674 (all V17n (mem(V17n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1675 (all V19n (mem(V19n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V19n) <-> c_2Earithmetic_2EZERO = V19n))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1676 (all V21n (mem(V21n,ty_2Enum_2Enum) -> (all V22m (mem(V22m,ty_2Enum_2Enum) -> (V22m = V21n <-> ap(c_2Earithmetic_2ENUMERAL,V22m) = ap(c_2Earithmetic_2ENUMERAL,V21n)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1677 (all V23n (mem(V23n,ty_2Enum_2Enum) -> ($F <-> p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1678 (all V24n (mem(V24n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1679 (all V25n (mem(V25n,ty_2Enum_2Enum) -> (all V26m (mem(V26m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m)))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1680 (all V29n (mem(V29n,ty_2Enum_2Enum) -> (all V30m (mem(V30m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1681 (all V40n (mem(V40n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,V40n)) <-> p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1682 (all V39n (mem(V39n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V39n)) <-> p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1683 (all V37n (mem(V37n,ty_2Enum_2Enum) -> (all V38m (mem(V38m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1684 (all V36n (mem(V36n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V36n <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1685 (all V35n (mem(V35n,ty_2Enum_2Enum) -> ($T <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1686 (all V33n (mem(V33n,ty_2Enum_2Enum) -> (all V34m (mem(V34m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m)))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1687 (all V32n (mem(V32n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1688 (all V31n (mem(V31n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n)) <-> $T))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1689 (all V28n (mem(V28n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1690 (all V27n (mem(V27n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n)) <-> $F))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1691 (all V20n (mem(V20n,ty_2Enum_2Enum) -> (V20n = c_2Earithmetic_2EZERO <-> ap(c_2Earithmetic_2ENUMERAL,V20n) = c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1692 (all V18n (mem(V18n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1693 (all V14n (mem(V14n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1694 (all V13n (mem(V13n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1695 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11m (mem(V11m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1696 (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0)) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1697 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1698 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,V0n) = ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral_2Enumeral__div2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1699 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V1n)) = ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))))) # label(conj_thm_2Enumeral_2Enumeral__div2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1700 (all A_27a (ne(A_27a) -> (all V0zf (mem(V0zf,A_27a) -> (all V1bf1 (mem(V1bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V2bf2 (mem(V2bf2,arr(ty_2Enum_2Enum,A_27a)) -> V0zf = ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),c_2Earithmetic_2EZERO),V0zf),V1bf1),V2bf2))))))) & (all V7n (mem(V7n,ty_2Enum_2Enum) -> (all V8zf (mem(V8zf,A_27a) -> (all V9bf1 (mem(V9bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V10bf2 (mem(V10bf2,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),ap(c_2Earithmetic_2EBIT2,V7n)),V8zf),V9bf1),V10bf2) = ap(V10bf2,V7n))))))))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4zf (mem(V4zf,A_27a) -> (all V5bf1 (mem(V5bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V6bf2 (mem(V6bf2,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),ap(c_2Earithmetic_2EBIT1,V3n)),V4zf),V5bf1),V6bf2) = ap(V5bf1,V3n))))))))))) # label(ax_thm_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1701 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = V0n & ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Enumeral_2EiiSUC,V0n) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) & ap(c_2Enumeral_2EiiSUC,V0n) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Enum_2ESUC,V0n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) & ap(c_2Enum_2ESUC,V0n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & V0n = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)))))) # label(conj_thm_2Enumeral_2Enumeral__add) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1702 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($F <-> ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO) & (ap(c_2Earithmetic_2EBIT2,V0n) = c_2Earithmetic_2EZERO <-> $F) & (ap(c_2Earithmetic_2EBIT2,V0n) = c_2Earithmetic_2EZERO <-> $F) & ($F <-> ap(c_2Earithmetic_2EBIT2,V1m) = ap(c_2Earithmetic_2EBIT1,V0n)) & (ap(c_2Earithmetic_2EBIT1,V1m) = ap(c_2Earithmetic_2EBIT1,V0n) <-> V1m = V0n) & (ap(c_2Earithmetic_2EBIT2,V1m) = ap(c_2Earithmetic_2EBIT2,V0n) <-> V0n = V1m) & ($F <-> ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT1,V1m)) & (ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO <-> $F))))) # label(conj_thm_2Enumeral_2Enumeral__eq) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1703 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Einternal__mult,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO & ap(ap(c_2Enumeral_2Einternal__mult,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO & ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m)),V1m))) & ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m))),V1m)) = ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V0n)),V1m))))) # label(conj_thm_2Enumeral_2Einternal__mult__characterisation) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1704 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO & ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m))),V1m)) & ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Enumeral__mult) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1705 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),ap(c_2Earithmetic_2EBIT2,V3n))))) = ap(ap(c_2Earithmetic_2EDIV,V2m),ap(c_2Earithmetic_2EBIT2,V3n)))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1706 (all V4m (mem(V4m,ty_2Enum_2Enum) -> (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V4m),ap(c_2Earithmetic_2EBIT1,V5n))))) = ap(ap(c_2Earithmetic_2EMOD,V4m),ap(c_2Earithmetic_2EBIT1,V5n)))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1707 (all V6m (mem(V6m,ty_2Enum_2Enum) -> (all V7n (mem(V7n,ty_2Enum_2Enum) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V6m),ap(c_2Earithmetic_2EBIT2,V7n))))) = ap(ap(c_2Earithmetic_2EMOD,V6m),ap(c_2Earithmetic_2EBIT2,V7n)))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1708 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),ap(c_2Earithmetic_2EBIT1,V1n))))) = ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2EBIT1,V1n)))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1709 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V12m ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V12m)) = ap(f198(V10n),V12m)))) # label(lameq_f198) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1710 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Enumeral_2EiiSUC,ap(c_2Earithmetic_2EBIT1,V0n)) & ap(c_2Enumeral_2EiiSUC,ap(c_2Earithmetic_2EBIT2,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Enumeral_2EiiSUC,c_2Earithmetic_2EZERO) = ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral_2Enumeral__iisuc) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1711 (all V0b (mem(V0b,bool) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V0b),c_2Earithmetic_2EZERO),V1x) = c_2Earithmetic_2EZERO)))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1712 (all V2b (mem(V2b,bool) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V2b),ap(c_2Earithmetic_2EBIT1,V3n)),V4x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V2b),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V4x),ap(c_2Earithmetic_2EBIT1,V3n)),f194(V3n)),f195(V3n))),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V4x),ap(c_2Enumeral_2EiDUB,V3n)),f196(V3n)),f197(V3n))))))))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1713 (all V9b (mem(V9b,bool) -> (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11x (mem(V11x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V9b),ap(c_2Earithmetic_2EBIT2,V10n)),V11x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V9b),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V11x),ap(c_2Earithmetic_2EBIT2,V10n)),f198(V10n)),f199(V10n))),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V11x),ap(c_2Earithmetic_2EBIT1,V10n)),f200(V10n)),f201(V10n))))))))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1714 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V7m ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V7m)) = ap(f196(V3n),V7m)))) # label(lameq_f196) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1715 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V8m ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V8m)) = ap(f197(V3n),V8m)))) # label(lameq_f197) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1716 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V13m ap(f199(V10n),V13m) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V13m))))) # label(lameq_f199) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1717 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))),ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n)))))) # label(conj_thm_2Enumeral_2Enumeral__fact_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1718 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2EFACT,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) = ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral_2Enumeral__fact_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1719 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Enumeral_2Eonecount,V0n),V1a))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Enumeral_2Eonecount,V0n),V1a)),V1a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n))))) # label(conj_thm_2Enumeral_2Eonecount__characterisation) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1720 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT1,V0n)) = c_2Earithmetic_2EZERO)) # label(ax_thm_2Enumeral_2Eexactlog__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1721 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f202),ap(ap(c_2Enumeral_2Eonecount,V1n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1n)))) # label(ax_thm_2Enumeral_2Eexactlog__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1722 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT1,V0n))) & p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT1,V0n))) & -p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT2,V0n))) & -p(ap(c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) & p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT2,V0n))) & p(ap(c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Enumeral__evenodd) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1723 (all V2x ap(f202,V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2x),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V2x))) # label(lameq_f202) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1724 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V6m ap(f195(V3n),V6m) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V6m))))) # label(lameq_f195) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1725 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($F <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO))) & ($F <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <-> -p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))) & ($T <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n))))))) # label(conj_thm_2Enumeral_2Enumeral__lte) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1726 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2EBIT1,V0x)))) # label(conj_thm_2Enumeral_2EDIV2__BIT1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1727 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0a),V1m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f185(V0a,V1m,V2n)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n)))))))))))) # label(conj_thm_2Enumeral_2Edivmod__POS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1728 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,V0n),c_2Enum_2E0) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Enumeral_2Etexp__help0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1729 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2EBIT1,V1m) = ap(c_2Enumeral_2Eexactlog,V0n) -> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0n))))) # label(conj_thm_2Enumeral_2Eexactlog__characterisation) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1730 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,V0n)) = ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,V0n)) & ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,V0n)) & c_2Earithmetic_2EZERO = ap(c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral_2EiDUB__removal) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1731 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n)))),ap(V0f,V1x)) & ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(V0f,V1x)) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),V1x) & ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) = V1x)))))))) # label(conj_thm_2Enumeral_2Enumeral__funpow) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1732 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V6n ap(f205(V1x,V2y,V5m),V6n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V5m)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V5m)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2y)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V6n)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V6n)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V1x)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT2,V2y))))))))))) # label(lameq_f205) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1733 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V14m ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V14m)) = ap(f200(V10n),V14m)))) # label(lameq_f200) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1734 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($F <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Earithmetic_2EZERO))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <-> -p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n))) & ($T <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT2,V0n)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V0n))) <-> $T))))) # label(conj_thm_2Enumeral_2Enumeral__lt) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1735 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,ap(c_2Earithmetic_2ENUMERAL,V0x)),ap(c_2Earithmetic_2ENUMERAL,V1y)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)),V0x),V1y)) & ap(ap(c_2Earithmetic_2EMIN,V0x),c_2Enum_2E0) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2EMIN,c_2Enum_2E0),V0x) = c_2Enum_2E0)))) # label(conj_thm_2Enumeral_2Enumeral__MIN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1736 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1p (mem(V1p,ty_2Enum_2Enum) & p(ap(c_2Edivides_2Eprime,V1p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1p)))))) # label(conj_thm_2Edivides_2EEUCLID) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1737 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),c_2Enum_2E0)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1b),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1b),c_2Enum_2E0)),c_2Ebool_2ET),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V1b),V0a)),c_2Enum_2E0)))))))))) # label(conj_thm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1738 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Edivides_2Eprime,ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EprimePRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1739 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ((all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1b),V0a)) -> V1b = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) | V0a = V1b))) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != V0a <-> p(ap(c_2Edivides_2Eprime,V0a))))) # label(ax_thm_2Edivides_2Eprime__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1740 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Edivides_2Eprime,V1p)),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),V1p)) = ap(f207(V0n),V1p)))) # label(lameq_f207) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1741 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V1b),V0a)) -> V1b = V0a))))) # label(conj_thm_2Edivides_2EDIVIDES__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1742 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ((exists V2q (mem(V2q,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,V2q),V0a) = V1b)) <-> p(ap(ap(c_2Edivides_2Edivides,V0a),V1b))))))) # label(ax_thm_2Edivides_2Edivides__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1743 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EINDEX__LESS__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1744 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V1n)) & p(ap(ap(c_2Edivides_2Edivides,V0m),V1n)) & p(ap(c_2Edivides_2Eprime,V0m)) -> V0m = V1n))))) # label(conj_thm_2Edivides_2Eprime__divides__only__self) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1745 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ewhile_2ELEAST,f207(V0n)) = ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))) # label(ax_thm_2Edivides_2EPRIMES__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1746 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V2c)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2D,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1747 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V1m = c_2Enum_2E0 | ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0n <-> p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))))))) # label(conj_thm_2Edivides_2EDIVIDES__MULT__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1748 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))))) # label(conj_thm_2Edivides_2EINFINITE__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1749 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V2c)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__ADD__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1750 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Edivides_2EPRIMES,V1n) = ap(c_2Edivides_2EPRIMES,V0m) -> V0m = V1n))))) # label(conj_thm_2Edivides_2EPRIMES__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1751 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> p(ap(ap(c_2Edivides_2Edivides,V0m),ap(c_2Earithmetic_2EFACT,V1n)))))))) # label(conj_thm_2Edivides_2ELEQ__DIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1752 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b))))))) # label(conj_thm_2Edivides_2EDIVIDES__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1753 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) -> -p(ap(ap(c_2Edivides_2Edivides,V0a),V1b))))))) # label(conj_thm_2Edivides_2ENOT__LT__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1754 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) | V1n = c_2Enum_2E0))))) # label(conj_thm_2Edivides_2EDIVIDES__LEQ__OR__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1755 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V0a)))) # label(conj_thm_2Edivides_2EDIVIDES__REFL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1756 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0p))))) # label(conj_thm_2Edivides_2EONE__LT__PRIME) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1757 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1b),V2c)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V2c))))))))) # label(conj_thm_2Edivides_2EDIVIDES__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1758 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c))) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V2c))))))))) # label(conj_thm_2Edivides_2EDIVIDES__ADD__2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1759 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EZERO__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1760 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & (all V2j (mem(V2j,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2j),V1i)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Edivides_2EPRIMES,V2j)),V0n))))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V1i))))))) # label(conj_thm_2Edivides_2ENEXT__LARGER__PRIME) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1761 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0b)) -> p(ap(ap(c_2Edivides_2Edivides,V0b),ap(c_2Earithmetic_2EFACT,V0b)))))) # label(conj_thm_2Edivides_2EDIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1762 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> (exists V1p (mem(V1p,ty_2Enum_2Enum) & p(ap(c_2Edivides_2Eprime,V1p)) & p(ap(ap(c_2Edivides_2Edivides,V1p),V0n))))))) # label(conj_thm_2Edivides_2EPRIME__FACTOR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1763 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,V0a),c_2Enum_2E0)))) # label(conj_thm_2Edivides_2EALL__DIVIDES__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1764 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0m)),ap(c_2Edivides_2EPRIMES,V1n)))))))) # label(conj_thm_2Edivides_2ELT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1765 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)))) # label(conj_thm_2Edivides_2EONE__DIVIDES__ALL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1766 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0x <-> p(ap(ap(c_2Edivides_2Edivides,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Edivides_2EDIVIDES__ONE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1767 (all V0p (mem(V0p,ty_2Enum_2Enum) -> ((exists V1i (mem(V1i,ty_2Enum_2Enum) & V0p = ap(c_2Edivides_2EPRIMES,V1i))) <-> p(ap(c_2Edivides_2Eprime,V0p))))) # label(conj_thm_2Edivides_2EPRIME__INDEX) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1768 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EONE__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1769 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2A,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1770 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V1p),ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))) & p(ap(c_2Edivides_2Eprime,V1p)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),V1p))))))) # label(conj_thm_2Edivides_2EPRIMES__NO__GAP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1771 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0p))))) # label(conj_thm_2Edivides_2EPRIME__POS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1772 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & ap(c_2Edivides_2EPRIMES,V1i) = V0p))))) # label(conj_thm_2Edivides_2EPRIMES__ONTO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1773 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V1i))))))) # label(conj_thm_2Edivides_2EEUCLID__PRIMES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1774 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V0m <-> p(ap(ap(c_2Edivides_2Edivides,c_2Enum_2E0),V0m))))) # label(conj_thm_2Edivides_2EZERO__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1775 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (ap(ap(c_2Eind__type_2ENUMPAIR,V0x1),V1y1) = ap(ap(c_2Eind__type_2ENUMPAIR,V2x2),V3y2) -> V0x1 = V2x2))))))))) # label(conj_thm_2Eind__type_2ENUMPAIR__INJ__LEMMA) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1776 (all A_27a all A_27b all V4r (mem(V4r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V1f (mem(V1f,arr(ty_2Eind__type_2Erecspace(A_27a),A_27b)) -> (all V5n ap(V1f,ap(V4r,V5n)) = ap(f221(A_27a,A_27b,V4r,V1f),V5n)))))) # label(lameq_f221) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1777 (all A_27a (ne(A_27a) -> (all V0ZRECSPACE_27 (mem(V0ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (p(ap(V0ZRECSPACE_27,c_2Eind__type_2EZBOT(A_27a))) & (all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(V0ZRECSPACE_27,ap(V3r,V4n))) & p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V3r,V4n))))) -> p(ap(V0ZRECSPACE_27,ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r)))))))))) -> (all V5a0 (mem(V5a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V5a0)) -> p(ap(V0ZRECSPACE_27,V5a0)))))))))) # label(conj_thm_2Eind__type_2EZRECSPACE__strongind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1778 (all A_27A (ne(A_27A) -> (all A_27B (ne(A_27B) -> (all A_27C (ne(A_27C) -> (all V0P (mem(V0P,arr(A_27A,arr(A_27B,A_27C))) -> ((all V1x1 (mem(V1x1,A_27A) -> (all V2y1 (mem(V2y1,A_27B) -> (all V3x2 (mem(V3x2,A_27A) -> (all V4y2 (mem(V4y2,A_27B) -> (ap(ap(V0P,V3x2),V4y2) = ap(ap(V0P,V1x1),V2y1) <-> V2y1 = V4y2 & V3x2 = V1x1))))))))) -> (exists V5X (mem(V5X,arr(A_27C,A_27A)) & (exists V6Y (mem(V6Y,arr(A_27C,A_27B)) & (all V7x (mem(V7x,A_27A) -> (all V8y (mem(V8y,A_27B) -> V8y = ap(V6Y,ap(ap(V0P,V7x),V8y)) & V7x = ap(V5X,ap(ap(V0P,V7x),V8y))))))))))))))))))) # label(conj_thm_2Eind__type_2EINJ__INVERSE2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1779 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> c_2Eind__type_2EZBOT(A_27a) != ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r))))))))) # label(conj_thm_2Eind__type_2EZCONSTR__ZBOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1780 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (V3y2 = V1y1 & V2x2 = V0x1 <-> ap(ap(c_2Eind__type_2ENUMPAIR,V0x1),V1y1) = ap(ap(c_2Eind__type_2ENUMPAIR,V2x2),V3y2)))))))))) # label(conj_thm_2Eind__type_2ENUMPAIR__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1781 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZCONSTR(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool))),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))))) # label(mem_c_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1782 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> V0a = ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V0a),V1f),c_2Enum_2E0))))) & (all V2a (mem(V2a,A_27a) -> (all V3f (mem(V3f,arr(ty_2Enum_2Enum,A_27a)) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(V3f,V4n) = ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V2a),V3f),ap(c_2Enum_2ESUC,V4n)))))))))) # label(ax_thm_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1783 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EFCONS(A_27a),arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1784 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V2r,V3n))))) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r)))))))))) & p(ap(c_2Eind__type_2EZRECSPACE(A_27a),c_2Eind__type_2EZBOT(A_27a))))) # label(conj_thm_2Eind__type_2EZRECSPACE__rules) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1785 (all A_27a (ne(A_27a) -> p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27a),i(A_27a)),i(A_27a))))) # label(conj_thm_2Eind__type_2EISO__REFL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1786 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2Emk__rec(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),ty_2Eind__type_2Erecspace(A_27a))))) # label(mem_c_2Eind__type_2Emk__rec) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1787 (all A_27a (ne(A_27a) -> ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJN(A_27a),c_2Enum_2E0)),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(A_27a,bool))),k(arr(ty_2Enum_2Enum,arr(A_27a,bool)),c_2Ebool_2ET))) = c_2Eind__type_2EZBOT(A_27a))) # label(ax_thm_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1788 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1y)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(ax_thm_2Eind__type_2ENUMPAIR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1789 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> f210(A_27a,V0f) = ap(c_2Eind__type_2EINJF(A_27a),V0f))))) # label(ax_thm_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1790 (all A_27a all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V3n ap(c_2Eind__type_2Edest__rec(A_27a),ap(V2r,V3n)) = ap(f220(A_27a,V2r),V3n)))) # label(lameq_f220) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1791 (all A_27a all V5r (mem(V5r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V6n ap(V1ZRECSPACE_27,ap(V5r,V6n)) = ap(f213(A_27a,V5r,V1ZRECSPACE_27),V6n)))))) # label(lameq_f213) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1792 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2Edest__rec(A_27a),arr(ty_2Eind__type_2Erecspace(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2Edest__rec) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1793 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> k(ty_2Enum_2Enum,f209(A_27a,V0a)) = ap(c_2Eind__type_2EINJA(A_27a),V0a))))) # label(ax_thm_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1794 (all A_27a (ne(A_27a) -> ap(c_2Eind__type_2Emk__rec(A_27a),c_2Eind__type_2EZBOT(A_27a)) = c_2Eind__type_2EBOTTOM(A_27a))) # label(ax_thm_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1795 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJA(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1796 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJN(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1797 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),ap(V1f,ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V0a),V1f),V2n))))))))) # label(conj_thm_2Eind__type_2EFCONS__DEST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1798 (all A_27d all A_27b all A_27a all A_27c all V4h (mem(V4h,arr(A_27a,A_27b)) -> (all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V5a_27 ap(f222(A_27d,A_27b,A_27a,A_27c,V4h,V1f_27,V2g),V5a_27) = ap(V2g,ap(V4h,ap(V1f_27,V5a_27)))))))))) # label(lameq_f222) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1799 (all A_27a (ne(A_27a) -> (all V0a0 (mem(V0a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V0a0)) <-> (exists V1c ((exists V2i ((exists V3r (ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r) = V0a0 & (all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V3r,V4n))))) & mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) & mem(V2i,A_27a))) & mem(V1c,ty_2Enum_2Enum))) | V0a0 = c_2Eind__type_2EZBOT(A_27a)))))) # label(conj_thm_2Eind__type_2EZRECSPACE__cases) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1800 (all A_27a (ne(A_27a) -> (exists V0rep (mem(V0rep,arr(ty_2Eind__type_2Erecspace(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool)))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(ty_2Enum_2Enum,arr(A_27a,bool)),ty_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EZRECSPACE(A_27a)),V0rep)))))) # label(ax_thm_2Eind__type_2Erecspace__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.24 1801 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eind__type_2Erecspace(A_27a)) -> (all V1y (mem(V1y,ty_2Eind__type_2Erecspace(A_27a)) -> (V0x = V1y <-> ap(c_2Eind__type_2Edest__rec(A_27a),V1y) = ap(c_2Eind__type_2Edest__rec(A_27a),V0x)))))))) # label(conj_thm_2Eind__type_2EDEST__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1802 (all A_27a all V0a0 ap(f219(A_27a),V0a0) = ap(c_2Ebool_2E_21(arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)),f218(A_27a,V0a0))) # label(lameq_f219) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1803 (all A_27a all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2n f211(A_27a,V0f1,V2n,V1f2) = ap(f212(A_27a,V0f1,V1f2),V2n)))))) # label(lameq_f212) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1804 (all A_27a all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n ap(f208(A_27a,V0m),V1n) = k(A_27a,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),V0m))))) # label(lameq_f208) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1805 (all A_27a (ne(A_27a) -> c_2Eind__type_2EZRECSPACE(A_27a) = f219(A_27a))) # label(ax_thm_2Eind__type_2EZRECSPACE__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1806 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> (p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27b),V0f),V1g)) -> (all V5P (mem(V5P,arr(A_27a,bool)) -> ((exists V6x (mem(V6x,A_27a) & p(ap(V5P,V6x)))) <-> (exists V7x (mem(V7x,A_27b) & p(ap(V5P,ap(V1g,V7x)))))))) & (all V8a (mem(V8a,A_27a) -> (all V9b (mem(V9b,A_27b) -> (V9b = ap(V0f,V8a) <-> V8a = ap(V1g,V9b)))))) & (all V2P (mem(V2P,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27b) -> p(ap(V2P,ap(V1g,V4x))))) <-> (all V3x (mem(V3x,A_27a) -> p(ap(V2P,V3x)))))))))))))))) # label(conj_thm_2Eind__type_2EISO__USAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1807 (all A_27a (ne(A_27a) -> (all V1r (mem(V1r,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V1r)) <-> ap(c_2Eind__type_2Edest__rec(A_27a),ap(c_2Eind__type_2Emk__rec(A_27a),V1r)) = V1r))) & (all V0a (mem(V0a,ty_2Eind__type_2Erecspace(A_27a)) -> ap(c_2Eind__type_2Emk__rec(A_27a),ap(c_2Eind__type_2Edest__rec(A_27a),V0a)) = V0a)))) # label(ax_thm_2Eind__type_2Erecspace__repfns) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1808 (all A_27a all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V2a0 ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,arr(A_27a,bool))),V2a0),c_2Eind__type_2EZBOT(A_27a))),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f216(A_27a,V2a0,V1ZRECSPACE_27)))),ap(V1ZRECSPACE_27,V2a0)) = ap(f217(A_27a,V1ZRECSPACE_27),V2a0)))) # label(lameq_f217) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1809 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJP(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(ty_2Enum_2Enum,arr(A_27a,bool))))))) # label(mem_c_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1810 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(c_2Eind__type_2ENUMLEFT,ap(ap(c_2Eind__type_2ENUMSUM,V0x),V1y))) <-> p(V0x)) & V1y = ap(c_2Eind__type_2ENUMRIGHT,ap(ap(c_2Eind__type_2ENUMSUM,V0x),V1y)))))) # label(ax_thm_2Eind__type_2ENUMSUM__DEST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1811 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EFNIL(A_27a),arr(ty_2Enum_2Enum,A_27a)))) # label(mem_c_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1812 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZRECSPACE(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)))) # label(mem_c_2Eind__type_2EZRECSPACE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1813 (all A_27a (ne(A_27a) -> (all V0n1 (mem(V0n1,ty_2Enum_2Enum) -> (all V1n2 (mem(V1n2,ty_2Enum_2Enum) -> (V1n2 = V0n1 <-> ap(c_2Eind__type_2EINJN(A_27a),V0n1) = ap(c_2Eind__type_2EINJN(A_27a),V1n2)))))))) # label(conj_thm_2Eind__type_2EINJN__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1814 (all A_27a (ne(A_27a) -> (all V0a1 (mem(V0a1,A_27a) -> (all V1a2 (mem(V1a2,A_27a) -> (ap(c_2Eind__type_2EINJA(A_27a),V1a2) = ap(c_2Eind__type_2EINJA(A_27a),V0a1) <-> V0a1 = V1a2))))))) # label(conj_thm_2Eind__type_2EINJA__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1815 (all A_27c all A_27d all A_27a all A_27b all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V4h f222(A_27d,A_27b,A_27a,A_27c,V4h,V1f_27,V2g) = ap(f223(A_27c,A_27d,A_27a,A_27b,V1f_27,V2g),V4h)))))) # label(lameq_f223) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1816 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eind__type_2Erecspace(A_27a),bool)) -> ((all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(V0P,ap(V3r,V4n))))) -> p(ap(V0P,ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V1c),V2i),V3r)))))))))) & p(ap(V0P,c_2Eind__type_2EBOTTOM(A_27a))) -> (all V5x (mem(V5x,ty_2Eind__type_2Erecspace(A_27a)) -> p(ap(V0P,V5x))))))))) # label(conj_thm_2Eind__type_2ECONSTR__IND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1817 (all A_27a all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3a ap(ap(ap(c_2Ebool_2ECOND(bool),ap(c_2Eind__type_2ENUMLEFT,V2n)),ap(ap(V0f1,ap(c_2Eind__type_2ENUMRIGHT,V2n)),V3a)),ap(ap(V1f2,ap(c_2Eind__type_2ENUMRIGHT,V2n)),V3a)) = ap(f211(A_27a,V0f1,V2n,V1f2),V3a)))))))) # label(lameq_f211) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1818 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Enum_2Enum) -> f208(A_27a,V0m) = ap(c_2Eind__type_2EINJN(A_27a),V0m))))) # label(ax_thm_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1819 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c),V1i),V2r) = ap(c_2Eind__type_2Emk__rec(A_27a),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),f220(A_27a,V2r))))))))))) # label(ax_thm_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1820 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V0x = ap(c_2Eind__type_2ENUMFST,ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y)) & V1y = ap(c_2Eind__type_2ENUMSND,ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y)))))) # label(ax_thm_2Eind__type_2ENUMPAIR__DEST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1821 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Ebool_2EARB(A_27a) = ap(c_2Eind__type_2EFNIL(A_27a),V0n))))) # label(ax_thm_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1822 (all A_27a all A_27b all A_27c all A_27d all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (all V6h ap(f225(A_27a,A_27b,A_27c,A_27d,V0f,V3g_27),V6h) = f224(A_27b,A_27d,A_27c,A_27a,V6h,V0f,V3g_27)))))) # label(lameq_f225) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1823 (all V0b (mem(V0b,bool) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(c_2Eind__type_2ENUMSUM,V0b),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V0b),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)))))) # label(ax_thm_2Eind__type_2ENUMSUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1824 (all A_27a all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V3c ap(f216(A_27a,V2a0,V1ZRECSPACE_27),V3c) = ap(c_2Ebool_2E_3F(A_27a),f215(A_27a,V1ZRECSPACE_27,V2a0,V3c))))))) # label(lameq_f216) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1825 (all A_27b all A_27d all A_27c all A_27a all V6h (mem(V6h,arr(A_27c,A_27d)) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (all V7a ap(V3g_27,ap(V6h,ap(V0f,V7a))) = ap(f224(A_27b,A_27d,A_27c,A_27a,V6h,V0f,V3g_27),V7a)))))))) # label(lameq_f224) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1826 (all V0b1 (mem(V0b1,bool) -> (all V1x1 (mem(V1x1,ty_2Enum_2Enum) -> (all V2b2 (mem(V2b2,bool) -> (all V3x2 (mem(V3x2,ty_2Enum_2Enum) -> (V3x2 = V1x1 & (p(V0b1) <-> p(V2b2)) <-> ap(ap(c_2Eind__type_2ENUMSUM,V2b2),V3x2) = ap(ap(c_2Eind__type_2ENUMSUM,V0b1),V1x1)))))))))) # label(conj_thm_2Eind__type_2ENUMSUM__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1827 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0Fn (mem(V0Fn,arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a)),arr(arr(ty_2Enum_2Enum,A_27b),A_27b))))) -> (exists V1f ((all V2c (mem(V2c,ty_2Enum_2Enum) -> (all V3i (mem(V3i,A_27a) -> (all V4r (mem(V4r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ap(V1f,ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V2c),V3i),V4r)) = ap(ap(ap(ap(V0Fn,V2c),V3i),V4r),f221(A_27a,A_27b,V4r,V1f)))))))) & mem(V1f,arr(ty_2Eind__type_2Erecspace(A_27a),A_27b)))))))))) # label(conj_thm_2Eind__type_2ECONSTR__REC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1828 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c),V1i),V2r) != c_2Eind__type_2EBOTTOM(A_27a))))))))) # label(conj_thm_2Eind__type_2ECONSTR__BOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1829 (all A_27a all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V4i ap(c_2Ebool_2E_3F(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))),f214(A_27a,V3c,V4i,V2a0,V1ZRECSPACE_27)) = ap(f215(A_27a,V1ZRECSPACE_27,V2a0,V3c),V4i)))))))) # label(lameq_f215) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1830 (all A0 (ne(A0) -> ne(ty_2Eind__type_2Erecspace(A0)))) # label(ne_ty_2Eind__type_2Erecspace) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1831 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (p(ap(ap(c_2Eind__type_2EISO(A_27b,A_27d),V2g),V3g_27)) & p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27c),V0f),V1f_27)) -> p(ap(ap(c_2Eind__type_2EISO(arr(A_27a,A_27b),arr(A_27c,A_27d)),f223(A_27c,A_27d,A_27a,A_27b,V1f_27,V2g)),f225(A_27a,A_27b,A_27c,A_27d,V0f,V3g_27)))))))))))))))))))) # label(conj_thm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1832 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJN(A_27a),ap(c_2Enum_2ESUC,V0c))),ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJA(A_27a),V1i)),ap(c_2Eind__type_2EINJF(A_27a),V2r))) = ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r))))))))) # label(ax_thm_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1833 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJF(A_27a),arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool))),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1834 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (V0f1 = V1f2 <-> ap(c_2Eind__type_2EINJF(A_27a),V0f1) = ap(c_2Eind__type_2EINJF(A_27a),V1f2)))))))) # label(conj_thm_2Eind__type_2EINJF__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1835 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> f212(A_27a,V0f1,V1f2) = ap(ap(c_2Eind__type_2EINJP(A_27a),V0f1),V1f2))))))) # label(ax_thm_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1836 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZBOT(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool))))) # label(mem_c_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1837 (all A_27a (ne(A_27a) -> (all V0ZRECSPACE_27 (mem(V0ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> ((all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(V0ZRECSPACE_27,ap(V3r,V4n))))) -> p(ap(V0ZRECSPACE_27,ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r)))))))))) & p(ap(V0ZRECSPACE_27,c_2Eind__type_2EZBOT(A_27a))) -> (all V5a0 (mem(V5a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V5a0)) -> p(ap(V0ZRECSPACE_27,V5a0)))))))))) # label(conj_thm_2Eind__type_2EZRECSPACE__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1838 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2ECONSTR(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a)),ty_2Eind__type_2Erecspace(A_27a))))))) # label(mem_c_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1839 (all A_27a (ne(A_27a) -> (all V0c1 (mem(V0c1,ty_2Enum_2Enum) -> (all V1i1 (mem(V1i1,A_27a) -> (all V2r1 (mem(V2r1,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V3c2 (mem(V3c2,ty_2Enum_2Enum) -> (all V4i2 (mem(V4i2,A_27a) -> (all V5r2 (mem(V5r2,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c1),V1i1),V2r1) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V3c2),V4i2),V5r2) <-> V3c2 = V0c1 & V5r2 = V2r1 & V1i1 = V4i2))))))))))))))) # label(conj_thm_2Eind__type_2ECONSTR__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1840 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eind__type_2EISO(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,A_27a),bool))))))) # label(mem_c_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1841 (all A_27a all V0a0 (mem(V0a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(arr(ty_2Enum_2Enum,arr(A_27a,bool))),f217(A_27a,V1ZRECSPACE_27))),ap(V1ZRECSPACE_27,V0a0)) = ap(f218(A_27a,V0a0),V1ZRECSPACE_27)))) # label(lameq_f218) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1842 (all A_27a all V0a (mem(V0a,A_27a) -> (all V2b ap(f209(A_27a,V0a),V2b) = ap(ap(c_2Emin_2E_3D(A_27a),V2b),V0a)))) # label(lameq_f209) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1843 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EBOTTOM(A_27a),ty_2Eind__type_2Erecspace(A_27a)))) # label(mem_c_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1844 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1n ap(ap(V0f,ap(c_2Eind__type_2ENUMFST,V1n)),ap(c_2Eind__type_2ENUMSND,V1n)) = ap(f210(A_27a,V0f),V1n)))) # label(lameq_f210) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1845 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> ((all V3y (mem(V3y,A_27a) -> ap(V1g,ap(V0f,V3y)) = V3y)) & (all V2x (mem(V2x,A_27b) -> V2x = ap(V0f,ap(V1g,V2x)))) <-> p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27b),V0f),V1g))))))))))) # label(ax_thm_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1846 (all A_27a all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V4i (mem(V4i,A_27a) -> (all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V5r ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,arr(A_27a,bool))),V2a0),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V3c),V4i),V5r))),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f213(A_27a,V5r,V1ZRECSPACE_27))) = ap(f214(A_27a,V3c,V4i,V2a0,V1ZRECSPACE_27),V5r)))))))))) # label(lameq_f214) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1847 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f1_27 (mem(V1f1_27,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2f2 (mem(V2f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3f2_27 (mem(V3f2_27,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (V1f1_27 = V0f1 & V3f2_27 = V2f2 <-> ap(ap(c_2Eind__type_2EINJP(A_27a),V0f1),V2f2) = ap(ap(c_2Eind__type_2EINJP(A_27a),V1f1_27),V3f2_27)))))))))))) # label(conj_thm_2Eind__type_2EINJP__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1848 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1y (mem(V1y,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (ap(c_2Eind__type_2Emk__rec(A_27a),V1y) = ap(c_2Eind__type_2Emk__rec(A_27a),V0x) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V1y)) & p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V0x)) -> V0x = V1y)))))))) # label(conj_thm_2Eind__type_2EMK__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1849 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V2x f226(A_27a,A_27b,V0f,V2x,V1g) = ap(f227(A_27b,A_27a,V0f,V1g),V2x)))))) # label(lameq_f227) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1850 (all A_27a (ne(A_27a) -> mem(c_2EbasicSize_2Eoption__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(A_27a),ty_2Enum_2Enum))))) # label(mem_c_2EbasicSize_2Eoption__size) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1851 (all V0b (mem(V0b,bool) -> ap(c_2EbasicSize_2Ebool__size,V0b) = c_2Enum_2E0)) # label(ax_thm_2EbasicSize_2Ebool__size__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1852 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EbasicSize_2Esum__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Enum_2Enum)))))))) # label(mem_c_2EbasicSize_2Esum__size) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1853 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V3y ap(f226(A_27a,A_27b,V0f,V2x,V1g),V3y) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V2x)),ap(V1g,V3y))))))))) # label(lameq_f226) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1854 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> c_2Enum_2E0 = ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V0f),c_2Eoption_2ENONE(A_27a)))) & (all V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> ap(c_2Enum_2ESUC,ap(V1f,V2x)) = ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V1f),ap(c_2Eoption_2ESOME(A_27a),V2x)))))))) # label(ax_thm_2EbasicSize_2Eoption__size__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1855 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> ap(ap(c_2EbasicSize_2Epair__size(A_27a,A_27b),V0f),V1g) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Enum_2Enum),f227(A_27b,A_27a,V0f,V1g)))))))))) # label(ax_thm_2EbasicSize_2Epair__size__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1856 (all V0x (mem(V0x,ty_2Eone_2Eone) -> c_2Enum_2E0 = ap(c_2EbasicSize_2Eone__size,V0x))) # label(ax_thm_2EbasicSize_2Eone__size__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1857 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V3f (mem(V3f,arr(A_27a,ty_2Enum_2Enum)) -> (all V4g (mem(V4g,arr(A_27b,ty_2Enum_2Enum)) -> (all V5y (mem(V5y,A_27b) -> ap(V4g,V5y) = ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5y)))))))) & (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> ap(V0f,V2x) = ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2x)))))))))))) # label(ax_thm_2EbasicSize_2Esum__size__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1858 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EbasicSize_2Epair__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum)))))))) # label(mem_c_2EbasicSize_2Epair__size) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1859 (exists V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) & (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,V1a),ap(c_2Enum_2ESUC,ap(ap(V0f,V1a),V2n))))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V1a),ap(ap(V0f,V1a),V2n))),V2n))))))))) # label(conj_thm_2Elogroot_2ELOG__exists) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1860 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> (exists V2rt (mem(V2rt,ty_2Enum_2Enum) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2rt),V0r)),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2rt)),V0r)))))))))) # label(conj_thm_2Elogroot_2EROOT__exists) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1861 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) -> ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Elogroot_2EROOT,V2r),V1x)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Elogroot_2ELOG,V0a),V1x)),V2r)))))))) # label(conj_thm_2Elogroot_2ELOG__ROOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1862 (all V1p ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f229(V1p)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))) = ap(f230,V1p)) # label(lameq_f230) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1863 (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V3c ap(f234(V2d),V3c) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f233(V3c,V2d)),ap(ap(c_2Earithmetic_2E_2D,V3c),V2d))))) # label(lameq_f234) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1864 (all V1p ap(f232,V1p) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f231(V1p)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) # label(lameq_f232) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1865 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,V0a),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0a),V1n))))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),ap(ap(c_2Elogroot_2ELOG,V0a),V1n))),V1n))))))) # label(ax_thm_2Elogroot_2ELOG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1866 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(f239(V1p),V2d) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f238(V2d)),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))))))) # label(lameq_f239) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1867 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f236),ap(c_2Elogroot_2ESQRTd,V0n)) = ap(c_2Elogroot_2EiSQRT2,V0n))) # label(ax_thm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1868 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) -> ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),ap(c_2Enum_2ESUC,V0n))),V2b)) = ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),V2b)))))))))) # label(conj_thm_2Elogroot_2ELOG__ADD1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1869 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V0a),ap(ap(c_2Earithmetic_2E_2A,V1b),V2c)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EEXP,V0a),V1b)),V2c))))))) # label(conj_thm_2Elogroot_2EEXP__MUL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1870 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) -> ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),V2b)) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Elogroot_2ELOG,V1a),V2b))))))))) # label(conj_thm_2Elogroot_2ELOG__EXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1871 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2EROOT,V0r),V1n))),V0r))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Elogroot_2EROOT,V0r),V1n)),V0r)),V1n))))))) # label(ax_thm_2Elogroot_2EROOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1872 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0m),ap(ap(c_2Earithmetic_2EDIV,V1n),V0m)))) = ap(ap(c_2Elogroot_2ELOG,V0m),V1n)))))) # label(conj_thm_2Elogroot_2ELOG__RWT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1873 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2y)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> ap(ap(c_2Elogroot_2EROOT,V0r),ap(ap(c_2Earithmetic_2EDIV,V1x),ap(ap(c_2Earithmetic_2EEXP,V2y),V0r))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Elogroot_2EROOT,V0r),V1x)),V2y)))))))) # label(conj_thm_2Elogroot_2EROOT__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1874 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Elogroot_2EiSQRT3,V0n) & ap(c_2Elogroot_2EiSQRT2,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,V0n))) & ap(c_2Elogroot_2EiSQRT0,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n)))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)))) = ap(c_2Elogroot_2EiSQRT1,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2EiSQRT2,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V0n)))) & ap(c_2Elogroot_2EiSQRT3,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,V0n)))) & ap(c_2Elogroot_2EiSQRT1,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V0n))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Elogroot_2EiSQRT0,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2ESQRTd,c_2Earithmetic_2EZERO) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0))) # label(conj_thm_2Elogroot_2Enumeral__sqrt) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1875 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2d),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V2d),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) = ap(f231(V1p),V2d)))) # label(lameq_f231) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1876 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Elogroot_2EiSQRT0,V0n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f230),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(ax_thm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1877 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2y)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1x),V0b)) -> ap(ap(c_2Elogroot_2ELOG,V0b),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0b),V2y)),V1x)) = ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0b),V2y))))))))) # label(conj_thm_2Elogroot_2ELOG__add__digit) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1878 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f240),ap(c_2Elogroot_2ESQRTd,V0n)) = ap(c_2Elogroot_2EiSQRT3,V0n))) # label(ax_thm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1879 (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V3c ap(f238(V2d),V3c) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f237(V3c,V2d)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V3c)),V2d))))) # label(lameq_f238) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1880 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Elogroot_2ELOG,V0a),V1x)),ap(ap(c_2Elogroot_2ELOG,V0a),V2y))))))))))) # label(conj_thm_2Elogroot_2ELOG__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1881 (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V4e ap(f233(V3c,V2d),V4e) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V4e),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2d),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3c))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,V2d)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4e)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(lameq_f233) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1882 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),V2r)),ap(ap(c_2Earithmetic_2EEXP,V1b),V2r))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)))))))))) # label(conj_thm_2Elogroot_2EEXP__LE__ISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1883 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f232),ap(c_2Elogroot_2ESQRTd,V0n)) = ap(c_2Elogroot_2EiSQRT1,V0n))) # label(ax_thm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1884 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> ap(ap(c_2Elogroot_2EROOT,V0r),V1n) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f228(V1n,V0r)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2EROOT,V0r),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0r))))) & ap(ap(c_2Elogroot_2EROOT,V0r),c_2Enum_2E0) = c_2Enum_2E0))))) # label(conj_thm_2Elogroot_2EROOT__COMPUTE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1885 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V0a)) <-> c_2Enum_2E0 = ap(ap(c_2Elogroot_2ELOG,V0a),V1b))))))) # label(conj_thm_2Elogroot_2ELOG__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1886 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,V0n)) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(conj_thm_2Elogroot_2Enumeral__root2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1887 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> c_2Enum_2E0 = ap(ap(c_2Elogroot_2ELOG,V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Elogroot_2ELOG__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1888 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(f229(V1p),V2d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2d),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2d)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(lameq_f229) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1889 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> V0n = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))) # label(conj_thm_2Elogroot_2ELOG__MOD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1890 (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V4e ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V4e),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2d),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3c)))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,V2d)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,V4e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) = ap(f237(V3c,V2d),V4e)))))) # label(lameq_f237) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1891 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0a),V2r)),ap(ap(c_2Earithmetic_2EEXP,V1b),V2r))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b)))))))))) # label(conj_thm_2Elogroot_2EEXP__LT__ISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1892 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> ap(ap(c_2Elogroot_2ELOG,V0a),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Elogroot_2ELOG__BASE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1893 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1x)) -> ap(ap(c_2Elogroot_2ELOG,V0a),V1x) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Earithmetic_2EDIV,V1x),V0a)))))))) # label(conj_thm_2Elogroot_2ELOG__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1894 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Elogroot_2EROOT,V0r),V1x)),ap(ap(c_2Elogroot_2EROOT,V0r),V2y))))))))))) # label(conj_thm_2Elogroot_2EROOT__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1895 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))) = ap(c_2Elogroot_2ESQRTd,V0n))) # label(ax_thm_2Elogroot_2ESQRTd__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1896 (all V1p ap(f240,V1p) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f239(V1p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) # label(lameq_f240) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1897 (all V0e (mem(V0e,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0e)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1a),V2b)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0e),V1a)),ap(ap(c_2Earithmetic_2EEXP,V0e),V2b))))))))))) # label(conj_thm_2Elogroot_2ELT__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1898 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),V2p)),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,V0a),ap(c_2Enum_2ESUC,V2p)))) -> ap(ap(c_2Elogroot_2ELOG,V0a),V1n) = V2p))))))) # label(conj_thm_2Elogroot_2ELOG__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1899 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V2x ap(f228(V1n,V0r),V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2x)),V0r))),V2x),ap(c_2Enum_2ESUC,V2x))))))) # label(lameq_f228) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1900 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) -> ap(ap(c_2Elogroot_2ELOG,V0b),ap(ap(c_2Earithmetic_2E_2A,V0b),V1x)) = ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0b),V1x))))))) # label(conj_thm_2Elogroot_2ELOG__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1901 (all V1p ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f235(V1p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))) = ap(f236,V1p)) # label(lameq_f236) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1902 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2p)),V0r))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2p),V0r)),V1n)) -> ap(ap(c_2Elogroot_2EROOT,V0r),V1n) = V2p))))))) # label(conj_thm_2Elogroot_2EROOT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1903 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(f235(V1p),V2d) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f234(V2d)),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))))))) # label(lameq_f235) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1904 (all V0e (mem(V0e,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0e)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0e),V1a)),ap(ap(c_2Earithmetic_2EEXP,V0e),V2b))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1a),V2b)))))))))) # label(conj_thm_2Elogroot_2ELE__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1905 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c))) -> V2c = ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c)))))))))) # label(conj_thm_2Elogroot_2ELOG__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1906 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2A,V2k),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2k),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V2k),ap(ap(c_2Egcd_2Egcd,V0m),V1n)))))))) # label(conj_thm_2Egcd_2EGCD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1907 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1n),V2p)) & p(ap(ap(c_2Edivides_2Edivides,V0m),V2p)) -> p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Elcm,V0m),V1n)),V2p))))) & p(ap(ap(c_2Edivides_2Edivides,V1n),ap(ap(c_2Egcd_2Elcm,V0m),V1n))) & p(ap(ap(c_2Edivides_2Edivides,V0m),ap(ap(c_2Egcd_2Elcm,V0m),V1n))))))) # label(conj_thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1908 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 & V1m != c_2Enum_2E0 -> (exists V2p ((exists V3q (V1m = ap(ap(c_2Earithmetic_2E_2A,V3q),ap(ap(c_2Egcd_2Egcd,V0n),V1m)) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Egcd_2Egcd,V2p),V3q) & ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Egcd_2Egcd,V0n),V1m)) = V0n & mem(V3q,ty_2Enum_2Enum))) & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Egcd_2EFACTOR__OUT__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1909 (all V0x (mem(V0x,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Egcd_2Elcm,V0x),c_2Enum_2E0) & ap(ap(c_2Egcd_2Elcm,c_2Enum_2E0),V0x) = c_2Enum_2E0)) # label(conj_thm_2Egcd_2ELCM__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1910 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Edivides_2Edivides,V0p),V1b)) | ap(ap(c_2Egcd_2Egcd,V0p),V1b) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Egcd_2EPRIME__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1911 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Elcm,V0a),V1b) = ap(ap(c_2Egcd_2Elcm,V1b),V0a))))) # label(conj_thm_2Egcd_2ELCM__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1912 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4y (mem(V4y,ty_2Enum_2Enum) -> ((-p(ap(ap(c_2Earithmetic_2E_3C_3D,V4y),V3x)) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V3x)),ap(ap(c_2Earithmetic_2E_2D,V4y),V3x)))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V4y),V3x)) -> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V3x),V4y)),ap(c_2Enum_2ESUC,V4y)))) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V3x)),ap(c_2Enum_2ESUC,V4y)))))))) & (all V2x (mem(V2x,ty_2Enum_2Enum) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V2x)),c_2Enum_2E0)))) & (all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(V0P,c_2Enum_2E0),V1y)))) -> (all V5v (mem(V5v,ty_2Enum_2Enum) -> (all V6v1 (mem(V6v1,ty_2Enum_2Enum) -> p(ap(ap(V0P,V5v),V6v1))))))))) # label(conj_thm_2Egcd_2Egcd__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1913 (all V0y (mem(V0y,ty_2Enum_2Enum) -> V0y = ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0y))) # label(conj_thm_2Egcd_2Egcd__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1914 (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V1x)),c_2Enum_2E0) = ap(c_2Enum_2ESUC,V1x))) # label(conj_thm_2Egcd_2Egcd__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1915 (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V2y),V3x)),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,V3x),V2y)),ap(c_2Enum_2ESUC,V2y))),ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V3x)),ap(ap(c_2Earithmetic_2E_2D,V2y),V3x))) = ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V3x)),ap(c_2Enum_2ESUC,V2y)))))) # label(conj_thm_2Egcd_2Egcd__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1916 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),ap(ap(c_2Egcd_2Egcd,V0a),V1b))))))) # label(conj_thm_2Egcd_2EGCD__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1917 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)),V0a))))) # label(conj_thm_2Egcd_2EGCD__ADD__L) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1918 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V1b),V0a) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1919 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V0a) = V0a)) # label(conj_thm_2Egcd_2EGCD__REF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1920 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),c_2Enum_2E0),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__0R) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1921 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V2c),V1b)) & (all V3d (mem(V3d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V3d),V0a)) & p(ap(ap(c_2Edivides_2Edivides,V3d),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V3d),V2c))))) & p(ap(ap(c_2Edivides_2Edivides,V2c),V0a)) <-> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(ax_thm_2Egcd_2Eis__gcd__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1922 (all V0a (mem(V0a,ty_2Enum_2Enum) -> V0a = ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0a))) # label(conj_thm_2Egcd_2EGCD__0L) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1923 (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x)))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1924 (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2x))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2x)))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1925 (all V5y (mem(V5y,ty_2Enum_2Enum) -> (all V6x (mem(V6x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x)))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6x))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1926 (all V7y (mem(V7y,ty_2Enum_2Enum) -> (all V8x (mem(V8x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V7y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V7y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1927 (all V9y (mem(V9y,ty_2Enum_2Enum) -> (all V10x (mem(V10x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x)))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x))))) = ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9y))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1928 (all V3y (mem(V3y,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1929 (all V0y (mem(V0y,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0y) = V0y)) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1930 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Elcm,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0x & V0x = ap(ap(c_2Egcd_2Elcm,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x))) # label(conj_thm_2Egcd_2ELCM__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1931 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (all V3d (mem(V3d,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V3d)) & p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c)) -> V2c = V3d))))))))) # label(conj_thm_2Egcd_2EIS__GCD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1932 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),c_2Enum_2E0)),V1b),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EMOD,V1b),V0a)),V0a)))))) # label(conj_thm_2Egcd_2EGCD__EFFICIENTLY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1933 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Egcd_2Elcm,V0m),V1n))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) -> -p(ap(ap(c_2Edivides_2Edivides,V1n),V2p)) | -p(ap(ap(c_2Edivides_2Edivides,V0m),V2p)))))))))) # label(conj_thm_2Egcd_2ELCM__LEAST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1934 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(ap(c_2Egcd_2Egcd,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Egcd_2EGCD__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1935 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V0a),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__REF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1936 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__ADD__R) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1937 (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V2a),ap(ap(c_2Earithmetic_2E_2B,V3b),V2a)) = ap(ap(c_2Egcd_2Egcd,V2a),V3b))))) # label(conj_thm_2Egcd_2EGCD__ADD__R__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1938 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(c_2Egcd_2Egcd,V0a),ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)))))) # label(conj_thm_2Egcd_2EGCD__ADD__R__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1939 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V2d),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V2d),V0a)) -> p(ap(ap(c_2Edivides_2Edivides,V2d),ap(ap(c_2Egcd_2Egcd,V0a),V1b)))))) & p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Egcd,V0a),V1b)),V1b)) & p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Egcd,V0a),V1b)),V0a)))))) # label(conj_thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1940 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)),V0a))))) # label(conj_thm_2Egcd_2EGCD__ADD__L__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1941 (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V3b),V2a)),V2a) = ap(ap(c_2Egcd_2Egcd,V2a),V3b))))) # label(conj_thm_2Egcd_2EGCD__ADD__L__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1942 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(ap(c_2Egcd_2Egcd,V0n),V1m) = c_2Enum_2E0 <-> c_2Enum_2E0 = V0n & V1m = c_2Enum_2E0))))) # label(conj_thm_2Egcd_2EGCD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1943 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),c_2Enum_2E0) = V0a)) # label(conj_thm_2Egcd_2EGCD__0R) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1944 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Edivides_2Edivides,V0p),V1b)) | p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0p),V1b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Egcd_2EPRIME__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1945 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) & p(ap(ap(c_2Edivides_2Edivides,V0p),ap(ap(c_2Earithmetic_2E_2A,V1a),V2b))) -> p(ap(ap(c_2Edivides_2Edivides,V0p),V1a)) | p(ap(ap(c_2Edivides_2Edivides,V0p),V2b))))))))) # label(conj_thm_2Egcd_2EP__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1946 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),ap(ap(c_2Earithmetic_2E_2D,V1b),V0a)),V2c)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__MINUS__R) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1947 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1b),ap(ap(c_2Earithmetic_2E_2A,V0a),V2c))) & ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> p(ap(ap(c_2Edivides_2Edivides,V1b),V2c))))))))) # label(conj_thm_2Egcd_2EL__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1948 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V1b),V2c)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__MINUS__L) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1949 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V0n -> (exists V2p ((exists V3q (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V1m)),ap(ap(c_2Egcd_2Egcd,V1m),V0n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),V0n) & mem(V3q,ty_2Enum_2Enum))) & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Egcd_2ELINEAR__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1950 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (ap(ap(c_2Egcd_2Egcd,V0m),V2k) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> ap(ap(c_2Egcd_2Egcd,V0m),ap(ap(c_2Earithmetic_2E_2A,V2k),V1n)) = ap(ap(c_2Egcd_2Egcd,V0m),V1n)))))))) # label(conj_thm_2Egcd_2EGCD__CANCEL__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1951 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,c_2Enum_2E0),V0a),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__0L) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1952 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Egcd_2Elcm,V1n),V0m))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Egcd_2Elcm,V0m),V1n)))))))) # label(conj_thm_2Egcd_2ELCM__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1953 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V1b),V0a),V2c)) <-> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1954 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Elcm,V0m),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),c_2Enum_2E0)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0))),c_2Enum_2E0),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Egcd_2Egcd,V0m),V1n))))))) # label(ax_thm_2Egcd_2Elcm__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1955 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(V0P,c_2Enum_2E0),V1y)))) & (all V5x (mem(V5x,ty_2Enum_2Enum) -> (all V6y (mem(V6y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V5x)) & p(ap(ap(V0P,V5x),V6y)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V6y)) -> p(ap(ap(V0P,V5x),ap(ap(c_2Earithmetic_2E_2B,V5x),V6y)))))))) & (all V4x (mem(V4x,ty_2Enum_2Enum) -> p(ap(ap(V0P,V4x),V4x)))) & (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(V0P,V2x),V3y)) -> p(ap(ap(V0P,V3y),V2x))))))) -> (all V7m (mem(V7m,ty_2Enum_2Enum) -> (all V8n (mem(V8n,ty_2Enum_2Enum) -> p(ap(ap(V0P,V7m),V8n))))))))) # label(conj_thm_2Egcd_2EGCD__SUCfree__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1956 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,V0m)) & p(ap(c_2Earithmetic_2EODD,V1n)) -> ap(ap(c_2Egcd_2Egcd,V0m),V1n) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n)) & (p(ap(c_2Earithmetic_2EEVEN,V1n)) & p(ap(c_2Earithmetic_2EEVEN,V0m)) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Egcd_2Egcd,V0m),V1n)))))) # label(conj_thm_2Egcd_2EBINARY__GCD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1957 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V6r ap(f245(A_27a,V0f,V4n),V6r) = f244(A_27a,V0f,V4n,V6r)))))) # label(lameq_f245) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1958 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V0n <-> c_2Enum_2E0 = ap(c_2Enumpair_2Etri,V0n)) & (c_2Enum_2E0 = ap(c_2Enumpair_2Etri,V0n) <-> V0n = c_2Enum_2E0))) # label(conj_thm_2Enumpair_2Etri__eq__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1959 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),c_2Enum_2E0)) = ap(c_2Enumpair_2Einvtri,V0n))) # label(ax_thm_2Enumpair_2Einvtri__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1960 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),V1a)),ap(ap(c_2Enumpair_2Einvtri0,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))))) # label(conj_thm_2Enumpair_2Einvtri0__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1961 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ((-p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) -> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) -> p(ap(ap(V0P,V1n),V2a))))))) -> (all V3v (mem(V3v,ty_2Enum_2Enum) -> (all V4v1 (mem(V4v1,ty_2Enum_2Enum) -> p(ap(ap(V0P,V3v),V4v1))))))))) # label(conj_thm_2Enumpair_2Einvtri0__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1962 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0y),V1x)) -> ap(c_2Enumpair_2Einvtri,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,V1x)),V0y)) = V1x))))) # label(conj_thm_2Enumpair_2Einvtri__linverse__r) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1963 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1t (mem(V1t,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Enlen,V1t)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Enumpair_2Enlen,ap(ap(c_2Enumpair_2Encons,V0h),V1t)) & c_2Enum_2E0 = ap(c_2Enumpair_2Enlen,c_2Enum_2E0))))) # label(conj_thm_2Enumpair_2Enlen__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1964 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ap(c_2Enumpair_2Enmap,V0f) = ap(ap(c_2Enumpair_2Enlistrec(ty_2Enum_2Enum),c_2Enum_2E0),f243(V0f)))) # label(ax_thm_2Enumpair_2Enmap__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1965 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,V0m)),ap(c_2Enumpair_2Etri,V1n)))))))) # label(conj_thm_2Enumpair_2Etri__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1966 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Etri,V0n) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Enumpair_2Etri__formula) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1967 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enumpair_2Etri,V0n)),ap(c_2Enumpair_2Etri,V1m)))))))) # label(conj_thm_2Enumpair_2Etri__LT__I) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1968 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enumpair_2Etri,V1a)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a)))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))))))) # label(conj_thm_2Enumpair_2Einvtri0__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1969 (all V0l1 (mem(V0l1,ty_2Enum_2Enum) -> (all V1l2 (mem(V1l2,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enapp,V0l1),V1l2) = ap(ap(ap(c_2Enumpair_2Enlistrec(ty_2Enum_2Enum),V1l2),f248),V0l1))))) # label(ax_thm_2Enumpair_2Enapp__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1970 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Einvtri,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Einvtri__le) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1971 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))),V0n)))) # label(conj_thm_2Enumpair_2Einvtri__lower) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1972 (all V2n k(ty_2Enum_2Enum,f247(V2n)) = ap(f248,V2n)) # label(lameq_f248) # label(axiom) # label(non_clause). [assumption]. 6.29/6.25 1973 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))),ap(c_2Enum_2ESUC,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))))))))) # label(conj_thm_2Enumpair_2ESND__invtri0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1974 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Enumpair_2Etri,V0n))))) # label(conj_thm_2Enumpair_2Etri__le) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1975 (all V0nlist (mem(V0nlist,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Encons,V1h),ap(ap(c_2Enumpair_2Enapp,V2t),V0nlist)) = ap(ap(c_2Enumpair_2Enapp,ap(ap(c_2Enumpair_2Encons,V1h),V2t)),V0nlist) & ap(ap(c_2Enumpair_2Enapp,c_2Enum_2E0),V0nlist) = V0nlist)))))) # label(conj_thm_2Enumpair_2Enapp__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1976 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),c_2Enum_2E0) = V0n & ap(ap(ap(V1f,V2h),V3t),ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),V3t)) = ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),ap(ap(c_2Enumpair_2Encons,V2h),V3t)))))))))))) # label(conj_thm_2Enumpair_2Enlistrec__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1977 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enpair,ap(c_2Enumpair_2Enfst,V0n)),ap(c_2Enumpair_2Ensnd,V0n)) = V0n)) # label(conj_thm_2Enumpair_2Enpair) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1978 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V6r (mem(V6r,arr(A_27a,A_27a)) -> (all V7a ap(f244(A_27a,V0f,V4n,V6r),V7a) = ap(V6r,ap(ap(V0f,V4n),V7a))))))))) # label(lameq_f244) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1979 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))) = ap(c_2Enumpair_2Ensnd,V0n))) # label(ax_thm_2Enumpair_2Ensnd__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1980 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Einvtri,V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(conj_thm_2Enumpair_2Einvtri__upper) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1981 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1n k(ty_2Enum_2Enum,f242(V0f,V1n)) = ap(f243(V0f),V1n)))) # label(lameq_f243) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1982 (all V2r ap(ap(c_2Earithmetic_2E_2B,V2r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(f241,V2r)) # label(lameq_f241) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1983 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enumpair_2Etri,V0n)),ap(c_2Enumpair_2Etri,V1m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m))))))) # label(conj_thm_2Enumpair_2Etri__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1984 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Enfst,V0n) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))),ap(c_2Enumpair_2Einvtri,V0n))),V0n))) # label(ax_thm_2Enumpair_2Enfst__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1985 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Einvtri,ap(c_2Enumpair_2Etri,V0n)) = V0n)) # label(conj_thm_2Enumpair_2Einvtri__linverse) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1986 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Encons,ap(V0f,V1h)),ap(ap(c_2Enumpair_2Enmap,V0f),V2t)) = ap(ap(c_2Enumpair_2Enmap,V0f),ap(ap(c_2Enumpair_2Encons,V1h),V2t)) & ap(ap(c_2Enumpair_2Enmap,V0f),c_2Enum_2E0) = c_2Enum_2E0)))))) # label(conj_thm_2Enumpair_2Enmap__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1987 (all A_27a (ne(A_27a) -> mem(c_2Enumpair_2Enlistrec(A_27a),arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Enumpair_2Enlistrec) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1988 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Ensnd,ap(ap(c_2Enumpair_2Enpair,V0x),V1y)) = V1y)))) # label(conj_thm_2Enumpair_2Ensnd__npair) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1989 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> (ap(ap(c_2Enumpair_2Encons,V2h),V3t) = ap(ap(c_2Enumpair_2Encons,V0x),V1y) <-> V1y = V3t & V0x = V2h))))))))) # label(conj_thm_2Enumpair_2Encons__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1990 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,V0y)),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,V0y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) -> ap(c_2Enumpair_2Einvtri,V1n) = V0y))))) # label(conj_thm_2Enumpair_2Einvtri__unique) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1991 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1t (mem(V1t,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumpair_2Enpair,V0h),V1t)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Enumpair_2Encons,V0h),V1t))))) # label(ax_thm_2Enumpair_2Encons__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1992 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumpair_2Etri__def__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1993 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))),ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n)))))) # label(conj_thm_2Enumpair_2Etri__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1994 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))),arr(ty_2Enum_2Enum,bool)))) -> ((all V1n (mem(V1n,A_27a) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V3l (mem(V3l,ty_2Enum_2Enum) -> ((c_2Enum_2E0 != V3l -> p(ap(ap(ap(V0P,V1n),V2f),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V3l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) -> p(ap(ap(ap(V0P,V1n),V2f),V3l))))))))) -> (all V4v (mem(V4v,A_27a) -> (all V5v1 (mem(V5v1,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V6v2 (mem(V6v2,ty_2Enum_2Enum) -> p(ap(ap(ap(V0P,V4v),V5v1),V6v2))))))))))))) # label(conj_thm_2Enumpair_2Enlistrec__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1995 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enumpair_2Etri,V0n)))) # label(conj_thm_2Enumpair_2Etwotri__formula) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1996 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n k(ty_2Enum_2Enum,f245(A_27a,V0f,V4n)) = ap(f246(A_27a,V0f),V4n)))) # label(lameq_f246) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1997 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V1a (mem(V1a,A_27a) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),ap(ap(V0f,V2h),V1a)),V3t) = ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),ap(ap(c_2Enumpair_2Encons,V2h),V3t)) & ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),c_2Enum_2E0) = V1a)))))))))) # label(conj_thm_2Enumpair_2Enfoldl__thm) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1998 (all A_27a (ne(A_27a) -> mem(c_2Enumpair_2Enfoldl(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,A_27a)),arr(A_27a,arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Enumpair_2Enfoldl) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 1999 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Ensnd,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Ensnd__le) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2000 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1x ((exists V2y (ap(ap(c_2Enumpair_2Enpair,V1x),V2y) = V0n & mem(V2y,ty_2Enum_2Enum))) & mem(V1x,ty_2Enum_2Enum))))) # label(conj_thm_2Enumpair_2Enpair__cases) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2001 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> c_2Enum_2E0 != ap(ap(c_2Enumpair_2Encons,V0x),V1y))))) # label(conj_thm_2Enumpair_2Encons__not__nnil) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2002 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V4r ap(ap(c_2Enumpair_2Encons,V2n),V4r) = ap(f247(V2n),V4r)))) # label(lameq_f247) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2003 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Enfst,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Enfst__le) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2004 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V3r ap(ap(c_2Enumpair_2Encons,ap(V0f,V1n)),V3r) = ap(f242(V0f,V1n),V3r)))))) # label(lameq_f242) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2005 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Enum_2E0)) & (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> (p(ap(V0P,V2t)) -> p(ap(V0P,ap(ap(c_2Enumpair_2Encons,V1h),V2t)))))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Enumpair_2Enlist__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2006 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1h (mem(V1h,ty_2Enum_2Enum) & (exists V2t (mem(V2t,ty_2Enum_2Enum) & V0n = ap(ap(c_2Enumpair_2Encons,V1h),V2t))))) | c_2Enum_2E0 = V0n)) # label(conj_thm_2Enumpair_2Enlist__cases) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2007 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enumpair_2Etri,V1n) = ap(c_2Enumpair_2Etri,V0m) <-> V0m = V1n))))) # label(conj_thm_2Enumpair_2Etri__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2008 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V0x = ap(c_2Enumpair_2Enfst,ap(ap(c_2Enumpair_2Enpair,V0x),V1y)))))) # label(conj_thm_2Enumpair_2Enfst__npair) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2009 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enpair,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))),V1n))))) # label(ax_thm_2Enumpair_2Enpair__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2010 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,A_27a) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V2f),V1l) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1l),c_2Enum_2E0)),V0n),ap(ap(ap(V2f,ap(c_2Enumpair_2Enfst,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V2f),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))))))) # label(conj_thm_2Enumpair_2Enlistrec__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2011 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (V0x1 = V2x2 & V1y1 = V3y2 <-> ap(ap(c_2Enumpair_2Enpair,V2x2),V3y2) = ap(ap(c_2Enumpair_2Enpair,V0x1),V1y1)))))))))) # label(conj_thm_2Enumpair_2Enpair__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2012 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Etri,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enumpair_2Etri,V0n)))) # label(ax_thm_2Enumpair_2Etri__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2013 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V1a (mem(V1a,A_27a) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Enumpair_2Enlistrec(arr(A_27a,A_27a)),i(A_27a)),f246(A_27a,V0f)),V2l),V1a) = ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),V2l))))))))) # label(ax_thm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2014 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ((all V4x (mem(V4x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V4x)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V4x),V0h)) -> (p(ap(ap(c_2Ebit_2EBIT,V4x),V2a)) <-> p(ap(ap(c_2Ebit_2EBIT,V4x),V3b)))))) <-> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2a)))))))))) # label(conj_thm_2Ebit_2EBIT__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2015 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))))) # label(conj_thm_2Ebit_2EBITWISE__COR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2016 (all V0b (mem(V0b,ty_2Enum_2Enum) -> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))))) # label(conj_thm_2Ebit_2EBIT__B) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2017 (all V0wl (mem(V0wl,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),V2a),V3b) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V2a)),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V3b)))))))))) # label(conj_thm_2Ebit_2EBITWISE__BITS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2018 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) <-> p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,V0n),V1a))))))) # label(ax_thm_2Ebit_2EMOD__2EXP__MAX__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2019 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (c_2Enum_2E0 != ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) <-> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Ebit_2ENOT__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2020 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ((p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),V2b))) <-> ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V1a) = ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V2b)))))))) # label(conj_thm_2Ebit_2EBIT__SLICE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2021 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (V1b != V0a -> -p(ap(ap(c_2Ebit_2EBIT,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2EBIT__B__NEQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2022 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i ap(f249(V0n),V1i) = ap(ap(c_2Ebit_2EBIT,V1i),V0n)))) # label(lameq_f249) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2023 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))) # label(conj_thm_2Ebit_2ETWOEXP__DIVISION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2024 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__LEQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2025 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h)) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2l)))),ap(ap(ap(c_2Ebit_2EBITS,V1m),V2l),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n)))))))))) # label(conj_thm_2Ebit_2EBIT__COMP__THM3) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2026 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-(p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V1n)) <-> p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V0m))) <-> p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Ebit_2EADD__BIT0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2027 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) <-> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V0n),V2s)),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2028 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V0x)),V1n)) | V0x = c_2Enum_2E0 <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)))))))) # label(conj_thm_2Ebit_2ELT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2029 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Ebit_2EMOD__2EXP,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Ebit_2EMOD__2EXP,V1l),V2n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n))))))) # label(ax_thm_2Ebit_2ESLICE__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2030 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0a),V1b)),V0a))))))) # label(conj_thm_2Ebit_2EMOD__LEQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2031 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3y),V1l)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V2x)) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V4n) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V2x),V3y),V4n))))))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2032 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a) = V1a))))) # label(conj_thm_2Ebit_2EBITS__ZEROL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2033 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m_27 (mem(V1m_27,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3l (mem(V3l,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V2m)) & V1m_27 = ap(ap(c_2Earithmetic_2E_2B,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0h)) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V3l),V4n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1m_27),V4n)),ap(ap(ap(c_2Ebit_2ESLICE,V2m),V3l),V4n))))))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__RWT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2034 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) = c_2Enum_2E0 <-> -p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM3) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2035 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Ebit_2ENOT__MOD2__LEM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2036 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0b),V1n)) <-> ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b)))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2037 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V2b))),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)))))))) # label(conj_thm_2Ebit_2EADD__BITS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2038 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))) & V1n != c_2Enum_2E0 -> (exists V2i (mem(V2i,ty_2Enum_2Enum) & p(ap(ap(c_2Ebit_2EBIT,V2i),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V0b))))))))) # label(conj_thm_2Ebit_2EEXISTS__BIT__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2039 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)),ap(ap(c_2Ebit_2EDIV__2EXP,V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))) # label(ax_thm_2Ebit_2EBITS__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2040 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ((all V2i (mem(V2i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2i),V0n)) -> -p(ap(ap(c_2Ebit_2EBIT,V2i),V1m))))) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1m)))))) # label(conj_thm_2Ebit_2EBITS__ZERO5) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2041 (all V0h1 (mem(V0h1,ty_2Enum_2Enum) -> (all V1l1 (mem(V1l1,ty_2Enum_2Enum) -> (all V2h2 (mem(V2h2,ty_2Enum_2Enum) -> (all V3l2 (mem(V3l2,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),V0h1)) -> ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n) = ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n))))))))))))) # label(conj_thm_2Ebit_2EBITS__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2042 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V1n),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)))))) # label(conj_thm_2Ebit_2EDIV__MULT__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2043 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))))))) # label(ax_thm_2Ebit_2EDIVMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2044 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (-p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0)))))))))))) # label(conj_thm_2Ebit_2EBITWISE__NOT__COR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2045 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))) # label(conj_thm_2Ebit_2EBITS__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2046 (all V0h1 (mem(V0h1,ty_2Enum_2Enum) -> (all V1l1 (mem(V1l1,ty_2Enum_2Enum) -> (all V2h2 (mem(V2h2,ty_2Enum_2Enum) -> (all V3l2 (mem(V3l2,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h1),ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1))),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n) = ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n)))))))))))) # label(conj_thm_2Ebit_2EBITS__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2047 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))))))))) # label(conj_thm_2Ebit_2EDIV__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2048 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3i (mem(V3i,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V0l -> (p(ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n))) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Earithmetic_2E_3C_3D,V0l),V1h)),ap(ap(c_2Eprim__rec_2E_3C,V3i),V0l))),ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V3i),V1h)),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)))))))))))))) # label(conj_thm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2049 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V1i),V0n)),V2a)) <-> p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM4) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2050 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)),V1y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(c_2Ebit_2ELOG2,V1y)))))))) # label(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2051 (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2y))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V3x)),V2y)))))))) # label(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2052 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) != c_2Enum_2E0 -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n))))))) # label(conj_thm_2Ebit_2EMOD__ADD__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2053 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1h)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1h)))))))))))) # label(conj_thm_2Ebit_2EMOD__2EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2054 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),ap(c_2Enum_2ESUC,V0h))) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2055 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) -> ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__LT__HIGH) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2056 (all V0op (mem(V0op,arr(bool,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,c_2Enum_2E0),V0op),V1x),V2y) = c_2Enum_2E0)))))) # label(ax_thm_2Ebit_2EBITWISE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2057 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4op (mem(V4op,arr(bool,arr(bool,bool))) -> (all V5x (mem(V5x,ty_2Enum_2Enum) -> (all V6y (mem(V6y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V3n),V4op),V5x),V6y)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V4op,ap(ap(c_2Ebit_2EBIT,V3n),V5x)),ap(ap(c_2Ebit_2EBIT,V3n),V6y))),V3n)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V3n)),V4op),V5x),V6y))))))))) # label(ax_thm_2Ebit_2EBITWISE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2058 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2ESLICE,V1h),V0l),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ESLICE__ZERO2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2059 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2EBITS__ZERO2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2060 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) = ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n))))) # label(ax_thm_2Ebit_2EDIV__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2061 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2s)) -> -p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM3) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2062 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESLICE,V0x),V0x),V1n) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0x),V1n)),V0x))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2063 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOG2,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = V0n)) # label(conj_thm_2Ebit_2ELOG2__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2064 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2ESLICE,V1x),V1x),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0y)) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1x),V2n)),ap(ap(c_2Earithmetic_2E_2B,V1x),V0y)))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__LEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2065 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) <-> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) != c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ENOT__BITS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2066 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) <-> p(ap(c_2Earithmetic_2EODD,V0n))))) # label(conj_thm_2Ebit_2EODD__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2067 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V1a),V2b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))))))))) # label(conj_thm_2Ebit_2EBITS__MUL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2068 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),V2k)),V0n)))))))) # label(conj_thm_2Ebit_2EMOD__PLUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2069 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)))))))))) # label(conj_thm_2Ebit_2EBITSLT__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2070 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1i)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EDIV,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Ebit_2EBIT__DIV2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2071 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V2x))) -> -p(ap(ap(c_2Ebit_2EBIT,V2x),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3n)))))))))))) # label(conj_thm_2Ebit_2EBIT__OF__BITS__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2072 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i))) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2073 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) <-> p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b))))))))))))))) # label(conj_thm_2Ebit_2EBITWISE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2074 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n)),ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n)))))) # label(conj_thm_2Ebit_2EDIVMOD__2EXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2075 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)))))))) # label(conj_thm_2Ebit_2EBITS__SUM3) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2076 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2a))) <-> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x)),V2a)))))))))) # label(conj_thm_2Ebit_2EBIT__REVERSE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2077 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2k),V1j)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2k),V0n)),V1j)),V0n)))))))) # label(conj_thm_2Ebit_2EMOD__PLUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2078 (all V0x (mem(V0x,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),V0x))) # label(ax_thm_2Ebit_2EBIT__REVERSE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2079 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Enum_2ESUC,V1n)),V2x) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1n),V2x)),c_2Enum_2E0)))))) # label(ax_thm_2Ebit_2EBIT__REVERSE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2080 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2ETWOEXP__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2081 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))))))))) # label(conj_thm_2Ebit_2ESLICELT__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2082 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)))))) # label(ax_thm_2Ebit_2EMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2083 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),f251),V1a),V2b) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)))))))) # label(conj_thm_2Ebit_2EBITWISE__ONE__COMP__LEM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2084 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2ELESS__EQ__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2085 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) <-> -p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) & p(ap(ap(c_2Eprim__rec_2E_3C,V1i),V0n)) & ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) != c_2Enum_2E0 | V1i = V0n & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))))) # label(conj_thm_2Ebit_2EBIT__COMPLEMENT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2086 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V0n) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l)))))))) # label(conj_thm_2Ebit_2ESLICE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2087 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V0m -> (exists V1p (mem(V1p,ty_2Enum_2Enum) & V0m = ap(c_2Enum_2ESUC,V1p)))))) # label(conj_thm_2Ebit_2ENOT__ZERO__ADD1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2088 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = c_2Enum_2E0 & V1a != c_2Enum_2E0 -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),V1a))))))) # label(conj_thm_2Ebit_2EMOD__ZERO__GT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2089 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0b),V1n)) <-> ap(ap(ap(c_2Ebit_2EBITS,V0b),V0b),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(ax_thm_2Ebit_2EBIT__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2090 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (V2n != c_2Enum_2E0 & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),V2n)) -> (exists V3i (p(ap(ap(c_2Ebit_2EBIT,V3i),V2n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V1b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V3i)) & mem(V3i,ty_2Enum_2Enum)))))))))) # label(conj_thm_2Ebit_2EEXISTS__BIT__IN__RANGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2091 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Ebit_2ELOG2,V0n)),c_2Enum_2E0),V0n) = V0n))) # label(conj_thm_2Ebit_2EBITS__LOG2__ZERO__ID) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2092 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0b),V1n)) <-> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Ebit_2EBIT__EXP__SUB1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2093 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0a)),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Ebit_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2094 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) = ap(ap(c_2Ebit_2ETIMES__2EXP,V0x),V1n))))) # label(ax_thm_2Ebit_2ETIMES__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2095 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2x)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V3n)),V2x))))))))) # label(conj_thm_2Ebit_2EBITS__DIV__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2096 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 != ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) # label(conj_thm_2Ebit_2ETWOEXP__NOT__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2097 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1h2 (mem(V1h2,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V1h2)) -> ap(ap(ap(c_2Ebit_2EBITS,V1h2),V2l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n)))))))))) # label(conj_thm_2Ebit_2EBITS__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2098 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2099 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l)) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2ESLICE__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2100 (all V3x ap(f251,V3x) = k(bool,ap(c_2Ebool_2E_7E,V3x))) # label(lameq_f251) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2101 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V1h),c_2Enum_2E0),V0n) = ap(ap(ap(c_2Ebit_2ESLICE,V1h),c_2Enum_2E0),V0n))))) # label(conj_thm_2Ebit_2ESLICE__ZERO__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2102 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V0x)),ap(c_2Ebit_2ELOG2,V1y))))))))) # label(conj_thm_2Ebit_2ELOG2__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2103 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))) # label(conj_thm_2Ebit_2EMOD__2EXP__LT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2104 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1p)))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1p)),V0n)) -> ap(c_2Ebit_2ELOG2,V0n) = V1p))))) # label(conj_thm_2Ebit_2ELOG2__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2105 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = c_2Enum_2E0))))))) # label(conj_thm_2Ebit_2EBITS__LT__LOW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2106 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),V3b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b))))))))) # label(conj_thm_2Ebit_2EBITS__SUM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2107 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Ebit_2EDIV__MULT__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2108 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V2x)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V3y)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b)),ap(ap(c_2Earithmetic_2E_2A,V2x),V3y)))))))))))) # label(conj_thm_2Ebit_2ELESS__MULT__MONO2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2109 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,V0a),V1b))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a))))))) # label(conj_thm_2Ebit_2EEXP__SUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2110 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l)) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2111 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n)) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1n),V0r)),V1n)))))) # label(conj_thm_2Ebit_2EDIV__MULT__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2112 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOWEST__SET__BIT,V0n) = ap(c_2Ewhile_2ELEAST,f249(V0n)))) # label(ax_thm_2Ebit_2ELOWEST__SET__BIT__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2113 (all V0b (mem(V0b,bool) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1m)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Ebit_2ESBIT,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n)) = ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,V1m),V2n))))))))) # label(conj_thm_2Ebit_2ESBIT__DIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2114 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V3m ap(f250(V0l,V2n,V1h),V3m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1h)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))),V3m)),V3m)))))))) # label(lameq_f250) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2115 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) = c_2Enum_2E0 <-> V0n = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Ebit_2EMOD__PLUS__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2116 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V0h)) -> ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,V0h),V1l)),c_2Enum_2E0),V2a) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)))))))))) # label(conj_thm_2Ebit_2EBITS__ZERO4) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2117 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Ebit_2EONE__LE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2118 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a)))))) # label(conj_thm_2Ebit_2ENOT__BITS2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2119 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0i)) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)))))))))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__BITWISE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2120 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),V3b))))))))))) # label(conj_thm_2Ebit_2EBITS__SUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2121 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),V1m)) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))))) <-> p(ap(ap(c_2Ebit_2EBIT,V2i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))))))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM5) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2122 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V3b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ebit_2ESBIT,ap(ap(V1op,ap(c_2Earithmetic_2EODD,V2a)),ap(c_2Earithmetic_2EODD,V3b))),c_2Enum_2E0)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),V1op),V2a),V3b))))))))) # label(conj_thm_2Ebit_2EBITWISE__EVAL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2123 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(ap(c_2Ebit_2ESLICE,V1m),V2l),V3n))))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2124 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) <-> V1m = V0n))))) # label(conj_thm_2Ebit_2EBIT__TWO__POW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2125 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1n))))) # label(conj_thm_2Ebit_2EBITS__ZERO3) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2126 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),V0f),V1x))))) # label(ax_thm_2Ebit_2EBIT__MODIFY__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2127 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3f (mem(V3f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Enum_2ESUC,V2n)),V3f),V4x) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V2n),V3f),V4x)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V3f,V2n),ap(ap(c_2Ebit_2EBIT,V2n),V4x))),V2n)))))))) # label(ax_thm_2Ebit_2EBIT__MODIFY__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2128 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V1b),V1b),V0n) = ap(ap(c_2Ebit_2EBITV,V0n),V1b))))) # label(ax_thm_2Ebit_2EBITV__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2129 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0b),V1h)) & p(ap(ap(c_2Ebit_2EBIT,V0b),V3n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V0b)) <-> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V3n)))))))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM4) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2130 (all V0b (mem(V0b,bool) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2ESBIT,V0b),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),c_2Enum_2E0))))) # label(ax_thm_2Ebit_2ESBIT__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2131 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1P (mem(V1P,arr(ty_2Enum_2Enum,bool)) -> ((all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0n)) -> -p(ap(V1P,V2m))))) & p(ap(V1P,V0n)) -> V0n = ap(c_2Ewhile_2ELEAST,V1P)))))) # label(conj_thm_2Ebit_2ELEAST__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2132 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBITV,V1n),V0b) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0b),V1n)),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2EBITV__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2133 (all V0b (mem(V0b,ty_2Enum_2Enum) -> -p(ap(ap(c_2Ebit_2EBIT,V0b),c_2Enum_2E0)))) # label(conj_thm_2Ebit_2EBIT__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2134 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EDIV,V0a),V1b)))))))) # label(conj_thm_2Ebit_2EDIV__GT0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2135 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0i),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i)),V1n))))))) # label(conj_thm_2Ebit_2EBIT__IMP__GE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2136 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)),V0a)) & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))))))) # label(conj_thm_2Ebit_2EDIV__SUB1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2137 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) <-> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) = c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ENOT__BIT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2138 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V1h)) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V3a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V3a))))))))))))) # label(conj_thm_2Ebit_2EBIT__OF__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2139 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V1n),V2f),V3a))) <-> p(ap(ap(V2f,V0x),ap(ap(c_2Ebit_2EBIT,V0x),V3a))))))))))))) # label(conj_thm_2Ebit_2EBIT__MODIFY__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2140 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 -> p(ap(ap(c_2Ebit_2EBIT,ap(c_2Ebit_2ELOG2,V0n)),V0n))))) # label(conj_thm_2Ebit_2EBIT__LOG2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2141 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))))))))) # label(conj_thm_2Ebit_2EBITSLT__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2142 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),V2a),V3b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))))))) # label(conj_thm_2Ebit_2EBITWISE__LT__2EXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2143 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0h)),V1l)),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))))) # label(conj_thm_2Ebit_2EBITS__SUC__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2144 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2ETWOEXP__MONO2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2145 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))))))))) # label(conj_thm_2Ebit_2EBITS__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2146 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Ebit_2EZERO__LT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2147 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b))) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b)))),ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b)))))))))))) # label(conj_thm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2148 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f250(V0l,V2n,V1h)),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))))))))) # label(ax_thm_2Ebit_2ESIGN__EXTEND__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2149 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V1n)),V0i)) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__LOG2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2150 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2s),V0n)) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0n),V2s)),V1a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s)))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2151 (all V0b (mem(V0b,bool) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2ESBIT,V0b),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) = ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2B,V2n),V1m)))))))) # label(conj_thm_2Ebit_2ESBIT__MULT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2152 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V0n),V1a),V2b)) <-> ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V2b) = ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a)))))))) # label(ax_thm_2Ebit_2EMOD__2EXP__EQ__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2153 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))),V0s))))))) # label(conj_thm_2Epred__set_2EINSERT__SING__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2154 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0s)) -> (c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) = V0s -> c_2Enum_2E0 = ap(c_2Epred__set_2EMAX__SET,V0s)) & (V0s != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) -> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(c_2Epred__set_2EMAX__SET,V0s)),V0s)) & (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1y),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1y),ap(c_2Epred__set_2EMAX__SET,V0s)))))))))) # label(ax_thm_2Epred__set_2EMAX__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.26 2155 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2ECROSS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2156 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Epred__set_2EEMPTY(A_27a) != ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2ENOT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2157 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) | p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),ap(c_2Epred__set_2Eenumerate(A_27a),V0s)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__ALT__BIJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2158 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t),V2x))))))))))) # label(conj_thm_2Epred__set_2EDIFF__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2159 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) <-> (exists V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Enum_2Enum),V1f),V0s),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))))))))) # label(ax_thm_2Epred__set_2Ecountable__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2160 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q))) <-> c_2Epred__set_2EEMPTY(A_27a) = V0P | c_2Epred__set_2EEMPTY(A_27b) = V1Q | p(ap(c_2Epred__set_2EFINITE(A_27a),V0P)) & p(ap(c_2Epred__set_2EFINITE(A_27b),V1Q))))))))))) # label(conj_thm_2Epred__set_2EFINITE__CROSS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2161 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a))))))) # label(conj_thm_2Epred__set_2EIN__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2162 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0x (mem(V0x,A_27a) -> (all V2y ap(f266(A_27a,V1s,V0x),V2y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2y),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(A_27a),V2y),V0x)),ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1s)))))))) # label(lameq_f266) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2163 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x))))))))) # label(conj_thm_2Epred__set_2EELT__IN__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2164 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V2t)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V2t))),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2165 (all A_27a (ne(A_27a) -> p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2EFINITE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2166 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> (all V2s (mem(V2s,arr(A_27c,bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)),V2s) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EIMAGE(A_27c,A_27a),V1g),V2s)))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2167 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -(exists V1f (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,arr(A_27a,bool)),V1f),V0s),ap(c_2Epred__set_2EPOW(A_27a),V0s))) & mem(V1f,arr(A_27a,arr(A_27a,bool))))))))) # label(conj_thm_2Epred__set_2Epow__no__surj) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2168 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2ESING(A_27a),V0s)) <-> (exists V1x (ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)) = V0s & mem(V1x,A_27a)))))))) # label(ax_thm_2Epred__set_2ESING__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2169 (all A_27a (ne(A_27a) -> c_2Epred__set_2EEMPTY(A_27a) != c_2Epred__set_2EUNIV(A_27a))) # label(conj_thm_2Epred__set_2EEMPTY__NOT__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2170 (all A_27a (ne(A_27a) -> (all V0X (mem(V0X,arr(A_27a,bool)) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),bool)) -> ((all V2Y (mem(V2Y,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2Y),V1P)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2Y),V0X))))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1P)),V0X))))))))) # label(conj_thm_2Epred__set_2EBIGUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2171 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ELINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))))))) # label(mem_c_2Epred__set_2ELINV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2172 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0x),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(c_2Epred__set_2ESUM__SET,V1s)))))))) # label(conj_thm_2Epred__set_2ESUM__SET__IN__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2173 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)) = ap(ap(c_2Epred__set_2EUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2t)))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2174 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f266(A_27a,V1s,V0x)))))))) # label(ax_thm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2175 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EBIGUNION(A_27a),V0P) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f278(A_27a,V0P)))))) # label(ax_thm_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2176 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(V0f,V2x)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Enum_2Enum),V0f),V1s))) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Enum_2Enum),V0f),V1s))) -> ap(c_2Epred__set_2EPROD__SET,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Enum_2Enum),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V1s))) = ap(ap(c_2Earithmetic_2E_2A,ap(V0f,V2x)),ap(c_2Epred__set_2EPROD__SET,ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Enum_2Enum),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2EPROD__SET__IMAGE__REDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2177 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),V0f),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V1s))),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V1s))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__CLOSED) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2178 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V0s))))) # label(conj_thm_2Epred__set_2EINTER__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2179 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)))))) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2180 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2u)),V3t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2u)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),V3t))))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__SUBSET__gen) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2181 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27b) -> ap(ap(ap(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),V0f),V1s),V2y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Ebool_2EIN(A_27b),V2y),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Emin_2E_40(A_27a),f273(A_27b,A_27a,V2y,V0f,V1s)))),c_2Eoption_2ENONE(A_27a)))))))))))) # label(ax_thm_2Epred__set_2ELINV__OPT__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2182 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27a) -> (all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (ap(V0f,V1y) = V2x & p(ap(V3P,V1y)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),V2x),ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f259(A_27b,A_27a,V0f,V3P))))))))))))))))) # label(conj_thm_2Epred__set_2EIN__GSPEC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2183 (all V0n1 (mem(V0n1,ty_2Enum_2Enum) -> (all V1n2 (mem(V1n2,ty_2Enum_2Enum) -> (V0n1 = V1n2 <-> ap(c_2Epred__set_2Ecount,V1n2) = ap(c_2Epred__set_2Ecount,V0n1)))))) # label(conj_thm_2Epred__set_2ECOUNT__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),V0s)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27a),V1g),V0s),c_2Epred__set_2EUNIV(A_27a))) -> (all V2f (mem(V2f,arr(A_27a,ty_2Enum_2Enum)) -> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27b),ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Enum_2Enum,A_27a),V2f),V1g)),V0s) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V2f),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V1g),V0s)))))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__INJ__o) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2185 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1f (mem(V1f,arr(A_27a,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27a),V1f),V0s),V0s)) & -p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27a),V1f),V0s),V0s)))) <-> -p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2EINFINITE__INJ__NOT__SURJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2186 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V0s))))))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2187 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2188 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),c_2Epred__set_2EREST(A_27a)),V0n),V1s)),V1s)))))))) # label(conj_thm_2Epred__set_2EEXPLICIT__ENUMERATE__MONO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2189 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V0s))))) # label(conj_thm_2Epred__set_2EDIFF__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2190 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1s),V2t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2191 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V0s),V1t)) -> (all V3e (mem(V3e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),V0s)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V3e)),ap(ap(c_2Epred__set_2EDELETE(A_27b),V1t),ap(V2f,V3e)))))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2192 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1e (mem(V1e,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3b (mem(V3b,A_27b) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27b) -> ap(ap(V0f,V4x),ap(ap(V0f,V5y),V6z)) = ap(ap(V0f,V5y),ap(ap(V0f,V4x),V6z)))))))) -> ap(ap(V0f,V1e),ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1e)),V3b)) = ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s)),V3b)))))))))))))) # label(conj_thm_2Epred__set_2ECOMMUTING__ITSET__RECURSES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2193 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> V1s = ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)))) & (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s) = V0s)))) # label(conj_thm_2Epred__set_2EUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2194 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V4x ap(ap(c_2Epair_2E_2C(A_27a,bool),V4x),ap(V1Q,V4x)) = ap(f298(A_27a,V1Q),V4x)))) # label(lameq_f298) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2195 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (V1s = ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2196 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0n),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))) = V0n)) # label(conj_thm_2Epred__set_2ESUM__SET__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2197 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ((exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),V0f)),V3n),V1s))))) <-> p(ap(ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V1s),V2x))))))))))) # label(ax_thm_2Epred__set_2Eschroeder__close__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2198 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) -> p(ap(V0P,V3x))))) <-> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) -> p(ap(V0P,V4x))))) & p(ap(V0P,V1a))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2199 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s = c_2Epred__set_2EUNIV(A_27a) -> (all V1v (mem(V1v,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),V0s))))))))) # label(conj_thm_2Epred__set_2EIN__EQ__UNIV__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2200 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1e (mem(V1e,A_27a) -> (all V2s2 (mem(V2s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1e)),V2s2)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s2)))))))))))) # label(conj_thm_2Epred__set_2EDELETE__SUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2201 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27b),V1t)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) -> p(ap(c_2Epred__set_2Ecountable(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t)))))))))))) # label(conj_thm_2Epred__set_2Ecross__countable) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2202 (all A_27a all V0set (mem(V0set,arr(A_27a,bool)) -> (all V1s ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V1s),ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V0set)) = ap(f289(A_27a,V0set),V1s)))) # label(lameq_f289) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2203 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)) = c_2Epred__set_2EUNIV(arr(A_27a,A_27b)))))) # label(conj_thm_2Epred__set_2EUNIV__FUNSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2204 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s)) -> ap(ap(c_2Epred__set_2ESUM__IMAGE(arr(A_27a,bool)),c_2Epred__set_2ECARD(A_27a)),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s)) = ap(c_2Epred__set_2ECARD(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2Epartition__CARD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2205 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1M (mem(V1M,arr(arr(A_27a,bool),bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Epred__set_2EBIGUNION(A_27a),V1M)) = ap(c_2Epred__set_2EBIGUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27b,bool)),ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f)),V1M)))))))))) # label(conj_thm_2Epred__set_2EIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2206 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) = k(A_27a,c_2Ebool_2ET))) # label(ax_thm_2Epred__set_2EUNIV__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2207 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Epred__set_2Echooser(A_27a),ap(c_2Epred__set_2EREST(A_27a),V1s)),V2n) = ap(ap(c_2Epred__set_2Echooser(A_27a),V1s),ap(c_2Enum_2ESUC,V2n)))))) & (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2Echooser(A_27a),V0s),c_2Enum_2E0) = ap(c_2Epred__set_2ECHOICE(A_27a),V0s))))) # label(ax_thm_2Epred__set_2Echooser__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2208 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2209 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))))))))))) # label(conj_thm_2Epred__set_2ESURJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2210 (all A_27a (ne(A_27a) -> (all V0sp (mem(V0sp,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),f281(A_27a,V0sp)),V1s)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0sp),ap(c_2Epred__set_2EBIGINTER(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2EDIFF__BIGINTER1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2211 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V1s))))))))))) # label(conj_thm_2Epred__set_2Epartition__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2212 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s)) = V0s))))) # label(conj_thm_2Epred__set_2ECHOICE__INSERT__REST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2213 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))))))) # label(mem_c_2Epred__set_2EGSPEC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2214 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2g (mem(V2g,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2g)),V1t) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V2g))))))))) # label(conj_thm_2Epred__set_2EDIFF__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2215 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2216 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EINJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2EINJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2217 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <-> p(ap(ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t),V2x))))))))))) # label(conj_thm_2Epred__set_2EUNION__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2218 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & (exists V2y (mem(V2y,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0s)))) <-> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__MEMBER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2219 (all A_27b all A_27a all V3y (mem(V3y,A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V4x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)),ap(ap(c_2Emin_2E_3D(A_27b),V3y),ap(V0f,V4x))) = ap(f272(A_27b,A_27a,V3y,V0f,V1s),V4x)))))))) # label(lameq_f272) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2220 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> (p(ap(c_2Epred__set_2EFINITE(arr(A_27a,bool)),V1s)) & (all V2e (mem(V2e,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2e),V1s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V2e)) & V0n = ap(c_2Epred__set_2ECARD(A_27a),V2e)))) & (all V3e1 (mem(V3e1,arr(A_27a,bool)) -> (all V4e2 (mem(V4e2,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3e1),V1s)) & V3e1 != V4e2 & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V4e2),V1s)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V3e1),V4e2))))))) -> ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1s)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Epred__set_2ECARD(arr(A_27a,bool)),V1s)),V0n)))))))) # label(conj_thm_2Epred__set_2ECARD__BIGUNION__SAME__SIZED__SETS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2221 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f256(A_27a,V1P)))) <-> p(ap(V1P,V0y))))))))) # label(conj_thm_2Epred__set_2EIN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2222 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27b)) = c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2223 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V0s)))))) # label(conj_thm_2Epred__set_2ESUBSET__REFL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2224 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2e (mem(V2e,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(A_27a),V2e),V1s)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)),ap(V0f,V2e))),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V2e))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2225 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V0x)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s)))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__IN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2226 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t))))))))) # label(conj_thm_2Epred__set_2EINSERT__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2227 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2EGSPEC(ty_2Enum_2Enum,ty_2Enum_2Enum),f275(V0n)) = ap(c_2Epred__set_2Ecount,V0n))) # label(ax_thm_2Epred__set_2Ecount__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2228 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPSUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EPSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2229 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V3x)),ap(V1g,V3x)))))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V2s)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1g),V2s))))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2230 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V2t)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27b),V1s),V2t)))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2231 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> (all V1B (mem(V1B,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0A),V1B)),V0A) = V0A & ap(ap(c_2Epred__set_2EINTER(A_27a),V0A),ap(ap(c_2Epred__set_2EUNION(A_27a),V0A),V1B)) = V0A & V0A = ap(ap(c_2Epred__set_2EINTER(A_27a),V0A),ap(ap(c_2Epred__set_2EUNION(A_27a),V1B),V0A)) & ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V1B),V0A)),V0A) = V0A)))))) # label(conj_thm_2Epred__set_2EINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2232 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u) = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)))))))))) # label(conj_thm_2Epred__set_2EUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2233 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> (all V1B (mem(V1B,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0A),V1B)),V2x) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0A),V2x)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1B),V2x)))))))))) # label(conj_thm_2Epred__set_2EUNION__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2234 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s)))))) # label(conj_thm_2Epred__set_2ENOT__UNIV__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2235 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V2t))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2236 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2f ap(c_2Ebool_2E_21(A_27a),f270(A_27b,A_27a,V1Q,V2f,V0P)) = ap(f271(A_27b,A_27a,V0P,V1Q),V2f)))))) # label(lameq_f271) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2237 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),arr(A_27b,bool))) -> ((all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3b (mem(V3b,A_27b) -> ((V2s != c_2Epred__set_2EEMPTY(A_27a) & p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> p(ap(ap(V1P,ap(c_2Epred__set_2EREST(A_27a),V2s)),ap(ap(V0f,ap(c_2Epred__set_2ECHOICE(A_27a),V2s)),V3b)))) -> p(ap(ap(V1P,V2s),V3b))))))) -> (all V4v (mem(V4v,arr(A_27a,bool)) -> (all V5v1 (mem(V5v1,A_27b) -> p(ap(ap(V1P,V4v),V5v1))))))))))))))) # label(conj_thm_2Epred__set_2EITSET__IND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2238 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ENOT__PSUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2239 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s))) & (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2EINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2240 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(c_2Epred__set_2ECARD(arr(A_27a,bool)),ap(c_2Epred__set_2EPOW(A_27a),V0s)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epred__set_2ECARD(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECARD__POW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2241 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(arr(A_27a,bool),bool)) -> ((all V1x (mem(V1x,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1x),V0s)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V1x))))) & p(ap(c_2Epred__set_2Ecountable(arr(A_27a,bool)),V0s)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V0s)))))))) # label(conj_thm_2Epred__set_2Ebigunion__countable) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2242 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> (all V2x (mem(V2x,A_27a) -> (all V3P (mem(V3P,arr(A_27b,bool)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),f261(A_27a,A_27b,V2x,V3P)))) <-> V0a = V2x & p(ap(V3P,V1b))))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2243 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Epred__set_2ECARD(A_27a),V0s)) = ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))))))))) # label(conj_thm_2Epred__set_2ECARD__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2244 (all A_27a all V0sp (mem(V0sp,arr(A_27a,bool)) -> (all V3u ap(f282(A_27a,V0sp),V3u) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0sp),V3u)))) # label(lameq_f282) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2245 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a)) = c_2Epred__set_2EUNIV(A_27a))))) # label(conj_thm_2Epred__set_2EINSERT__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2246 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)))) # label(mem_c_2Epred__set_2EEMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2247 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27a),V0f),V1s))))))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__IMAGE__NUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2248 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))),ap(ap(c_2Epred__set_2EINTER(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2t)))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2249 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> ((exists V3g (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s)) & mem(V3g,arr(A_27b,A_27a)))) <-> (exists V2f (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) & mem(V2f,arr(A_27a,A_27b))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2250 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V1t)) | p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2Einter__countable) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2251 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = V0s))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2252 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(c_2Epred__set_2ECARD(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)) = ap(c_2Epred__set_2ECARD(A_27a),V1s))))))))))))) # label(conj_thm_2Epred__set_2EINJ__CARD__IMAGE__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2253 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> -p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)))))))) # label(conj_thm_2Epred__set_2Einfinite__rest) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2254 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1s)) -> ap(ap(c_2Earithmetic_2E_2A,V0x),ap(c_2Epred__set_2EPROD__SET,ap(ap(c_2Epred__set_2EDELETE(ty_2Enum_2Enum),V1s),V0x))) = ap(c_2Epred__set_2EPROD__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0x),V1s))))))) # label(conj_thm_2Epred__set_2EPROD__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2255 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t)))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2256 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V0s) = V0s)))) # label(conj_thm_2Epred__set_2EUNION__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2257 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) <-> V0x = V1y))))))) # label(conj_thm_2Epred__set_2EEQUAL__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2258 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)))))) # label(conj_thm_2Epred__set_2EEMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2259 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1t))))))))) # label(conj_thm_2Epred__set_2EFINITE__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2260 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V1s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V2t)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2261 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) != c_2Epred__set_2EEMPTY(A_27a))) # label(conj_thm_2Epred__set_2EUNIV__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2262 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s)) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s)) = V1s))))))) # label(conj_thm_2Epred__set_2EBIGUNION__partition) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2263 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V1t))))))))) # label(conj_thm_2Epred__set_2Esubset__countable) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2264 (all A_27a all V2t (mem(V2t,arr(A_27a,bool)) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V3x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V2t),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f300(A_27a,V1s,V3x,V0R)))) = ap(f301(A_27a,V2t,V0R,V1s),V3x)))))))) # label(lameq_f301) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2265 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> ap(ap(c_2Epred__set_2EPROD__IMAGE(A_27a),V0f),c_2Epred__set_2EEMPTY(A_27a)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & (all V1e (mem(V1e,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> ap(ap(c_2Epred__set_2EPROD__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s)) = ap(ap(c_2Earithmetic_2E_2A,ap(V0f,V1e)),ap(ap(c_2Epred__set_2EPROD__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1e)))))))))))) # label(conj_thm_2Epred__set_2EPROD__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2266 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ERINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))))))) # label(mem_c_2Epred__set_2ERINV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2267 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (all V4u (mem(V4u,arr(A_27c,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27b,A_27c),V1g),V3t),V4u)) -> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u))))))))))))))))))) # label(conj_thm_2Epred__set_2ESURJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2268 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EUNIV(A_27a) = V0s <-> (all V1x (mem(V1x,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))))))))) # label(conj_thm_2Epred__set_2EEQ__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2269 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) != c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2ENOT__EMPTY__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.27 2270 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2s (mem(V2s,arr(A_27c,bool)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EPREIMAGE(A_27b,A_27c),V1g),V2s)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s))))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__COMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2271 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ((all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (all V7z (mem(V7z,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V5x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V6y),V1s)) & p(ap(ap(V0R,V5x),V6y)) & p(ap(ap(V0R,V6y),V7z)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V7z),V1s)) -> p(ap(ap(V0R,V5x),V7z))))))))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V1s)) -> (p(ap(ap(V0R,V4y),V3x)) <-> p(ap(ap(V0R,V3x),V4y)))))))) & (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) -> p(ap(ap(V0R,V2x),V2x))))) <-> p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s))))))))) # label(ax_thm_2Epred__set_2Eequiv__on__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2272 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2273 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2ESUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2274 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V2x)),ap(V1Q,V2x))) = ap(f299(A_27a,V1Q,V0P),V2x)))))) # label(lameq_f299) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2275 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27b))) -> (all V2b (mem(V2b,A_27b) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0s),c_2Epred__set_2EEMPTY(A_27a))),V2b),ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),ap(c_2Epred__set_2EREST(A_27a),V0s)),ap(ap(V1f,ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),V2b))) = ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),V0s),V2b)))))))))))) # label(conj_thm_2Epred__set_2EITSET__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2276 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (all V2z (mem(V2z,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1y),V2z)))))))))) # label(conj_thm_2Epred__set_2EDIFF__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2277 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(c_2Epred__set_2ECARD(A_27b),V2t) = ap(c_2Epred__set_2ECARD(A_27a),V1s) & p(ap(c_2Epred__set_2EFINITE(A_27b),V2t))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__BIJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2278 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1N (mem(V1N,ty_2Enum_2Enum) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1N),V2n)) -> ap(V0f,V2n) = c_2Epred__set_2EEMPTY(A_27a)))) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,arr(A_27a,bool)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,arr(A_27a,bool)),V0f),ap(c_2Epred__set_2Ecount,V1N)))))))))) # label(conj_thm_2Epred__set_2EBIGUNION__IMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2279 (all A_27a (ne(A_27a) -> (all V0sp (mem(V0sp,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> (c_2Epred__set_2EEMPTY(arr(A_27a,bool)) != V1s & (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t),V1s)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V0sp))))) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0sp),ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),f282(A_27a,V0sp)),V1s))) = ap(c_2Epred__set_2EBIGINTER(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2EDIFF__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2280 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) <-> (exists V1f ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> (exists V3n (mem(V3n,ty_2Enum_2Enum) & V2x = ap(V1f,V3n)))))) & mem(V1f,arr(ty_2Enum_2Enum,A_27a))))))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__ALT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2281 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c))) -> (all V1a (mem(V1a,arr(A_27b,bool)) -> (all V2b (mem(V2b,arr(A_27c,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,ty_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2EFST(A_27b,A_27c)),V0f)),V1a)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,ty_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2ESND(A_27b,A_27c)),V0f)),V2b)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),V0f),ap(ap(c_2Epred__set_2ECROSS(A_27b,A_27c),V1a),V2b)))))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__CROSS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2282 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27b) -> ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),ap(ap(c_2Epred__set_2EINSERT(A_27b),V2x),c_2Epred__set_2EEMPTY(A_27b)))),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q)) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),ap(ap(c_2Epred__set_2EINSERT(A_27b),V2x),V1Q)))))))))))) # label(conj_thm_2Epred__set_2ECROSS__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2283 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)),ap(c_2Epred__set_2ECOMPL(A_27a),V1t)))))))) # label(conj_thm_2Epred__set_2ECOMPL__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2284 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2EDISJOINT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2285 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) -> p(ap(ap(c_2Epred__set_2ESUBSET(arr(A_27a,bool)),ap(c_2Epred__set_2EPOW(A_27a),V0s1)),ap(c_2Epred__set_2EPOW(A_27a),V1s2)))))))))) # label(conj_thm_2Epred__set_2ESUBSET__POW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2286 (all A_27b all A_27a all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f270(A_27b,A_27a,V1Q,V2f,V0P),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0P)),ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V3x)),ap(V1Q,V3x)))))))))) # label(lameq_f270) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2287 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Epred__set_2EUNIV(ty_2Esum_2Esum(A_27a,A_27b)) = ap(ap(c_2Epred__set_2EUNION(ty_2Esum_2Esum(A_27a,A_27b)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,ty_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL(A_27a,A_27b)),c_2Epred__set_2EUNIV(A_27a))),ap(ap(c_2Epred__set_2EIMAGE(A_27b,ty_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR(A_27a,A_27b)),c_2Epred__set_2EUNIV(A_27b))))))) # label(conj_thm_2Epred__set_2ESUM__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2288 (all A_27a all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> (all V1x ap(f280(A_27a,V0P),V1x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f279(A_27a,V0P,V1x)))))) # label(lameq_f280) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2289 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ((exists V4x (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) & p(ap(V0P,V4x)) & mem(V4x,A_27a))) | p(ap(V0P,V1a)) <-> (exists V3x (mem(V3x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) & p(ap(V0P,V3x))))))))))))) # label(conj_thm_2Epred__set_2EEXISTS__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2290 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)))))))))) # label(conj_thm_2Epred__set_2EUNION__OVER__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2291 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s))),V1s)))))))))) # label(conj_thm_2Epred__set_2EIMAGE__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2292 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECARD__REST) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2293 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0s)) -> (all V1e (mem(V1e,ty_2Enum_2Enum) -> ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EDELETE(ty_2Enum_2Enum),V0s),V1e)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1e),V0s)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epred__set_2ESUM__SET,V0s)),V1e)),ap(c_2Epred__set_2ESUM__SET,V0s))))))) # label(conj_thm_2Epred__set_2ESUM__SET__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2294 (all A_27a all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3x ap(f262(A_27a,V2P),V3x) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V3x)),ap(V2P,V3x))))) # label(lameq_f262) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2295 (all A_27a all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(V1P,V2x)) = ap(f256(A_27a,V1P),V2x)))) # label(lameq_f256) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2296 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27b) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ((exists V3x (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & V0y = ap(V2f,V3x) & mem(V3x,A_27a))) <-> p(ap(ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s),V0y))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2297 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eequiv__on(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2Eequiv__on) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2298 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Epairwise(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2Epairwise) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2299 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2ECARD(ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V0n)) = V0n)) # label(conj_thm_2Epred__set_2ECARD__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2300 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> c_2Epred__set_2EEMPTY(A_27a) != ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)))))))) # label(conj_thm_2Epred__set_2EINFINITE__DIFF__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2301 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> V1t = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)) & V1t = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)),V0s)))))))) # label(conj_thm_2Epred__set_2EUNION__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2302 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a)) = V0s)))) # label(conj_thm_2Epred__set_2EDIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2303 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V1f),V0s),V2t)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27b),V2t))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__SURJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2304 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> ap(ap(c_2Ecombin_2Eo(A_27a,bool,A_27b),V1s),V0f) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__ALT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2305 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)) = V0s)))) # label(conj_thm_2Epred__set_2ECOMPL__COMPL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2306 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(arr(A_27a,bool),bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2s_27),V0s)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2s_27),V1t))))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V0s)),V1t))))))) & (all V3s (mem(V3s,arr(arr(A_27a,bool),bool)) -> (all V4t (mem(V4t,arr(A_27a,bool)) -> ((all V5s_27 (mem(V5s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V5s_27),V3s)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V4t),V5s_27))))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V4t),ap(c_2Epred__set_2EBIGUNION(A_27a),V3s)))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2307 (all A_27a (ne(A_27a) -> (all V0g (mem(V0g,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V1f,V4n)),ap(V1f,ap(c_2Enum_2ESUC,V4n)))))) & V2m != V3n & (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(V0g,V5n) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(V1f,ap(c_2Enum_2ESUC,V5n))),ap(V1f,V5n)))) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(V0g,V2m)),ap(V0g,V3n)))))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DIFFS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2308 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EITSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(arr(A_27a,bool),arr(A_27b,A_27b)))))))) # label(mem_c_2Epred__set_2EITSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2309 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),c_2Ecombin_2EI(A_27a)),V0s) = V0s)))) # label(conj_thm_2Epred__set_2EIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2310 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2ESUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2311 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V0x)),V1y) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),V0x))))))))) # label(conj_thm_2Epred__set_2EDELETE__COMM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2312 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)),V1y) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y))))))))))) # label(conj_thm_2Epred__set_2EDELETE__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2313 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))) <-> (exists V1x (mem(V1x,A_27a) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2314 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V2u)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__PSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2315 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eis__measure__maximal(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2Eis__measure__maximal) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2316 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))) -> p(ap(V0P,V3x))))) <-> (all V5x (mem(V5x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t)) -> p(ap(V0P,V5x))))) & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) -> p(ap(V0P,V4x)))))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2317 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))))))) # label(conj_thm_2Epred__set_2EIN__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2318 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EBIJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2EBIJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2319 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ECOMPL(A_27a),V1s),V0x)) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2ECOMPL__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2320 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(V0f,V3x)))))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Epred__set_2ECARD(A_27a),V1s)),V2n)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s))))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__lower__bound) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2321 (all A_27a (ne(A_27a) -> ((exists V0f ((exists V3y (mem(V3y,A_27a) & (all V4x (mem(V4x,A_27a) -> ap(V0f,V4x) != V3y)))) & (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (ap(V0f,V1x) = ap(V0f,V2y) -> V1x = V2y))))) & mem(V0f,arr(A_27a,A_27a)))) <-> -p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Epred__set_2EINFINITE__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2322 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Epred__set_2ECARD(A_27a),V1t))))))))))) # label(conj_thm_2Epred__set_2ECARD__UNION__LE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2323 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f299(A_27a,V1Q,V0P)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f297(A_27a,V0P))),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f298(A_27a,V1Q))))))))) # label(conj_thm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2324 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27b) -> ap(ap(V0f,V2x),ap(ap(V0f,V3y),V4z)) = ap(ap(V0f,V3y),ap(ap(V0f,V2x),V4z)))))))) -> (all V5x (mem(V5x,A_27a) -> (all V6b (mem(V6b,A_27b) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V5x),V1s)),V6b) = ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V5x)),ap(ap(V0f,V5x),V6b))))))))))))))) # label(conj_thm_2Epred__set_2ECOMMUTING__ITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2325 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((exists V1s (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1s),V0P)) & mem(V1s,arr(A_27a,bool)))) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V0P)))))))) # label(conj_thm_2Epred__set_2EFINITE__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2326 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,arr(A_27a,bool)) -> (V0c = c_2Epred__set_2EEMPTY(A_27a) | (exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & V0c = ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),V0c))))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__ENUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2327 (all A_27a (ne(A_27a) -> ap(c_2Epred__set_2ECARD(A_27a),c_2Epred__set_2EEMPTY(A_27a)) = c_2Enum_2E0)) # label(conj_thm_2Epred__set_2ECARD__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2328 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))) = ap(f264(A_27a,V1t,V0s),V2x)))))) # label(lameq_f264) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2329 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> -p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)))))))))) # label(conj_thm_2Epred__set_2EINFINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2330 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESING(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2ESING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2331 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) = ap(c_2Epred__set_2ECOMPL(A_27a),c_2Epred__set_2EEMPTY(A_27a)))) # label(conj_thm_2Epred__set_2ECOMPL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2332 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s))))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2333 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ((all V1x (mem(V1x,A_27b) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f274(A_27b,A_27a,V1x,V0f)))))) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V3s)) <-> p(ap(c_2Epred__set_2EFINITE(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V3s))))))))))))) # label(conj_thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2334 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),V1s),V2t)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V2t)))))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2335 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2ESING(A_27a),V1t)) & c_2Epred__set_2EEMPTY(A_27a) = V0s | p(ap(c_2Epred__set_2ESING(A_27a),V0s)) & p(ap(c_2Epred__set_2ESING(A_27a),V1t)) & V0s = V1t | p(ap(c_2Epred__set_2ESING(A_27a),V0s)) & c_2Epred__set_2EEMPTY(A_27a) = V1t <-> p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2ESING__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2336 (all A_27a (ne(A_27a) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) <-> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V1x (mem(V1x,A_27a) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)))))))))) # label(conj_thm_2Epred__set_2ENOT__IN__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2337 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & ap(c_2Epred__set_2EGSPEC(A_27a,ty_2Enum_2Enum),f276(A_27a,V1f,V0s)) = V0s & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m),ap(c_2Epred__set_2ECARD(A_27a),V0s))) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Epred__set_2ECARD(A_27a),V0s))) -> (ap(V1f,V3m) = ap(V1f,V2n) -> V3m = V2n))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__ISO__NUM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2338 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1f (p(ap(ap(ap(c_2Epred__set_2ESURJ(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)) & mem(V1f,arr(ty_2Enum_2Enum,A_27a)))) | V0s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2Ecountable__surj) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2339 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> V3x = ap(ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V0f),V1s),ap(V0f,V3x)))))))))))))))) # label(conj_thm_2Epred__set_2ELINV__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2340 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),V0x) = c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2ESING__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2341 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27b)) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),c_2Epred__set_2EEMPTY(A_27b)) & ap(ap(c_2Epred__set_2ECROSS(A_27c,A_27a),c_2Epred__set_2EEMPTY(A_27c)),V0P) = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27c,A_27a)))))))))) # label(conj_thm_2Epred__set_2ECROSS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2342 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))) = ap(f265(A_27a,V1t,V0s),V2x)))))) # label(lameq_f265) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2343 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) -> (all V3e (mem(V3e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),V0s)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V3e)),ap(ap(c_2Epred__set_2EDELETE(A_27b),V1t),ap(V2f,V3e)))))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2344 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> ((all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (V2n != V1m -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(V0f,V1m)),ap(V0f,V2n)))))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(V0f,V3n)),ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,arr(A_27a,bool)),V0f),ap(c_2Epred__set_2Ecount,V3n)))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2345 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(arr(A_27b,bool),bool)) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27b,bool),arr(A_27a,bool)),ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f)),V1s)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(c_2Epred__set_2EBIGUNION(A_27b),V1s)))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2346 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eschroeder__close(A_27a),arr(arr(A_27a,A_27a),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2Eschroeder__close) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2347 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),V1s)))) <-> p(ap(c_2Erelation_2EWF(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),V1s))))))))))) # label(conj_thm_2Epred__set_2EFINITE__WF__noloops) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2348 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0s),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V1t),c_2Epred__set_2EEMPTY(arr(A_27a,bool))))))))))) # label(conj_thm_2Epred__set_2EBIGUNION__PAIR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2349 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V2x)),V1s)) <-> p(ap(ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s),V2x))))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2350 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V0n)),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V0n)),ap(c_2Epred__set_2Ecount,V1m))) = ap(c_2Epred__set_2Ecount,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)))))) # label(conj_thm_2Epred__set_2Ecount__add) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2351 (all A_27a all V0e (mem(V0e,A_27a) -> (all V2ps ap(ap(c_2Epred__set_2EUNION(arr(A_27a,bool)),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),ap(c_2Epred__set_2EINSERT(A_27a),V0e)),V2ps)),V2ps) = ap(f290(A_27a,V0e),V2ps)))) # label(lameq_f290) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2352 (all A_27a all V0y (mem(V0y,A_27a) -> (all V1x ap(f295(A_27a,V0y),V1x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(ap(c_2Emin_2E_3D(A_27a),V0y),V1x))))) # label(lameq_f295) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2353 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x f254(A_27a,A_27b,V0P,V1x) = ap(f255(A_27b,A_27a,V0P),V1x)))) # label(lameq_f255) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2354 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) = ap(c_2Epred__set_2EBIGINTER(A_27a),c_2Epred__set_2EEMPTY(arr(A_27a,bool))))) # label(conj_thm_2Epred__set_2EBIGINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2355 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V0f),V1s)),V2t),V1s))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__LINV__BIJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2356 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (mem(V1n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1n),V0s)))) <-> (exists V2n (mem(V2n,ty_2Enum_2Enum) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3m),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),V3m))))) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2n),V0s))))))) # label(conj_thm_2Epred__set_2ENUM__SET__WOP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2357 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f264(A_27a,V1t,V0s)) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))))))) # label(ax_thm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2358 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V4y ap(f300(A_27a,V1s,V3x,V0R),V4y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V4y),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V4y),V1s)),ap(ap(V0R,V3x),V4y)))))))))) # label(lameq_f300) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2359 (all A_27b all A_27a all V1s (mem(V1s,arr(A_27b,bool)) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x ap(f309(A_27b,A_27a,V1s,V0f),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V2x)),V1s))))))) # label(lameq_f309) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2360 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)))))))))) # label(conj_thm_2Epred__set_2EFINITE__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2361 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__SUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2362 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V0s = V1t -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EEQ__SUBSET__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2363 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(c_2Epred__set_2EFINITE(arr(A_27a,bool)),ap(c_2Epred__set_2EPOW(A_27a),V0s)))))))) # label(conj_thm_2Epred__set_2EFINITE__POW) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2364 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V1P),V2Q),V0f)) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),ap(V2Q,V3x))))))))))))))))) # label(conj_thm_2Epred__set_2EDFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2365 (all A_27b all A_27a all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4y),V2x)),ap(V3P,V4y)) = ap(f260(A_27b,A_27a,V2x,V3P),V4y)))))) # label(lameq_f260) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2366 (all A_27a all V0x ap(f292(A_27a),V0x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V0x),c_2Ebool_2ET)) # label(lameq_f292) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2367 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V0s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1t)))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2368 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2369 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27b))) -> (all V2b (mem(V2b,A_27b) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),V0s),V2b) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Epred__set_2EFINITE(A_27a),V0s)),ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0s),c_2Epred__set_2EEMPTY(A_27a))),V2b),ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),ap(c_2Epred__set_2EREST(A_27a),V0s)),ap(ap(V1f,ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),V2b)))),c_2Ebool_2EARB(A_27b)))))))))))) # label(conj_thm_2Epred__set_2EITSET__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2370 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,A_27a) -> (all V1x (mem(V1x,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a)))) <-> V1x = c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2EPSUBSET__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2371 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x ap(f267(A_27b,A_27a,V0f,V1s),V2x) = ap(ap(c_2Epair_2E_2C(A_27b,bool),ap(V0f,V2x)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))))))) # label(lameq_f267) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2372 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (ap(V0f,V1x) = ap(V0f,V2y) -> V1x = V2y))))) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V3s)) -> -p(ap(c_2Epred__set_2EFINITE(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V3s))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__11__INFINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2373 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V0s)))))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V3t),V2s)),V2s)))))))) # label(conj_thm_2Epred__set_2EINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2374 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27b),V1s),V2t)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V2t)))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2375 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27b,bool)) -> c_2Epred__set_2EUNIV(arr(A_27a,A_27b)) = ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),c_2Epred__set_2EEMPTY(A_27a)),V0s))))))) # label(conj_thm_2Epred__set_2EEMPTY__FUNSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2376 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2ESING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2377 (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> (all V2e1 (mem(V2e1,ty_2Enum_2Enum) -> (all V3e2 (mem(V3e2,ty_2Enum_2Enum) -> ap(c_2Epred__set_2EMIN__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V2e1),ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V3e2),V1s))) = ap(ap(c_2Earithmetic_2EMIN,V2e1),ap(c_2Epred__set_2EMIN__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V3e2),V1s))))))))) # label(conj_thm_2Epred__set_2EMIN__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2378 (all V0e (mem(V0e,ty_2Enum_2Enum) -> V0e = ap(c_2Epred__set_2EMIN__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0e),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))))) # label(conj_thm_2Epred__set_2EMIN__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2379 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2f ap(c_2Ebool_2E_21(A_27a),f268(A_27b,A_27a,V1Q,V2f,V0P)) = ap(f269(A_27b,A_27a,V0P,V1Q),V2f)))))) # label(lameq_f269) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2380 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (ap(c_2Epred__set_2ECARD(A_27a),V0s) = c_2Enum_2E0 <-> V0s = c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ECARD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2381 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s))) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V2t)) -> p(ap(ap(V0R,V3x),V4y))))))))))))))))) # label(conj_thm_2Epred__set_2Epartition__elements__interrelate) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2382 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,arr(A_27a,ty_2Enum_2Enum)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V2y = V1x <-> p(ap(ap(ap(c_2Epred__set_2Eis__measure__maximal(A_27a),V0m),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))),V2y))))))))))) # label(conj_thm_2Epred__set_2Eis__measure__maximal__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.28 2383 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f265(A_27a,V1t,V0s)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))))))) # label(ax_thm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2384 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))))))))))) # label(conj_thm_2Epred__set_2EIN__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2385 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),arr(A_27a,bool)))))))) # label(mem_c_2Epred__set_2EPREIMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2386 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EUNIV(A_27a) = ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)))) & (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s) = c_2Epred__set_2EUNIV(A_27a))))) # label(conj_thm_2Epred__set_2EUNION__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2387 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & -p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> -p(ap(c_2Epred__set_2EFINITE(A_27b),V2t))))))))))))) # label(conj_thm_2Epred__set_2EINFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2388 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27b) -> ap(c_2Eoption_2ETHE(A_27a),ap(ap(ap(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),V0f),V1s),V2y)) = ap(ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V0f),V1s),V2y))))))))))) # label(ax_thm_2Epred__set_2ELINV__LO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2389 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(f263(A_27a,V1t,V0s),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))) # label(lameq_f263) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2390 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2e (mem(V2e,A_27a) -> (all V3acc ap(f287(A_27a,V0f,V2e),V3acc) = ap(ap(c_2Earithmetic_2E_2A,ap(V0f,V2e)),V3acc)))))) # label(lameq_f287) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2391 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))))) <-> V0s = V1t))))))) # label(conj_thm_2Epred__set_2EEXTENSION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2392 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ENOT__IN__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2393 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((all V1x (mem(V1x,arr(A_27a,bool)) -> ((all V2y (mem(V2y,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V2y),V1x)) -> p(ap(V0P,V2y))))) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1x)) -> p(ap(V0P,V1x)))))) -> (all V3x (mem(V3x,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V3x)) -> p(ap(V0P,V3x)))))))))) # label(conj_thm_2Epred__set_2EFINITE__COMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2394 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (V3y = V2x <-> ap(V0f,V3y) = ap(V0f,V2x)))))) -> ap(c_2Epred__set_2ECARD(A_27a),V1s) = ap(c_2Epred__set_2ECARD(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))))))))))) # label(conj_thm_2Epred__set_2ECARD__INJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2395 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Enum_2ESUC,ap(c_2Epred__set_2ECARD(A_27a),V0s))) = ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s))))))))) # label(conj_thm_2Epred__set_2ECARD__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2396 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECOMPL(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2ECOMPL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2397 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V0x),V1P)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),ap(c_2Epred__set_2EBIGUNION(A_27a),V1P)))))))))) # label(conj_thm_2Epred__set_2ESUBSET__BIGUNION__I) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2398 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Esum_2Esum(A_27a,A_27b)),ap(c_2Esum_2EINL(A_27a,A_27b),V2x)),V1t))))) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL(A_27a,A_27b)),V0s),V1t))))))))))) # label(conj_thm_2Epred__set_2EINJ__INL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2399 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) != c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ENOT__INSERT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2400 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V2x),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V2x)),V0P)) & p(ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V2x)),V1Q))))))))))))) # label(conj_thm_2Epred__set_2EIN__CROSS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2401 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2x_27 (mem(V2x_27,A_27a) -> ((p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),V0s))) <-> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x_27))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2402 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1g (mem(V1g,arr(A_27a,A_27a)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27a),V1g),V0s),V0s)) -> (all V2f (mem(V2f,arr(A_27a,ty_2Enum_2Enum)) -> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V2f),V0s) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Enum_2Enum,A_27a),V2f),V1g)),V0s))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__PERMUTES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2403 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x = V2y <-> ap(V0f,V1x) = ap(V0f,V2y))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__IMP__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2404 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V0s)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__SYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2405 (all A_27a all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2s ap(f277(A_27a,V0P,V1x),V2s) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2s),V0P)),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s))))))) # label(lameq_f277) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2406 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s) = c_2Enum_2E0 <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) -> c_2Enum_2E0 = ap(V0f,V2x)))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__ZERO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2407 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1s1 (mem(V1s1,arr(A_27a,bool)) -> (all V2s2 (mem(V2s2,arr(A_27b,bool)) -> c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27b)) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),c_2Epred__set_2EEMPTY(A_27a)),V2s2) & ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2EIMAGE(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),f305(A_27a,A_27b,V0a)),V2s2)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V1s1),V2s2)) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0a),V1s1)),V2s2))))))))))) # label(conj_thm_2Epred__set_2ECROSS__EQNS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2408 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Epred__set_2ECARD(A_27b),V2t)),ap(c_2Epred__set_2ECARD(A_27a),V1s))) & p(ap(c_2Epred__set_2EFINITE(A_27b),V2t)) -> -p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(conj_thm_2Epred__set_2EPHP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2409 (all A_27a (ne(A_27a) -> ($F <-> p(ap(c_2Epred__set_2ESING(A_27a),c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2ESING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2410 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2411 (all A_27a all A_27b all V0a (mem(V0a,A_27a) -> (all V3y ap(f305(A_27a,A_27b,V0a),V3y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V3y)))) # label(lameq_f305) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2412 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Epartition(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))))) # label(mem_c_2Epred__set_2Epartition) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2413 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),V2t))))))))))))) # label(conj_thm_2Epred__set_2EINJ__IMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2414 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (all V3s0 (mem(V3s0,arr(A_27a,bool)) -> (all V4t0 (mem(V4t0,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V2t),V4t0)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s0),V1s)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V3s0),V4t0))))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2415 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f296(A_27a,V1Q,V0P)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f297(A_27a,V0P))),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f298(A_27a,V1Q))))))))) # label(conj_thm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2416 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((exists V2t (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V1f),V0s),V2t)) & mem(V2t,arr(A_27b,bool)))) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V1f),V0s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0s)))))))))))) # label(conj_thm_2Epred__set_2EINJ__IMAGE__BIJ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2417 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2sp (mem(V2sp,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V2sp),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1t)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27b),V1t))),V2sp))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__COMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2418 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eenumerate(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))))) # label(mem_c_2Epred__set_2Eenumerate) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2419 (all V0e (mem(V0e,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1s)) -> ap(ap(c_2Earithmetic_2EMAX,V0e),ap(c_2Epred__set_2EMAX__SET,V1s)) = ap(c_2Epred__set_2EMAX__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0e),V1s))))))) # label(conj_thm_2Epred__set_2EMAX__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2420 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0t)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Epred__set_2ECARD(A_27a),V0t)),ap(c_2Epred__set_2ECARD(A_27a),V1s))) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V0t))))))))))))) # label(conj_thm_2Epred__set_2ELESS__CARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2421 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2Echooser(A_27a),V0s),c_2Enum_2E0) = ap(c_2Epred__set_2ECHOICE(A_27a),V0s))) & (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Epred__set_2Echooser(A_27a),V1s),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))) = ap(ap(c_2Epred__set_2Echooser(A_27a),ap(c_2Epred__set_2EREST(A_27a),V1s)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) & (all V3s (mem(V3s,arr(A_27a,bool)) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(c_2Epred__set_2Echooser(A_27a),ap(c_2Epred__set_2EREST(A_27a),V3s)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))) = ap(ap(c_2Epred__set_2Echooser(A_27a),V3s),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))))))))) # label(conj_thm_2Epred__set_2Echooser__def__compute) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2422 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> V1t = V0s))))))) # label(conj_thm_2Epred__set_2ESUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2423 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> (all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),f260(A_27b,A_27a,V2x,V3P)))) <-> V1b = V2x & p(ap(V3P,V0a))))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__1) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2424 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epred__set_2EIN__INFINITE__NOT__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2425 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s),ap(ap(c_2Epred__set_2EUNION(A_27a),V3t),V2s))))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2426 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1e (mem(V1e,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s)),V3t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1e),V2s)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),V3t)) | p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),ap(ap(c_2Epred__set_2EDELETE(A_27b),V3t),ap(V0f,V1e)))) & p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V1e)),V3t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1e),V2s))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2427 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Enum_2Enum,bool)) -> (V0P != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) & (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2x),V0P)) & (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3y),V0P)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2x),V3y))))) -> p(ap(V1Q,V2x))))) -> p(ap(V1Q,ap(c_2Epred__set_2EMIN__SET,V0P)))))))) # label(conj_thm_2Epred__set_2EMIN__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2428 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27b) -> ap(ap(ap(c_2Epred__set_2ERINV(A_27a,A_27b),V0f),V1s),V2y) = ap(c_2Eoption_2ETHE(A_27a),ap(ap(ap(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),V0f),V1s),V2y)))))))))))) # label(ax_thm_2Epred__set_2ERINV__LO) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2429 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) = V0s <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s))))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2430 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <-> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))) # label(ax_thm_2Epred__set_2EDISJOINT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2431 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0P),V1s)) <-> (all V2e1 (mem(V2e1,A_27a) -> (all V3e2 (mem(V3e2,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3e2),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2e1),V1s)) -> p(ap(ap(V0P,V2e1),V3e2)))))))))))))) # label(ax_thm_2Epred__set_2Epairwise__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2432 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> (exists V3f_27 (mem(V3f_27,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27b,A_27a),V3f_27),V2t),V1s)))) | c_2Epred__set_2EEMPTY(A_27a) = V1s))))))))))) # label(conj_thm_2Epred__set_2Einj__surj) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2433 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s1 (mem(V1s1,arr(A_27a,bool)) -> (all V2s2 (mem(V2s2,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(V0f,V4y) = ap(V0f,V3x) <-> V3x = V4y))))) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1s1),V2s2)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s1)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s2))))))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2434 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s1 (mem(V1s1,arr(A_27a,bool)) -> (all V2s2 (mem(V2s2,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(V0f,V3x) = ap(V0f,V4y) <-> V3x = V4y))))) -> (V1s1 = V2s2 <-> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s2) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s1))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__11) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2435 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f267(A_27b,A_27a,V0f,V1s)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))))))))) # label(ax_thm_2Epred__set_2EIMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2436 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V0s)))))) # label(conj_thm_2Epred__set_2EPSUBSET__IRREFL) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2437 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (all V4u (mem(V4u,arr(A_27c,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27c),V1g),V3t),V4u)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u))))))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2438 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V3n)),ap(V0f,ap(c_2Enum_2ESUC,V3n)))))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1n)),ap(V0f,ap(ap(c_2Earithmetic_2E_2B,V1n),V2d))))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__ADD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2439 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,bool) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) | p(V1y) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),ap(c_2Ecombin_2EK(bool,A_27a),V1y)))))))))) # label(conj_thm_2Epred__set_2ESUBSET__K) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2440 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(V0P,V1x)) = ap(f253(A_27a,V0P),V1x)))) # label(lameq_f253) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2441 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPROD__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))))) # label(mem_c_2Epred__set_2EPROD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2442 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27a) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (p(ap(V2P,V0a)) & V1b = V0a <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f262(A_27a,V2P))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__same) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2443 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECARD(A_27a),arr(arr(A_27a,bool),ty_2Enum_2Enum)))) # label(mem_c_2Epred__set_2ECARD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2444 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V0t)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epred__set_2ECARD(A_27a),V1s)),ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V0t)))))))))) # label(conj_thm_2Epred__set_2ECARD__DIFF__EQN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2445 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((exists V2x (mem(V2x,A_27a) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)))) <-> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__INSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2446 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) & p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0R),V2t)) -> p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0R),V1s))))))))))) # label(conj_thm_2Epred__set_2Epairwise__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2447 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27a),i(A_27a)),V0s),V0s)))))) # label(conj_thm_2Epred__set_2EINJ__ID) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2448 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s))) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2EFINITE__REST__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2449 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2ESING(A_27a),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ESING__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2450 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2e (mem(V2e,A_27a) -> (all V3acc ap(f284(A_27a,V0f,V2e),V3acc) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V2e)),V3acc)))))) # label(lameq_f284) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2451 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V2f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0s),V1t))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V3x)),V1t))))))))))))))) # label(conj_thm_2Epred__set_2EFUNSET__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2452 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))) # label(conj_thm_2Epred__set_2EINSERT__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2453 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0P)) & p(ap(c_2Epred__set_2EFINITE(A_27b),V1Q)) -> p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q)))))))))))) # label(conj_thm_2Epred__set_2EFINITE__CROSS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2454 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1e (mem(V1e,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V1e)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1e))) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s))))))) & ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),c_2Epred__set_2EEMPTY(A_27a)) = c_2Enum_2E0)))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2455 (all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(ap(c_2Epair_2E_2C(A_27a,bool),V4y),ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3x),V4y)) = ap(f304(A_27a,V0R,V3x),V4y)))))) # label(lameq_f304) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2456 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,ty_2Enum_2Enum),f285(A_27a,V0f)),V1s),c_2Enum_2E0) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s))))))) # label(ax_thm_2Epred__set_2ESUM__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2457 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) <-> V1s = c_2Epred__set_2EEMPTY(A_27a) | V1s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))))) # label(conj_thm_2Epred__set_2ESING__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2458 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),arr(A_27b,bool))) -> ((all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3b (mem(V3b,A_27b) -> ((p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) & V2s != c_2Epred__set_2EEMPTY(A_27a) -> p(ap(ap(V1P,ap(c_2Epred__set_2EREST(A_27a),V2s)),ap(ap(V0f,ap(c_2Epred__set_2ECHOICE(A_27a),V2s)),V3b)))) -> p(ap(ap(V1P,V2s),V3b))))))) -> (all V4v (mem(V4v,arr(A_27a,bool)) -> (all V5v1 (mem(V5v1,A_27b) -> p(ap(ap(V1P,V4v),V5v1))))))))))))))) # label(conj_thm_2Epred__set_2EITSET__ind) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2459 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (V1t = c_2Epred__set_2EEMPTY(A_27b) | p(ap(c_2Epred__set_2Ecountable(A_27b),V1t)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) | V0s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(c_2Epred__set_2Ecountable(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t)))))))))))) # label(conj_thm_2Epred__set_2Ecross__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2460 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Epred__set_2EUNIV(ty_2Epair_2Eprod(A_27a,A_27b)) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)))))) # label(conj_thm_2Epred__set_2ECROSS__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2461 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27a),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))))))) # label(conj_thm_2Epred__set_2Ecountable__image__nats) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2462 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f309(A_27b,A_27a,V1s,V0f)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s))))))))) # label(ax_thm_2Epred__set_2EPREIMAGE__def) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2463 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2464 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,bool)))))))) # label(mem_c_2Epred__set_2EIMAGE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2465 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EBIGINTER(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2466 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EPOW(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0e),V1s)) = ap(ap(c_2Epred__set_2EUNION(arr(A_27a,bool)),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),ap(c_2Epred__set_2EINSERT(A_27a),V0e)),ap(c_2Epred__set_2EPOW(A_27a),V1s))),ap(c_2Epred__set_2EPOW(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2EPOW__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2467 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (-p(ap(ap(c_2Ebool_2EIN(A_27b),V4y),V2t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0b),V1s),V2t)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V3x),V4y),V0b)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V3x),V1s)),ap(ap(c_2Epred__set_2EINSERT(A_27b),V4y),V2t)))))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__EXTEND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2468 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) <-> c_2Epred__set_2EEMPTY(A_27a) = V0s & c_2Epred__set_2EEMPTY(A_27a) = V1t))))))) # label(conj_thm_2Epred__set_2EEMPTY__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2469 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1e (mem(V1e,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),V2s)),V3t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1e),V2s)) -> (exists V4u (ap(ap(c_2Epred__set_2EINSERT(A_27b),ap(V0f,V1e)),V4u) = V3t & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),V4u)) & -p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V1e)),V4u)) & mem(V4u,arr(A_27b,bool))))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__INSERT__IMP) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2470 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Epred__set_2EUNIV(A_27a),V0x)))))) # label(conj_thm_2Epred__set_2EUNIV__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2471 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))),ap(c_2Epred__set_2ECARD(A_27a),V0s)))))))))) # label(conj_thm_2Epred__set_2ECARD__INTER__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2472 (all A_27a (ne(A_27a) -> (all V0set (mem(V0set,arr(A_27a,bool)) -> ap(c_2Epred__set_2EPOW(A_27a),V0set) = ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f289(A_27a,V0set)))))) # label(ax_thm_2Epred__set_2EPOW__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2473 (all A_27a all V0x ap(ap(c_2Epair_2E_2C(A_27a,bool),V0x),c_2Ebool_2EF) = ap(f291(A_27a),V0x)) # label(lameq_f291) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2474 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0x)),V0x) = c_2Epred__set_2EEMPTY(A_27a) & ap(ap(c_2Epred__set_2EINTER(A_27a),V0x),ap(c_2Epred__set_2ECOMPL(A_27a),V0x)) = c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2ECOMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2475 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Echooser(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))))) # label(mem_c_2Epred__set_2Echooser) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2476 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((all V1P (mem(V1P,arr(arr(A_27a,bool),bool)) -> (p(ap(V1P,c_2Epred__set_2EEMPTY(A_27a))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(V1P,V2s)) -> (all V3e (mem(V3e,A_27a) -> p(ap(V1P,ap(ap(c_2Epred__set_2EINSERT(A_27a),V3e),V2s)))))))) -> p(ap(V1P,V0s))))) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(ax_thm_2Epred__set_2EFINITE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2477 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(ty_2Esum_2Esum(A_27b,A_27a),bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Esum_2Esum(A_27b,A_27a)),ap(c_2Esum_2EINR(A_27b,A_27a),V2x)),V1t))))) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR(A_27b,A_27a)),V0s),V1t))))))))))) # label(conj_thm_2Epred__set_2EINJ__INR) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2478 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f253(A_27a,V0P)) = V0P)))) # label(conj_thm_2Epred__set_2EGSPEC__ETA) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2479 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2480 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V2u)))))))))) # label(conj_thm_2Epred__set_2EINTER__OVER__UNION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2481 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),V1P)) -> ap(c_2Epred__set_2ECARD(A_27b),V1P) = ap(c_2Epred__set_2ECARD(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),V1P))))))))))) # label(conj_thm_2Epred__set_2ECARD__SING__CROSS) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2482 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s)) -> (all V2t1 (mem(V2t1,arr(A_27a,bool)) -> (all V3t2 (mem(V3t2,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3t2),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s))) & V3t2 != V2t1 & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t1),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s))) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t1),V3t2)))))))))))))) # label(conj_thm_2Epred__set_2Epartition__elements__disjoint) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2483 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & ap(c_2Epred__set_2ECARD(A_27a),V0s) = ap(c_2Epred__set_2ECARD(A_27a),V1t) -> V1t = V0s)))))))) # label(conj_thm_2Epred__set_2ESUBSET__EQ__CARD) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2484 (all A_27a (ne(A_27a) -> (all V0I (mem(V0I,arr(ty_2Enum_2Enum,bool)) -> (all V1J (mem(V1J,arr(ty_2Enum_2Enum,bool)) -> (all V2n (mem(V2n,A_27a) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),V0I),V1J)) & V1J != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) & V0I != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2EMIN__SET,V1J)),ap(c_2Epred__set_2EMIN__SET,V0I)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__MIN__SET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2485 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s)))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER2) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2486 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (-p(V0x) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V1y)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Ecombin_2EK(bool,A_27a),V0x)),V1y))))))))) # label(conj_thm_2Epred__set_2EK__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2487 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (p(ap(c_2Epred__set_2Ecountable(ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epred__set_2EUNIV(ty_2Epair_2Eprod(A_27a,A_27b)))) <-> p(ap(c_2Epred__set_2Ecountable(A_27b),c_2Epred__set_2EUNIV(A_27b))) & p(ap(c_2Epred__set_2Ecountable(A_27a),c_2Epred__set_2EUNIV(A_27a)))))))) # label(conj_thm_2Epred__set_2Ecountable__Uprod) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2488 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Epred__set_2Ecountable(ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V0n))))) # label(conj_thm_2Epred__set_2ECOUNTABLE__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2489 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> ((exists V2s (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2s),V1sos)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) & mem(V2s,arr(A_27a,bool)))) <-> p(ap(ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos),V0x))))))))) # label(conj_thm_2Epred__set_2EBIGUNION__applied) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2490 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)),V0s) = c_2Epred__set_2EEMPTY(A_27a) & c_2Epred__set_2EUNIV(A_27a) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)),V0s))))) # label(conj_thm_2Epred__set_2ECOMPL__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2491 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),i(A_27a)),V0s) = V0s)))) # label(conj_thm_2Epred__set_2EIMAGE__ID) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2492 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) -> (ap(V0f,V5y) = ap(V0f,V4x) <-> V5y = V4x)))))) <-> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(conj_thm_2Epred__set_2EINJ__IFF) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2493 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EINSERT) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2494 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2f_27 (mem(V2f_27,arr(A_27a,A_27b)) -> (all V3s_27 (mem(V3s_27,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V3s_27)) -> ap(V0f,V4x) = ap(V2f_27,V4x)))) & V1s = V3s_27 -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f_27),V3s_27) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2495 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1s)) -> V0x = V2y))) <-> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) = V1s))))))) # label(conj_thm_2Epred__set_2EUNIQUE__MEMBER__SING) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2496 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2t),V0x))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2497 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(c_2Epred__set_2Ecountable(A_27b),V2t)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V1s))))))))))))) # label(conj_thm_2Epred__set_2Einj__countable) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2498 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = V1t <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2499 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Epred__set_2ECARD(A_27a),V1t))),ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))) = ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ECARD__UNION__EQN) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2500 (all A_27a (ne(A_27a) -> ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),c_2Ecombin_2EI(A_27a)) = c_2Ecombin_2EI(arr(A_27a,bool)))) # label(conj_thm_2Epred__set_2EIMAGE__II) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2501 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,ty_2Epair_2Eprod(A_27b,bool))) -> ((all V1x (mem(V1x,A_27a) -> -p(ap(c_2Epair_2ESND(A_27b,bool),ap(V0f,V1x))))) -> ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),V0f) = c_2Epred__set_2EEMPTY(A_27b)))))))) # label(conj_thm_2Epred__set_2EGSPEC__F__COND) # label(axiom) # label(non_clause). [assumption]. 6.29/6.29 2502 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0P)) -> (exists V1x (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0P)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Epred__set_2EINFINITE__INHAB) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2503 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2e ap(f285(A_27a,V0f),V2e) = f284(A_27a,V0f,V2e)))) # label(lameq_f285) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2504 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)))))))))) # label(conj_thm_2Epred__set_2EINSERT__COMM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2505 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V2s)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1g),V2s))),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),f286(A_27a,V0f,V1g)),V2s)))))))))))) # label(conj_thm_2Epred__set_2EABS__DIFF__SUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2506 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27b),ap(V0f,V1x)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2s)))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2507 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V1t (mem(V1t,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),V0s),V1t)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ESUM__SET,V0s)),ap(c_2Epred__set_2ESUM__SET,V1t)))))))) # label(conj_thm_2Epred__set_2ESUM__SET__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2508 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> ((exists V2f (mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V2f),V0s),V1t)))) -> (exists V3g (mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27a),V3g),V1t),V0s))))))))))))) # label(conj_thm_2Epred__set_2ESURJ__IMP__INJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2509 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0P),V1Q) = ap(c_2Epred__set_2EBIGINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0P),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V1Q),c_2Epred__set_2EEMPTY(arr(A_27a,bool))))))))))) # label(conj_thm_2Epred__set_2EBIGINTER__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2510 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1s),V0P)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))))) & p(ap(c_2Epred__set_2EFINITE(arr(A_27a,bool)),V0P)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V0P)))))))) # label(conj_thm_2Epred__set_2EFINITE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2511 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)),ap(c_2Epred__set_2ECOMPL(A_27a),V1t))) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))))))) # label(conj_thm_2Epred__set_2EINTER__UNION__COMPL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2512 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V1s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V2t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V1s)) -> (exists V3N (mem(V3N,ty_2Enum_2Enum) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3N),V4n)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),ap(V0f,V4n)),V2t)))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__FINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2513 (all V1p ap(f306,V1p) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V1p),ap(c_2Epred__set_2Ecount,V1p))) # label(lameq_f306) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2514 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t))))))))) # label(conj_thm_2Epred__set_2EINSERT__UNION__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2515 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDIFF(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EDIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2516 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2Efinite__countable) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2517 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(arr(A_27a,bool),bool)) -> (all V1s2 (mem(V1s2,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EUNION(arr(A_27a,bool)),V0s1),V1s2)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V0s1)),ap(c_2Epred__set_2EBIGUNION(A_27a),V1s2)))))))) # label(conj_thm_2Epred__set_2EBIGUNION__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2518 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s) = ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f302(A_27a,V0R,V1s)))))))) # label(ax_thm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2519 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (V1s = c_2Epred__set_2EEMPTY(A_27b) <-> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s))))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (V2s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b)))))))))))) # label(conj_thm_2Epred__set_2ESURJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2520 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) -> (exists V3g (mem(V3g,arr(A_27b,A_27a)) & (all V4y (mem(V4y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V4y),V2t)) -> V4y = ap(V0f,ap(V3g,V4y))))) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27a),V3g),V2t),V1s))))))))))))))) # label(conj_thm_2Epred__set_2ESURJ__INJ__INV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2521 (all A_27b all A_27a all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f268(A_27b,A_27a,V1Q,V2f,V0P),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0P)),ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V3x)),V1Q))))))))) # label(lameq_f268) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2522 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V1s))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__CLOSE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2523 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V1t)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2Eunion__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2524 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V1t != V0s & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2EPSUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2525 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2s)),V3t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V1x)),V3t)) & (all V4y (mem(V4y,A_27a) -> (ap(V0f,V1x) = ap(V0f,V4y) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V2s)) -> V4y = V1x))) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),V3t))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2526 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) <-> V2y != V1x & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2527 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) = ap(c_2Epred__set_2EREST(A_27a),V0s))))) # label(ax_thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2528 (all A_27a (ne(A_27a) -> ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27a),c_2Ecombin_2EI(A_27a)) = c_2Ecombin_2EI(arr(A_27a,bool)))) # label(conj_thm_2Epred__set_2EPREIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2529 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (V1y != V0x & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2P)) | V0x = V1y <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2P)))))))))))) # label(conj_thm_2Epred__set_2EIN__INSERT__EXPAND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2530 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__ALT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2531 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s1 (mem(V1s1,arr(A_27a,bool)) -> (all V2s2 (mem(V2s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0R),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s1),V2s2))) <-> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V2s2)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s1)) -> p(ap(ap(V0R,V3x),V4y)) & p(ap(ap(V0R,V4y),V3x))))))) & p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0R),V2s2)) & p(ap(ap(c_2Epred__set_2Epairwise(A_27a),V0R),V1s1))))))))))) # label(conj_thm_2Epred__set_2Epairwise__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2532 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))))))) # label(ax_thm_2Epred__set_2EDELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2533 (all A_27a (ne(A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Epred__set_2EBIGUNION(A_27a),c_2Epred__set_2EEMPTY(arr(A_27a,bool))))) # label(conj_thm_2Epred__set_2EBIGUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2534 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Epred__set_2ECARD(A_27a),V1t)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))),ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))))))))))) # label(conj_thm_2Epred__set_2ECARD__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2535 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enumpair_2Enfst,V0n)),ap(c_2Enumpair_2Ensnd,V0n)) = ap(c_2Epred__set_2Enum__to__pair,V0n))) # label(ax_thm_2Epred__set_2Enum__to__pair__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2536 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EDFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2EDFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2537 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a))))))))))) # label(conj_thm_2Epred__set_2EIN__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2538 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0P),V1Q))) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1Q)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V0P))))))))) # label(conj_thm_2Epred__set_2EFINITE__DIFF__down) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2539 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1b (mem(V1b,A_27b) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1b) = V1b)))))))) # label(conj_thm_2Epred__set_2EITSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2540 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a)) = c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2EDIFF__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2541 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),V1s)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__INSERT_27) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2542 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(V0P,V1s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2e (mem(V2e,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),V1s)) -> p(ap(V0P,ap(ap(c_2Epred__set_2EINSERT(A_27a),V2e),V1s))))))))) & p(ap(V0P,c_2Epred__set_2EEMPTY(A_27a))) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V3s)) -> p(ap(V0P,V3s)))))))))) # label(conj_thm_2Epred__set_2EFINITE__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2543 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1e (mem(V1e,A_27a) -> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1e),c_2Epred__set_2EEMPTY(A_27a))) = ap(V0f,V1e))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.29 2544 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s))) <-> V0x = V1y | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s))))))))))) # label(conj_thm_2Epred__set_2EIN__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2545 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Ecountable(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2Ecountable) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2546 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREL__RESTRICT(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Epred__set_2EREL__RESTRICT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2547 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> (all V1B (mem(V1B,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0A),V1B)) <-> ap(ap(c_2Epred__set_2EINTER(A_27a),V0A),V1B) = V0A) & (ap(ap(c_2Epred__set_2EINTER(A_27a),V0A),V1B) = V1B <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1B),V0A))))))))) # label(conj_thm_2Epred__set_2EINTER__SUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2548 (all A_27a all A_27b all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f254(A_27a,A_27b,V0P,V1x),V2y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),ap(ap(V0P,V1x),V2y))))))) # label(lameq_f254) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2549 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27b) -> (all V3x (mem(V3x,A_27a) -> (ap(ap(ap(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),V0f),V1s),V2y) = ap(c_2Eoption_2ESOME(A_27a),V3x) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & V2y = ap(V0f,V3x)))))))))))))) # label(conj_thm_2Epred__set_2ELINV__OPT__THM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2550 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V0s)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Epred__set_2ECARD(A_27a),V1t)),ap(c_2Epred__set_2ECARD(A_27a),V0s))))))))))) # label(conj_thm_2Epred__set_2ECARD__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2551 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V1P),V2Q),V0f)) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2Q)))))))))))))))) # label(conj_thm_2Epred__set_2EFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2552 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s))))))) # label(conj_thm_2Epred__set_2EINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2553 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = V0s))))))) # label(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2554 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDISJOINT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EDISJOINT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2555 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V0s))))))) # label(conj_thm_2Epred__set_2EUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2556 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t))))) & (all V4x (mem(V4x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2t)) -> (exists V5y (mem(V5y,A_27a) & ap(V0f,V5y) = V4x & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s))))))) <-> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(ax_thm_2Epred__set_2ESURJ__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2557 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Epred__set_2Ecount,V1n),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Epred__set_2ECOUNT__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2558 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f295(A_27a,V0y)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0y),c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2EGSPEC__EQ2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2559 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1q (mem(V1q,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0p),V1q)),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0p)),V1q)) = V1q)))))) # label(conj_thm_2Epred__set_2ECOMPL__SPLITS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2560 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),c_2Epred__set_2EUNIV(A_27b))) & p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epred__set_2EUNIV(ty_2Epair_2Eprod(A_27a,A_27b))))))))) # label(conj_thm_2Epred__set_2EINFINITE__PAIR__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2561 (all A_27a all V0sp (mem(V0sp,arr(A_27a,bool)) -> (all V2u ap(f281(A_27a,V0sp),V2u) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0sp),V2u)))) # label(lameq_f281) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2562 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> p(ap(c_2Epred__set_2EFINITE(A_27b),V2t))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2563 (all A_27b all A_27a all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3x ap(f258(A_27b,A_27a,V2P),V3x) = f257(A_27a,A_27b,V2P,V3x)))) # label(lameq_f258) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2564 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2565 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))) -> (p(ap(c_2Epred__set_2Ecountable(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),V1s)))))))))))) # label(conj_thm_2Epred__set_2Einj__image__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2566 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s))) & (all V1s (mem(V1s,arr(A_27a,bool)) -> V1s = ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Epred__set_2EINTER__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2567 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f280(A_27a,V0P)) = ap(c_2Epred__set_2EBIGINTER(A_27a),V0P))))) # label(ax_thm_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2568 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)))) # label(mem_c_2Epred__set_2EUNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2569 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)) = V0s)))))) # label(conj_thm_2Epred__set_2EUNION__DIFF__2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2570 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2Ecount,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0n),ap(c_2Epred__set_2Ecount,V0n)))) # label(conj_thm_2Epred__set_2ECOUNT__SUC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2571 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDIFF(A_27b),V1s),V2t)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V2t)))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2572 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,A_27a)),f308(A_27a,V0s)) = ap(c_2Epred__set_2Eenumerate(A_27a),V0s))))) # label(ax_thm_2Epred__set_2Eenumerate__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2573 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> p(ap(c_2Epred__set_2EFINITE(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0s)))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2574 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2Eequiv__on(A_27a),V0R),V1s)) -> -p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s)))))))))) # label(conj_thm_2Epred__set_2EEMPTY__NOT__IN__partition) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2575 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (all V4u (mem(V4u,arr(A_27c,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27c),V1g),V3t),V4u)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u))))))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2576 (all A_27b all A_27a all V2y (mem(V2y,A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V3x ap(f273(A_27b,A_27a,V2y,V0f,V1s),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V3x)),V2y))))))))) # label(lameq_f273) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2577 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (all V2s3 (mem(V2s3,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s1),V2s3)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s2),V2s3)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2578 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2579 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (V0s != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) -> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),ap(c_2Epred__set_2EMIN__SET,V0s)),V0s)) & (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1x),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2EMIN__SET,V0s)),V1x)))))))) # label(conj_thm_2Epred__set_2EMIN__SET__LEM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2580 (all A_27a all V0y (mem(V0y,arr(A_27a,bool)) -> (all V1x ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0y)) = ap(f293(A_27a,V0y),V1x)))) # label(lameq_f293) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2581 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V3x ap(f286(A_27a,V0f,V1g),V3x) = ap(ap(c_2Earithmetic_2EABS__DIFF,ap(V0f,V3x)),ap(V1g,V3x))))))) # label(lameq_f286) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2582 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) <-> (exists V1x (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Epred__set_2EMEMBER__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2583 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECHOICE__NOT__IN__REST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2584 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)) = V1s))))))) # label(conj_thm_2Epred__set_2EINSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2585 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) & (all V1x (mem(V1x,A_27a) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f303(A_27a,V0R,V1x)))))) -> (all V3x (mem(V3x,A_27a) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f304(A_27a,V0R,V3x))))))))))) # label(conj_thm_2Epred__set_2EKoenigsLemma__WF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2586 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,ty_2Enum_2Enum),f288(A_27a,V0f)),V1s),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Epred__set_2EPROD__IMAGE(A_27a),V0f),V1s))))))) # label(ax_thm_2Epred__set_2EPROD__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2587 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EBIGUNION(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2588 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1B (mem(V1B,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EBIGINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0P),V1B)) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0P),ap(c_2Epred__set_2EBIGINTER(A_27a),V1B)))))))) # label(conj_thm_2Epred__set_2EBIGINTER__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2589 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(c_2Epred__set_2Epair__to__num,ap(c_2Epred__set_2Enum__to__pair,V0x)))) # label(conj_thm_2Epred__set_2Epair__to__num__inv_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2590 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(c_2Epred__set_2Enum__to__pair,ap(c_2Epred__set_2Epair__to__num,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1x),V2y))) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1x),V2y))))) # label(conj_thm_2Epred__set_2Epair__to__num__inv_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2591 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2ESING(A_27a),V0s)) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Epred__set_2ECARD(A_27a),V0s)))))) # label(conj_thm_2Epred__set_2ESING__IFF__CARD1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2592 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f263(A_27a,V1t,V0s)) = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))) # label(ax_thm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2593 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V1s),V2t)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V2t)))))))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2594 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & (exists V2b (mem(V2b,ty_2Enum_2Enum) & p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V1f),ap(c_2Epred__set_2Ecount,V2b)),V0s))))))))))) # label(conj_thm_2Epred__set_2EFINITE__BIJ__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2595 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s))) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V2t))))) & p(ap(c_2Epred__set_2EFINITE(arr(A_27a,bool)),ap(ap(c_2Epred__set_2Epartition(A_27a),V0R),V1s)))))))))) # label(conj_thm_2Epred__set_2EFINITE__partition) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2596 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(c_2Epred__set_2EBIGUNION(A_27a),V1P)) = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0s),V1P)))))))) # label(conj_thm_2Epred__set_2EBIGUNION__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2597 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f258(A_27b,A_27a,V2P))))) <-> p(ap(ap(V2P,V0x),V1y))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2598 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s1),V2x)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s2),V2x)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__DELETE__BOTH) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2599 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b))) <-> V2s = c_2Epred__set_2EEMPTY(A_27a)))) & (all V1s (mem(V1s,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s)) <-> c_2Epred__set_2EEMPTY(A_27b) = V1s))))))))) # label(conj_thm_2Epred__set_2EBIJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2600 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27a),i(A_27a)),V0s),V0s)))))) # label(conj_thm_2Epred__set_2EBIJ__ID) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2601 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) <-> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(ax_thm_2Epred__set_2EBIJ__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2602 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V0s != V1t <-> (exists V2x (mem(V2x,A_27a) & (-p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(conj_thm_2Epred__set_2ENOT__EQUAL__SETS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2603 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = V0s | (exists V1x ((exists V2t (mem(V2t,arr(A_27a,bool)) & ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) = V0s & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)))) & mem(V1x,A_27a))))))) # label(conj_thm_2Epred__set_2ESET__CASES) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2604 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) -> (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),V2t)) -> ap(V0f,ap(ap(ap(c_2Epred__set_2ELINV(A_27a,A_27b),V0f),V1s),V3x)) = V3x)))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__LINV__INV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2605 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(c_2Epred__set_2ECARD(A_27a),V0s)),ap(c_2Enum_2ESUC,ap(c_2Epred__set_2ECARD(A_27a),V0s))) = ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s))))))) & c_2Enum_2E0 = ap(c_2Epred__set_2ECARD(A_27a),c_2Epred__set_2EEMPTY(A_27a)))) # label(ax_thm_2Epred__set_2ECARD__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2606 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1M (mem(V1M,arr(A_27a,ty_2Enum_2Enum)) -> ((exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V1M,V3x)),ap(V1M,V4y)))))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s))))))))))) # label(conj_thm_2Epred__set_2ESET__MINIMUM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2607 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,ty_2Eoption_2Eoption(A_27a))))))))) # label(mem_c_2Epred__set_2ELINV__OPT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2608 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)))))))) # label(conj_thm_2Epred__set_2EFINITE__REST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2609 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2610 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,arr(A_27a,bool)) -> (all V1b (mem(V1b,arr(A_27b,bool)) -> (all V2c (mem(V2c,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EINTER(arr(A_27a,A_27b)),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),V1b)),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),V2c)) = ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),ap(ap(c_2Epred__set_2EINTER(A_27b),V1b),V2c)))))))))))) # label(conj_thm_2Epred__set_2EFUNSET__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2611 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(ap(c_2Epred__set_2Eis__measure__maximal(A_27a),V0m),V1s),V2x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0m,V3y)),ap(V0m,V2x))))))))))))))) # label(ax_thm_2Epred__set_2Eis__measure__maximal__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2612 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(c_2Epred__set_2EFINITE(A_27b),V2t)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27b),V2t)),ap(c_2Epred__set_2ECARD(A_27a),V1s))))))))))))))) # label(conj_thm_2Epred__set_2ESURJ__CARD) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2613 (all A_27a (ne(A_27a) -> p(ap(c_2Epred__set_2Ecountable(A_27a),c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2Ecountable__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2614 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2Ecount,ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0n),ap(c_2Epred__set_2Ecount,V0n)))) # label(conj_thm_2Epred__set_2Ecount__add1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2615 (all A_27a all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2s ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2s),V0P)),ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s)) = ap(f279(A_27a,V0P,V1x),V2s)))))) # label(lameq_f279) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2616 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (V0x != ap(c_2Epred__set_2ECHOICE(A_27a),V1s) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) <-> p(ap(ap(c_2Epred__set_2EREST(A_27a),V1s),V0x))))))))) # label(conj_thm_2Epred__set_2EREST__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2617 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(c_2Epred__set_2ECARD(A_27a),V1s) = ap(c_2Epred__set_2ECARD(A_27b),V2t)))))))))))) # label(conj_thm_2Epred__set_2EFINITE__BIJ__CARD) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2618 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))))) # label(conj_thm_2Epred__set_2EFINITE__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2619 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__FINITE__I) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2620 (all A_27a (ne(A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = k(A_27a,c_2Ebool_2EF))) # label(ax_thm_2Epred__set_2EEMPTY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2621 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0P)) & p(ap(c_2Epred__set_2EFINITE(A_27b),V1Q)) -> ap(c_2Epred__set_2ECARD(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Epred__set_2ECARD(A_27a),V0P)),ap(c_2Epred__set_2ECARD(A_27b),V1Q))))))))))) # label(conj_thm_2Epred__set_2ECARD__CROSS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2622 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0x) = c_2Epred__set_2EEMPTY(A_27a))))) # label(conj_thm_2Epred__set_2EEMPTY__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2623 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) -> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V2R),V0s1)),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V2R),V1s2)))))))))))) # label(conj_thm_2Epred__set_2EREL__RESTRICT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2624 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V3x)),V2n))))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Epred__set_2ECARD(A_27a),V1s)),V2n))))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__upper__bound) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2625 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V2x)),V1Q)) & p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V2x)),V0P)) <-> p(ap(ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q),V2x))))))))))))) # label(conj_thm_2Epred__set_2ECROSS__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2626 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f303(A_27a,V0R,V1x)))))) -> (all V3x (mem(V3x,A_27a) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f304(A_27a,V0R,V3x)))) -> (exists V5f (ap(V5f,c_2Enum_2E0) = V3x & (all V6n (mem(V6n,ty_2Enum_2Enum) -> p(ap(ap(V0R,ap(V5f,V6n)),ap(V5f,ap(c_2Enum_2ESUC,V6n)))))) & mem(V5f,arr(ty_2Enum_2Enum,A_27a)))))))))))) # label(conj_thm_2Epred__set_2EKoenigsLemma) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2627 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s) = ap(f308(A_27a,V0s),V1f)))) # label(lameq_f308) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2628 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> (all V1v (mem(V1v,A_27a) -> (p(ap(ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f),V1v)) <-> (exists V2x (mem(V2x,A_27b) & ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x)))))))))))) # label(conj_thm_2Epred__set_2EGSPECIFICATION__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2629 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V0f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V1s),V2t))) & (all V3y (mem(V3y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3y),V2t)) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f272(A_27b,A_27a,V3y,V0f,V1s)))))) <-> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__ALT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2630 (all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V2t),ap(c_2Ebool_2E_3F(A_27a),f301(A_27a,V2t,V0R,V1s))) = ap(f302(A_27a,V0R,V1s),V2t)))))) # label(lameq_f302) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2631 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V3P (mem(V3P,arr(A_27b,bool)) -> (all V4y ap(f261(A_27a,A_27b,V2x,V3P),V4y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V4y)),ap(V3P,V4y))))))) # label(lameq_f261) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2632 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2m (mem(V2m,arr(A_27a,ty_2Enum_2Enum)) -> (all V3e (mem(V3e,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(V2m,V3e)),ap(V2m,V0x))) -> (p(ap(ap(ap(c_2Epred__set_2Eis__measure__maximal(A_27a),V2m),V1s),V4y)) <-> p(ap(ap(ap(c_2Epred__set_2Eis__measure__maximal(A_27a),V2m),ap(ap(c_2Epred__set_2EINSERT(A_27a),V3e),V1s)),V4y)))))))))))))))) # label(conj_thm_2Epred__set_2Eis__measure__maximal__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2633 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s))) <-> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V2x)),V1s))))))))))))) # label(conj_thm_2Epred__set_2EIN__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2634 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (V1y = V0x | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) <-> p(ap(ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s),V0x))))))))))) # label(conj_thm_2Epred__set_2EINSERT__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2635 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EFINITE(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2EFINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2636 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(ap(c_2Epair_2E_2C(A_27a,bool),V3x),ap(V0P,V3x)) = ap(f297(A_27a,V0P),V3x)))) # label(lameq_f297) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2637 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,bool),V1m),ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) = ap(f275(V0n),V1m)))) # label(lameq_f275) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2638 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2Ecount,V0n) = ap(ap(ap(c_2Ebool_2ECOND(arr(ty_2Enum_2Enum,bool)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n),c_2Enum_2E0)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)),f306),ap(c_2Eprim__rec_2EPRE,V0n))))) # label(conj_thm_2Epred__set_2Ecount__EQN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2639 (all A_27a all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V4n ap(f276(A_27a,V1f,V0s),V4n) = ap(ap(c_2Epair_2E_2C(A_27a,bool),ap(V1f,V4n)),ap(ap(c_2Eprim__rec_2E_3C,V4n),ap(c_2Epred__set_2ECARD(A_27a),V0s)))))))) # label(lameq_f276) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2640 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0P) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f255(A_27b,A_27a,V0P))))))))) # label(conj_thm_2Epred__set_2EGSPEC__PAIR__ETA) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2641 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27b,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)),c_2Epred__set_2EUNIV(A_27b)),c_2Epred__set_2EEMPTY(A_27b)) = ap(ap(c_2Epred__set_2EPREIMAGE(A_27b,A_27a),ap(c_2Ecombin_2EK(A_27a,A_27b),V0x)),V1s))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__K) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2642 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2u),V1t)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2643 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0r),V1s)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0r),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0r),V2t)))))))))) # label(conj_thm_2Epred__set_2EDIFF__INTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2644 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u))))))))))) # label(conj_thm_2Epred__set_2EUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2645 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)))) <-> p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),ap(c_2Epred__set_2Eenumerate(A_27a),V0s)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s))))))) # label(conj_thm_2Epred__set_2EENUMERATE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2646 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),c_2Epred__set_2EUNIV(A_27a))) & p(ap(c_2Epred__set_2Ecountable(A_27b),c_2Epred__set_2EUNIV(A_27b))) <-> p(ap(c_2Epred__set_2Ecountable(ty_2Esum_2Esum(A_27a,A_27b)),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(A_27a,A_27b))))))))) # label(conj_thm_2Epred__set_2Ecountable__Usum) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2647 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) -> V2t = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2EBIJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2648 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (ap(c_2Epred__set_2EREST(A_27a),V0s) = c_2Epred__set_2EEMPTY(A_27a) & V0s != c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(c_2Epred__set_2ESING(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ESING__IFF__EMPTY__REST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2649 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V1y),V0x) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V0x) & ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V1y))))))) # label(conj_thm_2Epred__set_2EDIFF__SAME__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2650 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s) = V2t <-> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__SURJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2651 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Enum_2Enum,bool)) -> ((all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2x),V0P)) & (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3y),V0P)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V3y),V2x))))) -> p(ap(V1Q,V2x))))) & (V0P = c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) -> p(ap(V1Q,c_2Enum_2E0))) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0P)) -> p(ap(V1Q,ap(c_2Epred__set_2EMAX__SET,V0P)))))))) # label(conj_thm_2Epred__set_2EMAX__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2652 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0P)) -> (all V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2p (mem(V2p,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2p),V0P)) & (all V3q (mem(V3q,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3q),V0P)) -> ap(V1f,V3q) = ap(V1f,V2p)))) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Epred__set_2ECARD(A_27a),V0P)),ap(V1f,V2p)) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1f),V0P))))))))))) # label(conj_thm_2Epred__set_2ESUM__SAME__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2653 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)))) -> p(ap(c_2Epred__set_2Ecountable(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2EBIJ__NUM__COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2654 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),V1s))) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),V1s)))))))))) # label(conj_thm_2Epred__set_2EFINITE__StrongOrder__WF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2655 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) <-> (exists V1f ((exists V2b (mem(V2b,ty_2Enum_2Enum) & (all V3e (mem(V3e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),V0s)) <-> (exists V4n (mem(V4n,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V2b)) & V3e = ap(V1f,V4n)))))))) & mem(V1f,arr(ty_2Enum_2Enum,A_27a))))))))) # label(conj_thm_2Epred__set_2EFINITE__WEAK__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2656 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s0 (mem(V0s0,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3t (mem(V3t,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s0),V1s)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V1s),V3t)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s0),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V0s0)))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__BIJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2657 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> p(ap(c_2Epred__set_2Ecountable(ty_2Enum_2Enum),V0s)))) # label(conj_thm_2Epred__set_2ECOUNTABLE__NUM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2658 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y),V1x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & V1x != V2y))))))))) # label(conj_thm_2Epred__set_2EDELETE__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2659 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27b) -> ((exists V3x (mem(V3x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27b),V2y),ap(V0f,V3x))))) <-> p(ap(ap(c_2Ebool_2EIN(A_27b),V2y),ap(c_2Epred__set_2EBIGUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,arr(A_27b,bool)),V0f),V1s))))))))))))))) # label(conj_thm_2Epred__set_2EIN__BIGUNION__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2660 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))))))) # label(conj_thm_2Epred__set_2EDIFF__INTER2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2661 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V1t = V0s <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__SUBSET__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2662 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27c,bool)) -> (all V2u (mem(V2u,arr(A_27b,bool)) -> ((exists V3f (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27c),V3f),V0s),V1t)) & mem(V3f,arr(A_27a,A_27c)))) & (exists V4g (mem(V4g,arr(A_27c,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27c,A_27b),V4g),V1t),V2u)))) -> (exists V5h (mem(V5h,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V5h),V0s),V2u))))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__TRANS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2663 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Epred__set_2ELINV__OPT(A_27b,A_27a),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27b,ty_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME(A_27b)),V1s))))))))))) # label(conj_thm_2Epred__set_2EINJ__LINV__OPT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2664 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> c_2Epred__set_2EEMPTY(A_27b) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2EIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2665 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27b) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V0y),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s))) <-> (exists V3x (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & ap(V2f,V3x) = V0y & mem(V3x,A_27a)))))))))))))) # label(conj_thm_2Epred__set_2EIN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2666 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1s),V0P)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))))) & p(ap(c_2Epred__set_2EFINITE(arr(A_27a,bool)),V0P)) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V0P)))))))) # label(conj_thm_2Epred__set_2EFINITE__BIGUNION__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2667 (all A_27a all A_27b all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2p ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),V2p),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V2p)),V0P)),ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V2p)),V1Q))) = ap(f283(A_27a,A_27b,V1Q,V0P),V2p)))))) # label(lameq_f283) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2668 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4x ap(f259(A_27b,A_27a,V0f,V3P),V4x) = ap(ap(c_2Epair_2E_2C(A_27b,bool),ap(V0f,V4x)),ap(V3P,V4x))))))) # label(lameq_f259) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2669 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> ((exists V3x (p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V3x)),ap(V1g,V3x))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V2s)) & mem(V3x,A_27a))) & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V4x)),ap(V1g,V4x)))))) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V2s)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1g),V2s))))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__MONO__LESS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2670 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V0f),ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V1P),V2Q))) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),ap(V2Q,V3x))))))))))))))))) # label(conj_thm_2Epred__set_2EIN__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2671 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2EFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2672 (all A_27a (ne(A_27a) -> (all V0set (mem(V0set,arr(A_27a,bool)) -> (all V1e (mem(V1e,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1e),ap(c_2Epred__set_2EPOW(A_27a),V0set))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1e),V0set))))))))) # label(conj_thm_2Epred__set_2EIN__POW) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2673 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0P),V1Q)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1Q)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__THM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2674 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),c_2Epred__set_2EREST(A_27a)),V0n),V1s) != c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2EEXPLICIT__ENUMERATE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2675 (all V0I (mem(V0I,arr(ty_2Enum_2Enum,bool)) -> (all V1J (mem(V1J,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0I)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),V0I),V1J)) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1J)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2EMAX__SET,V0I)),ap(c_2Epred__set_2EMAX__SET,V1J)))))))) # label(conj_thm_2Epred__set_2ESUBSET__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2676 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2u) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)))))))))) # label(conj_thm_2Epred__set_2EINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2677 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s))))))) # label(conj_thm_2Epred__set_2EREST__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2678 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2Q))))) <-> p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V0f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V1P),V2Q)))))))))))))) # label(conj_thm_2Epred__set_2EIN__FUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2679 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESUM__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))))) # label(mem_c_2Epred__set_2ESUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2680 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> -p(ap(c_2Epred__set_2Ecountable(arr(A_27a,bool)),ap(c_2Epred__set_2EPOW(A_27a),V0s)))))))) # label(conj_thm_2Epred__set_2Einfinite__pow__uncountable) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2681 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> V1s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))) # label(conj_thm_2Epred__set_2EABSORPTION__RWT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2682 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (ap(c_2Eoption_2ESOME(A_27a),V3x) = ap(ap(ap(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),V0f),V1s),V4y) <-> ap(V0f,V3x) = V4y & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27b),V4y),V2t)))))))))))))))))) # label(conj_thm_2Epred__set_2EINJ__LINV__OPT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2683 (all A_27a (ne(A_27a) -> (all V0X (mem(V0X,arr(A_27a,bool)) -> (all V1Y (mem(V1Y,arr(A_27a,bool)) -> (all V2P (mem(V2P,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V1Y),V2P)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1Y),V0X)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V2P)),V0X)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0X),ap(c_2Epred__set_2EBIGINTER(A_27a),V2P)))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2684 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> V0x = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0x),c_2Epred__set_2EEMPTY(arr(A_27a,bool)))))))) # label(conj_thm_2Epred__set_2EBIGUNION__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2685 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((exists V2f (mem(V2f,arr(A_27a,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27a),V2f),V0s),V1t)))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> (exists V3g (mem(V3g,arr(A_27a,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27a),V3g),V0s),V1t))))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__BERNSTEIN__AUTO) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2686 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2687 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> ((exists V2f (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) & mem(V2f,arr(A_27a,A_27b)))) -> (exists V3g (mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__SYM__IMP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2688 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> ((exists V3g (mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27a),V3g),V1t),V0s)))) & (exists V2f (mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V0s),V1t)))) -> (exists V4h (mem(V4h,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V4h),V0s),V1t))))))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__BERNSTEIN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2689 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V2x)),ap(V1Q,V2x))) = ap(f296(A_27a,V1Q,V0P),V2x)))))) # label(lameq_f296) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2690 (all A_27a all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> (all V1x ap(f278(A_27a,V0P),V1x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(c_2Ebool_2E_3F(arr(A_27a,bool)),f277(A_27a,V0P,V1x)))))) # label(lameq_f278) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2691 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) != ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))) # label(conj_thm_2Epred__set_2ENOT__EMPTY__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2692 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2u),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u))) & (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__UNION__BOTH) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2693 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2s (mem(V2s,arr(A_27b,bool)) -> ((exists V3y (mem(V3y,A_27a) & p(ap(V0P,V3y)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V1f),V2s))))) <-> (exists V4x (p(ap(V0P,ap(V1f,V4x))) & p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2s)) & mem(V4x,A_27b)))))))))))))) # label(conj_thm_2Epred__set_2EEXISTS__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2694 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__DIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2695 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0m),ap(c_2Epred__set_2Ecount,V1n)))))))) # label(conj_thm_2Epred__set_2EIN__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2696 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDIFF(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s))))) # label(conj_thm_2Epred__set_2EEMPTY__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2697 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (p(ap(ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a)),V0x)) <-> V1y = V0x))))))) # label(conj_thm_2Epred__set_2ESING__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2698 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) <-> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V0s))))))))))) # label(conj_thm_2Epred__set_2EFINITE__PSUBSET__INFINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2699 (all V0e (mem(V0e,ty_2Enum_2Enum) -> ap(c_2Epred__set_2EMAX__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0e),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))) = V0e & c_2Enum_2E0 = ap(c_2Epred__set_2EMAX__SET,c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)))) # label(conj_thm_2Epred__set_2EMAX__SET__REWRITES) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2700 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0s,V2x)) -> p(ap(V1t,V2x))))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 2701 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2EFINITE__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2702 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2s (mem(V2s,arr(A_27b,bool)) -> ((all V4x (mem(V4x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2s)) -> p(ap(V0P,ap(V1f,V4x)))))) <-> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V1f),V2s))) -> p(ap(V0P,V3y)))))))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2703 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27b))) -> (all V2x (mem(V2x,A_27a) -> (all V3b (mem(V3b,A_27b) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V3b) = ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),ap(c_2Epred__set_2EREST(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s))),ap(ap(V1f,ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s))),V3b))))))))))))))) # label(conj_thm_2Epred__set_2EITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2704 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)))))))))))))) # label(conj_thm_2Epred__set_2EINJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2705 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> ((exists V2s (mem(V2s,arr(A_27a,bool)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2s),V1sos)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)))))))))) # label(conj_thm_2Epred__set_2EIN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2706 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0x),V1y)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,V0x),V1y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1y) = ap(c_2Epred__set_2Epair__to__num,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0x),V1y)))))) # label(conj_thm_2Epred__set_2Epair__to__num__formula) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2707 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,bool))) -> (all V2s (mem(V2s,arr(A_27b,bool)) -> ((all V3y (mem(V3y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3y),V2s)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(V1f,V3y)))))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGINTER(A_27a),ap(ap(c_2Epred__set_2EIMAGE(A_27b,arr(A_27a,bool)),V1f),V2s))))))))))))))) # label(conj_thm_2Epred__set_2EIN__BIGINTER__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2708 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t))))))))) # label(conj_thm_2Epred__set_2EINSERT__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2709 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(V1P,V0x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),f252(A_27a,V1P)))))))))) # label(conj_thm_2Epred__set_2EIN__ABS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2710 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1t)))))))))) # label(conj_thm_2Epred__set_2ESUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2711 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t))))) & (exists V4g (mem(V4g,arr(A_27b,A_27a)) & (all V5x (mem(V5x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V5x),V2t)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(V4g,V5x)),V1s))))) & (all V6x (mem(V6x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),V1s)) -> ap(V4g,ap(V0f,V6x)) = V6x))) & (all V7x (mem(V7x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V7x),V2t)) -> V7x = ap(V0f,ap(V4g,V7x)))))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__IFF__INV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2712 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(arr(A_27a,bool)) = ap(c_2Epred__set_2EPOW(A_27a),c_2Epred__set_2EUNIV(A_27a)))) # label(conj_thm_2Epred__set_2EUNIV__FUN__TO__BOOL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2713 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2e ap(f288(A_27a,V0f),V2e) = f287(A_27a,V0f,V2e)))) # label(lameq_f288) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2714 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x = V2y <-> ap(V0f,V1x) = ap(V0f,V2y)))))) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V3s))) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V3s)))))))))))) # label(conj_thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2715 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <-> -(exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epred__set_2EIN__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2716 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s2)) | p(ap(c_2Epred__set_2EFINITE(A_27a),V0s1)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s1),V1s2)))))))))) # label(conj_thm_2Epred__set_2EFINITE__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2717 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))))))))))) # label(conj_thm_2Epred__set_2EINSERT__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2718 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)) = V1t))))))) # label(conj_thm_2Epred__set_2EDIFF__DIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2719 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1x))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2720 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2P0 (mem(V2P0,arr(A_27a,bool)) -> (all V3Q0 (mem(V3Q0,arr(A_27b,bool)) -> (V3Q0 = c_2Epred__set_2EEMPTY(A_27b) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2P0),V0P)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V3Q0),V1Q)) | V2P0 = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V2P0),V3Q0)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q)))))))))))))))) # label(conj_thm_2Epred__set_2ECROSS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2721 (all A_27a all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x ap(f252(A_27a,V1P),V2x) = ap(V1P,V2x)))) # label(lameq_f252) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2722 (all A_27b all A_27a all V1x (mem(V1x,A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2y ap(ap(c_2Epair_2E_2C(A_27a,bool),V2y),ap(ap(c_2Emin_2E_3D(A_27b),V1x),ap(V0f,V2y))) = ap(f274(A_27b,A_27a,V1x,V0f),V2y)))))) # label(lameq_f274) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2723 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t),V2x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))))))))))) # label(conj_thm_2Epred__set_2EINTER__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2724 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Epred__set_2EBIGUNION(A_27a),V1s))) -> p(ap(V0P,V2x))))) <-> (all V3t (mem(V3t,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V3t)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3t),V1s)) -> p(ap(V0P,V4x)))))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2725 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EUNION(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2726 (all A_27a (ne(A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f291(A_27a)))) # label(conj_thm_2Epred__set_2EGSPEC__F) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2727 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,arr(A_27a,bool)) -> V0y = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f293(A_27a,V0y)))))) # label(conj_thm_2Epred__set_2EGSPEC__ID) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2728 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V1f),V0s),V2t)) & ap(c_2Epred__set_2ECARD(A_27b),V2t) = ap(c_2Epred__set_2ECARD(A_27a),V0s) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V1f),V0s),V2t))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__SURJ__BIJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2729 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),c_2Epred__set_2EEMPTY(A_27a)) = c_2Erelation_2EEMPTY__REL(A_27a))))) # label(conj_thm_2Epred__set_2EREL__RESTRICT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2730 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0S (mem(V0S,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0S)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),V1t)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0S),V1t)) -> ap(c_2Epred__set_2ECARD(A_27a),V0S) = ap(c_2Epred__set_2ECARD(A_27b),V1t))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__BIJ__CARD__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2731 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2ESUBSET__OF__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2732 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f) = ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),ap(ap(c_2Ecombin_2Eo(A_27b,A_27a,ty_2Epair_2Eprod(A_27a,bool)),c_2Epair_2EFST(A_27a,bool)),V0f)),ap(ap(c_2Ecombin_2Eo(A_27b,bool,ty_2Epair_2Eprod(A_27a,bool)),c_2Epair_2ESND(A_27a,bool)),V0f)))))))) # label(conj_thm_2Epred__set_2EGSPEC__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2733 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V1t)))))))))) # label(conj_thm_2Epred__set_2EDIFF__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2734 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0s)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1x),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(c_2Epred__set_2EMAX__SET,V0s))))))))) # label(conj_thm_2Epred__set_2Ein__max__set) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2735 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Epred__set_2EREST(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2EREST__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2736 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(ty_2Enum_2Enum,A_27a),f307(A_27a,V0s)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s))))))) # label(conj_thm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2737 (all A_27a (ne(A_27a) -> ap(c_2Epred__set_2EPOW(A_27a),c_2Epred__set_2EEMPTY(A_27a)) = ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),c_2Epred__set_2EEMPTY(arr(A_27a,bool))) & (all V0e (mem(V0e,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EPOW(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0e),V1s)) = ap(ap(c_2Ebool_2ELET(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),bool)),f290(A_27a,V0e)),ap(c_2Epred__set_2EPOW(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2EPOW__EQNS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2738 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2ECOMPONENT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2739 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) <-> p(ap(c_2Epred__set_2Ecountable(A_27a),V1s))))))))) # label(conj_thm_2Epred__set_2Ecountable__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2740 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) <-> V1s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))) # label(conj_thm_2Epred__set_2EABSORPTION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2741 (all V0A (mem(V0A,arr(ty_2Enum_2Enum,bool)) -> (all V1B (mem(V1B,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1B)) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0A)) -> ap(ap(c_2Earithmetic_2EMAX,ap(c_2Epred__set_2EMAX__SET,V0A)),ap(c_2Epred__set_2EMAX__SET,V1B)) = ap(c_2Epred__set_2EMAX__SET,ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),V0A),V1B))))))) # label(conj_thm_2Epred__set_2EMAX__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2742 (all A_27a (ne(A_27a) -> (all V0sp (mem(V0sp,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> ((all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2t),V1s)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V0sp))))) & V1s != c_2Epred__set_2EEMPTY(arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V1s)),V0sp))))))))) # label(conj_thm_2Epred__set_2EBIGINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2743 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (c_2Epred__set_2EEMPTY(A_27b) = V1t | c_2Epred__set_2EEMPTY(A_27a) = V0s <-> ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t) = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27b))))))))))) # label(conj_thm_2Epred__set_2ECROSS__EMPTY__EQN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2744 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0P)),V1Q) = ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a))),V1Q)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q)))))))))))) # label(conj_thm_2Epred__set_2ECROSS__INSERT__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2745 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (V0s = c_2Epred__set_2EEMPTY(A_27a) <-> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0s) = c_2Epred__set_2EEMPTY(A_27b)))))))))) # label(conj_thm_2Epred__set_2EIMAGE__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2746 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s = c_2Epred__set_2EUNIV(A_27a) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s))))))) # label(conj_thm_2Epred__set_2EUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2747 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2EINTER__FINITE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2748 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EREST(A_27a),V1s))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & V0x != ap(c_2Epred__set_2ECHOICE(A_27a),V1s)))))))) # label(conj_thm_2Epred__set_2EIN__REST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2749 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(ap(c_2Epred__set_2EINSERT(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27b))) = ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),ap(ap(c_2Epred__set_2EINSERT(A_27b),V1y),c_2Epred__set_2EEMPTY(A_27b))))))))))) # label(conj_thm_2Epred__set_2ECROSS__SINGS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2750 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1c ((exists V2n (p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,A_27a),V1c),ap(c_2Epred__set_2Ecount,V2n)),V0s)) & mem(V2n,ty_2Enum_2Enum))) & mem(V1c,arr(ty_2Enum_2Enum,A_27a)))) <-> p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2EFINITE__BIJ__COUNT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2751 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> V0P = ap(c_2Epred__set_2EBIGINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),V0P),c_2Epred__set_2EEMPTY(arr(A_27a,bool)))))))) # label(conj_thm_2Epred__set_2EBIGINTER__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2752 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) -> (V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)) <-> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))))))))) # label(conj_thm_2Epred__set_2EDELETE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2753 (all A_27a all V0y (mem(V0y,A_27a) -> (all V1x ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V0y)) = ap(f294(A_27a,V0y),V1x)))) # label(lameq_f294) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2754 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((exists V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(ty_2Enum_2Enum,A_27a),V1f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)))) <-> -p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2Einfinite__num__inj) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2755 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),V1s),V2x),V3y)) <-> p(ap(ap(V0R,V2x),V3y)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))))))))))))) # label(ax_thm_2Epred__set_2EREL__RESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2756 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(c_2Epred__set_2ECOMPL(A_27a),V0P) = ap(ap(c_2Epred__set_2EDIFF(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0P))))) # label(ax_thm_2Epred__set_2ECOMPL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2757 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1B (mem(V1B,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGINTER(A_27a),V1B))) <-> (all V2P (mem(V2P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2P),V1B)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2P)))))))))))) # label(conj_thm_2Epred__set_2EIN__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2758 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),ap(c_2Epred__set_2ECOMPL(A_27b),V1s)) = ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),V1s)))))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__COMPL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2759 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(c_2Epred__set_2ECOMPL(A_27a),V0s)),V1x) = ap(c_2Epred__set_2ECOMPL(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s)))))))) # label(conj_thm_2Epred__set_2Ecompl__insert) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2760 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V1f),V2s))) <-> (exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),V1f)),V3n),V2s)))))))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__CLOSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2761 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> f269(A_27b,A_27a,V0P,V1Q) = ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0P),V1Q))))))))) # label(ax_thm_2Epred__set_2EFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2762 (all A_27a (ne(A_27a) -> (-p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) <-> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))))))))) # label(conj_thm_2Epred__set_2EFINITE__PSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2763 (all V0A (mem(V0A,arr(ty_2Enum_2Enum,bool)) -> (all V1B (mem(V1B,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1B)) & c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) != V0A & V1B != c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0A)) -> ap(ap(c_2Earithmetic_2EMIN,ap(c_2Epred__set_2EMIN__SET,V0A)),ap(c_2Epred__set_2EMIN__SET,V1B)) = ap(c_2Epred__set_2EMIN__SET,ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),V0A),V1B))))))) # label(conj_thm_2Epred__set_2EMIN__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2764 (all A_27a all A_27b all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),ap(ap(V2P,V3x),V4y)) = ap(f257(A_27a,A_27b,V2P,V3x),V4y)))))) # label(lameq_f257) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2765 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V0x),ap(c_2Ecombin_2EK(arr(A_27b,bool),A_27a),V1y)))))))))) # label(conj_thm_2Epred__set_2EFUNSET__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2766 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V1s)) -> p(ap(c_2Epred__set_2Ecountable(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2Eimage__countable) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2767 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2z (mem(V2z,A_27a) -> (V1s != c_2Epred__set_2EEMPTY(A_27b) & (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),V1s)) -> V2z = ap(V0f,V3x)))) <-> ap(ap(c_2Epred__set_2EINSERT(A_27a),V2z),c_2Epred__set_2EEMPTY(A_27a)) = ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2768 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2Ecountable(A_27a),V0s)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V1t)) -> p(ap(c_2Epred__set_2Ecountable(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)))))))))) # label(conj_thm_2Epred__set_2Eunion__countable) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2769 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> (exists V2t (-p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)) & V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) & mem(V2t,arr(A_27a,bool))))))))))) # label(conj_thm_2Epred__set_2EDECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2770 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V1t (mem(V1t,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1t)) & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0s)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Epred__set_2ESUM__SET,V0s)),ap(c_2Epred__set_2ESUM__SET,V1t))),ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EINTER(ty_2Enum_2Enum),V0s),V1t))) = ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EUNION(ty_2Enum_2Enum),V0s),V1t))))))) # label(conj_thm_2Epred__set_2ESUM__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2771 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f292(A_27a)))) # label(conj_thm_2Epred__set_2EGSPEC__T) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2772 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V0n))))) # label(conj_thm_2Epred__set_2EFINITE__COUNT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2773 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V2y = V1x & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2y),c_2Epred__set_2EEMPTY(A_27a)))) <-> ap(ap(c_2Epred__set_2EINSERT(A_27a),V2y),c_2Epred__set_2EEMPTY(A_27a)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s)))))))))) # label(conj_thm_2Epred__set_2EINSERT__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2774 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (all V2z (mem(V2z,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V2z)),V1y))))))))) # label(conj_thm_2Epred__set_2EDIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2775 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27c),V0f),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1g),V2s)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)),V2s))))))))))))) # label(conj_thm_2Epred__set_2EIMAGE__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2776 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Epred__set_2ECARD__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2777 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2t),V1s)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27a)),V0f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27a),V1s),V1s))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V2t)),V1s))))))))))) # label(conj_thm_2Epred__set_2ESCHROEDER__CLOSE__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2778 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EREST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2779 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27b),V2t)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),V1s)),ap(c_2Epred__set_2ECARD(A_27b),V2t)))))))))))))) # label(conj_thm_2Epred__set_2EINJ__CARD) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2780 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V2s)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),V1t)) -> ap(c_2Epred__set_2ECARD(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s)) = ap(c_2Epred__set_2ECARD(A_27a),V2s))))))))))))) # label(conj_thm_2Epred__set_2EINJ__CARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2781 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1s1 (mem(V1s1,arr(A_27a,bool)) -> (all V2s2 (mem(V2s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s1),V2s2)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s1),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0e),V2s2)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2782 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V0s)))))))) # label(conj_thm_2Epred__set_2EDIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2783 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s2),V0s1)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) <-> V0s1 = V1s2))))))) # label(conj_thm_2Epred__set_2ESET__EQ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2784 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(c_2Epred__set_2EFINITE(A_27b),V2t)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))))))))))))) # label(conj_thm_2Epred__set_2EFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2785 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2x) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t))))))))) # label(conj_thm_2Epred__set_2EDELETE__INTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2786 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V0P),V1Q) = f271(A_27b,A_27a,V0P,V1Q))))))))) # label(ax_thm_2Epred__set_2EDFUNSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2787 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t))))))))))) # label(conj_thm_2Epred__set_2EINSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2788 (all A_27a (ne(A_27a) -> (all V0X (mem(V0X,arr(A_27a,bool)) -> (all V1P (mem(V1P,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0X),ap(c_2Epred__set_2EBIGINTER(A_27a),V1P))) <-> (all V2Y (mem(V2Y,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2Y),V1P)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0X),V2Y)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2789 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> (ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),c_2Epred__set_2EEMPTY(arr(A_27a,bool))) = V0P | V0P = c_2Epred__set_2EEMPTY(arr(A_27a,bool)) <-> ap(c_2Epred__set_2EBIGUNION(A_27a),V0P) = c_2Epred__set_2EEMPTY(A_27a)) & (V0P = ap(ap(c_2Epred__set_2EINSERT(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),c_2Epred__set_2EEMPTY(arr(A_27a,bool))) | V0P = c_2Epred__set_2EEMPTY(arr(A_27a,bool)) <-> c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Epred__set_2EBIGUNION(A_27a),V0P)))))) # label(conj_thm_2Epred__set_2EBIGUNION__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2790 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (V2s = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b)))))) & (all V1s (mem(V1s,arr(A_27b,bool)) -> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s)))))))))) # label(conj_thm_2Epred__set_2EINJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2791 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),f283(A_27a,A_27b,V1Q,V0P)))))))))) # label(ax_thm_2Epred__set_2ECROSS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2792 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V1s)))))))) # label(conj_thm_2Epred__set_2EDELETE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2793 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),V0s))))))) # label(ax_thm_2Epred__set_2ECHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2794 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(V0P,V1x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0P))))))))) # label(conj_thm_2Epred__set_2ESPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2795 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(arr(A_27a,bool),bool)) -> (all V1s2 (mem(V1s2,arr(arr(A_27a,bool),bool)) -> ap(c_2Epred__set_2EBIGINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(arr(A_27a,bool)),V0s1),V1s2)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V0s1)),ap(c_2Epred__set_2EBIGINTER(A_27a),V1s2)))))))) # label(conj_thm_2Epred__set_2EBIGINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2796 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0t)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epred__set_2ECARD(A_27a),V1s)),ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V0t))) = ap(c_2Epred__set_2ECARD(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V0t)))))))))) # label(conj_thm_2Epred__set_2ECARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2797 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s1),V1s2)) & -p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s2),V0s1)) <-> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s1),V1s2))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2798 (all A_27a (ne(A_27a) -> (all V0B (mem(V0B,arr(arr(A_27a,bool),bool)) -> (all V1x (mem(V1x,A_27a) -> ((all V2P (mem(V2P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2P),V0B)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2P))))) <-> p(ap(ap(c_2Epred__set_2EBIGINTER(A_27a),V0B),V1x))))))))) # label(conj_thm_2Epred__set_2EBIGINTER__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2799 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27a),i(A_27a)),V0s),V0s)))))) # label(conj_thm_2Epred__set_2ESURJ__ID) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2800 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (V1s != c_2Epred__set_2EEMPTY(A_27a) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Epred__set_2Eis__measure__maximal(A_27a),V0m),V1s),V2x))))))))))) # label(conj_thm_2Epred__set_2EFINITE__is__measure__maximal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2801 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27b)) = c_2Epred__set_2EUNIV(A_27a))))))) # label(conj_thm_2Epred__set_2EPREIMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2802 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1n ap(f307(A_27a,V0s),V1n) = ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),c_2Epred__set_2EREST(A_27a)),V1n),V0s))))) # label(lameq_f307) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 2803 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1t),V2x)),V0s)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DELETE__SYM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2804 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2ECOMPL(A_27a),V1s))) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2EIN__COMPL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2805 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t))))))) # label(conj_thm_2Epred__set_2EDIFF__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2806 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),V1t)),ap(c_2Epred__set_2ECARD(A_27a),V0s))))))))))) # label(conj_thm_2Epred__set_2ECARD__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2807 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V0x))))))) # label(conj_thm_2Epred__set_2EDELETE__DELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2808 (all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f303(A_27a,V0R,V1x),V2y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2y),ap(ap(V0R,V1x),V2y))))))) # label(lameq_f303) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2809 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) -> (ap(V0f,V4x) = ap(V0f,V5y) -> V4x = V5y)))))) <-> p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t))))))))))))) # label(ax_thm_2Epred__set_2EINJ__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2810 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> ((exists V3g (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V3g),V0s),V1t)) & mem(V3g,arr(A_27a,A_27b)))) & (exists V2f (mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V0s),V1t)))) -> (exists V4h (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V4h),V0s),V1t)) & mem(V4h,arr(A_27a,A_27b))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__INJ__SURJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2811 (all A_27a (ne(A_27a) -> (all V0s1 (mem(V0s1,arr(A_27a,bool)) -> (all V1s2 (mem(V1s2,arr(A_27a,bool)) -> (all V2f1 (mem(V2f1,arr(A_27a,ty_2Enum_2Enum)) -> (all V3f2 (mem(V3f2,arr(A_27a,ty_2Enum_2Enum)) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s2)) -> ap(V2f1,V4x) = ap(V3f2,V4x)))) & V1s2 = V0s1 -> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V2f1),V0s1) = ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V3f2),V1s2)))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2812 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($F <-> p(ap(c_2Epred__set_2EEMPTY(A_27a),V0x))))))) # label(conj_thm_2Epred__set_2EEMPTY__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2813 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (c_2Epred__set_2EEMPTY(ty_2Enum_2Enum) != V0s & p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2EMIN__SET,V0s)),ap(c_2Epred__set_2EMAX__SET,V0s)))))) # label(conj_thm_2Epred__set_2EMIN__SET__LEQ__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2814 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))),ap(c_2Epred__set_2ECARD(A_27a),V1s)))))))))))) # label(conj_thm_2Epred__set_2ECARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2815 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1P)) <-> p(ap(V1P,V0x))))))))) # label(conj_thm_2Epred__set_2EIN__APP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2816 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ECHOICE__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2817 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> (p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),V1s)) -> ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0x),V1s)) = ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Epred__set_2ESUM__SET,ap(ap(c_2Epred__set_2EDELETE(ty_2Enum_2Enum),V1s),V0x)))))))) # label(conj_thm_2Epred__set_2ESUM__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2818 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPOW(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EPOW) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2819 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDELETE(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EDELETE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2820 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EPOW(A_27a),V0s) != c_2Epred__set_2EEMPTY(arr(A_27a,bool)))))) # label(conj_thm_2Epred__set_2EPOW__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2821 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2EFINITE__SING) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2822 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2e (mem(V2e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),V1s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V2e)),ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),V1s)))))))))))) # label(conj_thm_2Epred__set_2ESUM__IMAGE__IN__LE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2823 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> (all V1v (mem(V1v,A_27a) -> ((exists V2x (ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) & mem(V2x,A_27b))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f)))))))))))) # label(ax_thm_2Epred__set_2EGSPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2824 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) -> (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),V2t)) -> ap(V0f,ap(ap(ap(c_2Epred__set_2ERINV(A_27a,A_27b),V0f),V1s),V3x)) = V3x)))))))))))))) # label(conj_thm_2Epred__set_2ERINV__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2825 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EINTER(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EINTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2826 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) -> (exists V3g ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) -> V4x = ap(ap(ap(c_2Ecombin_2Eo(A_27a,A_27a,A_27b),V3g),V0f),V4x)))) & (all V5x (mem(V5x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V5x),V2t)) -> ap(ap(ap(c_2Ecombin_2Eo(A_27b,A_27b,A_27a),V0f),V3g),V5x) = V5x))) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V2t),V1s)) & mem(V3g,arr(A_27b,A_27a))))))))))))))) # label(conj_thm_2Epred__set_2EBIJ__INV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2827 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Epred__set_2Epair__to__num,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)) = ap(ap(c_2Enumpair_2Enpair,V0m),V1n))))) # label(ax_thm_2Epred__set_2Epair__to__num__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2828 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V1f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0s),c_2Epred__set_2EEMPTY(A_27b)))) <-> V0s = c_2Epred__set_2EEMPTY(A_27a)))))))))) # label(conj_thm_2Epred__set_2EFUNSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2829 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))))))))))) # label(conj_thm_2Epred__set_2EIN__UNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2830 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ESURJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2ESURJ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2831 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0y),c_2Epred__set_2EEMPTY(A_27a)) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f294(A_27a,V0y)))))) # label(conj_thm_2Epred__set_2EGSPEC__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2832 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> k(A_27a,c_2Epred__set_2EEMPTY(A_27b)) = c_2EfixedPoint_2Eempty(A_27a,A_27b))))) # label(ax_thm_2EfixedPoint_2Eempty__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2833 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(V0f,V1X))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(c_2EfixedPoint_2Egfp(A_27a),V0f))))))))))) # label(conj_thm_2EfixedPoint_2Egfp__coinduction) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2834 (all A_27a (ne(A_27a) -> mem(c_2EfixedPoint_2Eclosed(A_27a),arr(arr(arr(A_27a,bool),arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2EfixedPoint_2Eclosed) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2835 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> ap(c_2Epred__set_2EBIGUNION(A_27a),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f311(A_27a,V0f))) = ap(c_2EfixedPoint_2Egfp(A_27a),V0f))))) # label(ax_thm_2EfixedPoint_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2836 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EfixedPoint_2Efnsum(A_27a,A_27b),arr(arr(A_27b,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27a,bool)),arr(A_27b,arr(A_27a,bool))))))))) # label(mem_c_2EfixedPoint_2Efnsum) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2837 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27b,bool))) -> ((all V1X (mem(V1X,arr(A_27a,bool)) -> (all V2Y (mem(V2Y,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),V2Y)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(V0f,V1X)),ap(V0f,V2Y)))))))) <-> p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27b),V0f))))))))) # label(ax_thm_2EfixedPoint_2Emonotone__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2838 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27b),c_2EfixedPoint_2Eempty(arr(A_27a,bool),A_27b))))))) # label(conj_thm_2EfixedPoint_2Eempty__monotone) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2839 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (all V2y (mem(V2y,A_27a) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),ap(V0f,V1X))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(c_2EfixedPoint_2Elfp(A_27a),V0f))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)))))))))))) # label(conj_thm_2EfixedPoint_2Elfp__rule__applied) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2840 (all A_27a (ne(A_27a) -> mem(c_2EfixedPoint_2Elfp(A_27a),arr(arr(arr(A_27a,bool),arr(A_27a,bool)),arr(A_27a,bool))))) # label(mem_c_2EfixedPoint_2Elfp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2841 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(V0f,V1X))) <-> p(ap(ap(c_2EfixedPoint_2Edense(A_27a),V0f),V1X))))))))) # label(ax_thm_2EfixedPoint_2Edense__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2842 (all A_27a all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1X ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V1X),ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1X)),V1X)) = ap(f310(A_27a,V0f),V1X)))) # label(lameq_f310) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2843 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(arr(A_27a,bool),arr(A_27b,bool))) -> (all V1f2 (mem(V1f2,arr(arr(A_27a,bool),arr(A_27b,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27b),V0f1)) & p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27b),V1f2)) -> p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27b),ap(ap(c_2EfixedPoint_2Efnsum(A_27b,arr(A_27a,bool)),V0f1),V1f2)))))))))))) # label(conj_thm_2EfixedPoint_2Efnsum__monotone) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2844 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,ap(ap(c_2Epred__set_2EINTER(A_27a),V1X),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)))),V1X)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)),V1X)))))))))) # label(conj_thm_2EfixedPoint_2Elfp__strong__induction) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2845 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),c_2EfixedPoint_2Eempty(A_27a,A_27b)) = V0f & V0f = ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),c_2EfixedPoint_2Eempty(A_27a,A_27b)),V0f))))))) # label(conj_thm_2EfixedPoint_2Efnsum__empty) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2846 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EfixedPoint_2Emonotone(A_27a,A_27b),arr(arr(arr(A_27a,bool),arr(A_27b,bool)),bool)))))) # label(mem_c_2EfixedPoint_2Emonotone) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2847 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EfixedPoint_2Eempty(A_27a,A_27b),arr(A_27a,arr(A_27b,bool))))))) # label(mem_c_2EfixedPoint_2Eempty) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2848 (all A_27a all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1X ap(f311(A_27a,V0f),V1X) = ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V1X),ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(V0f,V1X)))))) # label(lameq_f311) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2849 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(V0f,ap(ap(c_2Epred__set_2EUNION(A_27a),V1X),ap(c_2EfixedPoint_2Egfp(A_27a),V0f))))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(c_2EfixedPoint_2Egfp(A_27a),V0f))))))))))) # label(conj_thm_2EfixedPoint_2Egfp__strong__coinduction) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2850 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> ap(c_2Epred__set_2EBIGINTER(A_27a),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f310(A_27a,V0f))) = ap(c_2EfixedPoint_2Elfp(A_27a),V0f))))) # label(ax_thm_2EfixedPoint_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2851 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,bool))) -> (all V2X (mem(V2X,A_27a) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(V0f,V2X)),ap(ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),V1g),V2X))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(V1g,V2X)),ap(ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),V1g),V2X))))))))))))) # label(conj_thm_2EfixedPoint_2Efnsum__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2852 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1X)),V1X)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)),V1X)))))))))) # label(conj_thm_2EfixedPoint_2Elfp__induction) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2853 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2EfixedPoint_2Eclosed(A_27a),V0f),V1X)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1X)),V1X))))))))) # label(ax_thm_2EfixedPoint_2Eclosed__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2854 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,bool))) -> (all V2h (mem(V2h,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V1g),V2h)) = ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),V1g)),V2h))))))))))) # label(conj_thm_2EfixedPoint_2Efnsum__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2855 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V1f2)) & p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f1)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V1f2)),ap(c_2EfixedPoint_2Elfp(A_27a),ap(ap(c_2EfixedPoint_2Efnsum(A_27a,arr(A_27a,bool)),V0f1),V1f2)))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V0f1)),ap(c_2EfixedPoint_2Elfp(A_27a),ap(ap(c_2EfixedPoint_2Efnsum(A_27a,arr(A_27a,bool)),V0f1),V1f2))))))))))) # label(conj_thm_2EfixedPoint_2Elfp__fnsum) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2856 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(V0f,c_2Epred__set_2EEMPTY(A_27a)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)))))))))) # label(conj_thm_2EfixedPoint_2Elfp__empty) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2857 (all A_27a (ne(A_27a) -> mem(c_2EfixedPoint_2Edense(A_27a),arr(arr(arr(A_27a,bool),arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2EfixedPoint_2Edense) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2858 (all A_27a (ne(A_27a) -> mem(c_2EfixedPoint_2Egfp(A_27a),arr(arr(arr(A_27a,bool),arr(A_27a,bool)),arr(A_27a,bool))))) # label(mem_c_2EfixedPoint_2Egfp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2859 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V0f),V1g) = ap(ap(c_2EfixedPoint_2Efnsum(A_27b,A_27a),V1g),V0f))))))))) # label(conj_thm_2EfixedPoint_2Efnsum__COMM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2860 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2EfixedPoint_2Edense(A_27a),V0f),V1X)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(c_2EfixedPoint_2Egfp(A_27a),V0f)))))) & p(ap(ap(c_2EfixedPoint_2Edense(A_27a),V0f),ap(c_2EfixedPoint_2Egfp(A_27a),V0f)))))))) # label(conj_thm_2EfixedPoint_2Egfp__greatest__dense) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2861 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> ap(c_2EfixedPoint_2Egfp(A_27a),V0f) = ap(V0f,ap(c_2EfixedPoint_2Egfp(A_27a),V0f)) & (all V1X (mem(V1X,arr(A_27a,bool)) -> (ap(V0f,V1X) = V1X -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1X),ap(c_2EfixedPoint_2Egfp(A_27a),V0f))))))))))) # label(conj_thm_2EfixedPoint_2Egfp__greatest__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2862 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(A_27b,arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(A_27b,arr(A_27a,bool))) -> (all V2X (mem(V2X,A_27b) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(V0f1,V2X)),ap(V1f2,V2X)) = ap(ap(ap(c_2EfixedPoint_2Efnsum(A_27a,A_27b),V0f1),V1f2),V2X))))))))))) # label(ax_thm_2EfixedPoint_2Efnsum__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2863 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> ap(c_2EfixedPoint_2Elfp(A_27a),V0f) = ap(V0f,ap(c_2EfixedPoint_2Elfp(A_27a),V0f)) & (all V1X (mem(V1X,arr(A_27a,bool)) -> (ap(V0f,V1X) = V1X -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)),V1X)))))))))) # label(conj_thm_2EfixedPoint_2Elfp__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2864 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(arr(A_27a,bool),arr(A_27a,bool))) -> (p(ap(c_2EfixedPoint_2Emonotone(A_27a,A_27a),V0f)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2EfixedPoint_2Eclosed(A_27a),V0f),V1X)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)),V1X))))) & p(ap(ap(c_2EfixedPoint_2Eclosed(A_27a),V0f),ap(c_2EfixedPoint_2Elfp(A_27a),V0f)))))))) # label(conj_thm_2EfixedPoint_2Elfp__least__closed) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2865 (all A_27a (ne(A_27a) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4f (mem(V4f,arr(bool,arr(bool,bool))) -> (all V5a (mem(V5a,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,V3x),V4f),ap(c_2Earithmetic_2ENUMERAL,V5a)),c_2Enum_2E0)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,V3x),V4f),ap(c_2Earithmetic_2ENUMERAL,V5a)),c_2Enum_2E0))))))) & (all V9x (mem(V9x,ty_2Enum_2Enum) -> (all V10f (mem(V10f,arr(bool,arr(bool,bool))) -> (all V11a (mem(V11a,ty_2Enum_2Enum) -> (all V12b (mem(V12b,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,V9x),V10f),ap(c_2Earithmetic_2ENUMERAL,V11a)),ap(c_2Earithmetic_2ENUMERAL,V12b))) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,V9x),V10f),ap(c_2Earithmetic_2ENUMERAL,V11a)),ap(c_2Earithmetic_2ENUMERAL,V12b)))))))))) & (all V6x (mem(V6x,ty_2Enum_2Enum) -> (all V7f (mem(V7f,arr(bool,arr(bool,bool))) -> (all V8b (mem(V8b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,V6x),V7f),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V8b)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,V6x),V7f),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V8b))))))))) & (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,A_27a) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0x),V1f),c_2Enum_2E0),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,V0x),V1f),c_2Enum_2E0),c_2Enum_2E0)))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BITWISE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2866 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOG2,ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Enumeral__bit_2EiLOG2,V0n))) # label(ax_thm_2Enumeral__bit_2EiLOG2__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2867 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,V1n),ap(c_2Earithmetic_2EDIV2,V2a))) & p(ap(c_2Earithmetic_2EODD,V2a)) <-> p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,ap(c_2Enum_2ESUC,V1n)),V2a))))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2868 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,c_2Enum_2E0),V0a)) <-> $T))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2869 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),V2y),c_2Enum_2E0) = c_2Enum_2E0)) & (all V5n (mem(V5n,ty_2Enum_2Enum) -> (all V6x (mem(V6x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V5n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V6x))) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V5n))),V6x))))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V3n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V4x)))))) & (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Enum_2E0),V1x) = V1x)))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2870 (all V0opr (mem(V0opr,arr(bool,arr(bool,bool))) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> c_2Earithmetic_2EZERO = ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,c_2Enum_2E0),V0opr),V1a),V2b))))))) # label(conj_thm_2Enumeral__bit_2EiBITWISE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2871 (all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4opr (mem(V4opr,arr(bool,arr(bool,bool))) -> (all V5a (mem(V5a,ty_2Enum_2Enum) -> (all V6b (mem(V6b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),V4opr),V5a),V6b) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f312(V6b,V4opr,V5a)),ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V4opr),ap(c_2Earithmetic_2EDIV2,V5a)),ap(c_2Earithmetic_2EDIV2,V6b))))))))))) # label(conj_thm_2Enumeral__bit_2EiBITWISE_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2872 (all V8x (mem(V8x,ty_2Enum_2Enum) -> (all V9opr (mem(V9opr,arr(bool,arr(bool,bool))) -> (all V10a (mem(V10a,ty_2Enum_2Enum) -> (all V11b (mem(V11b,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f313(V11b,V9opr,V10a)),ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),V9opr),ap(c_2Earithmetic_2EDIV2,V10a)),ap(c_2Earithmetic_2EDIV2,V11b))) = ap(ap(ap(ap(c_2Enumeral__bit_2EiBITWISE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V8x))),V9opr),V10a),V11b))))))))) # label(conj_thm_2Enumeral__bit_2EiBITWISE_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2873 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2),V0x) = ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiDIV2,V0x)))) # label(conj_thm_2Enumeral__bit_2EFDUB__iDIV2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2874 (all V0i (mem(V0i,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V0i)) = ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2ENUMERAL,V0i)))) # label(conj_thm_2Enumeral__bit_2EiDUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2875 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Earithmetic_2EZERO = ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,c_2Enum_2E0),V0n))) & (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,A_27a) -> c_2Earithmetic_2EZERO = ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,V1x),c_2Earithmetic_2EZERO))))) & (all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V4n)) = ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),ap(c_2Earithmetic_2EBIT1,V4n)))))) & (all V9x (mem(V9x,ty_2Enum_2Enum) -> (all V10n (mem(V10n,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9x))),ap(c_2Enum_2ESUC,V10n))) = ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9x))),ap(c_2Earithmetic_2EBIT2,V10n)))))) & (all V7x (mem(V7x,ty_2Enum_2Enum) -> (all V8n (mem(V8n,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7x))),ap(c_2Earithmetic_2EBIT2,V8n)) = ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V8n))))))) & (all V5x (mem(V5x,ty_2Enum_2Enum) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5x))),V6n)) = ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V5x))),ap(c_2Earithmetic_2EBIT1,V6n)))))))) # label(conj_thm_2Enumeral__bit_2Enumeral__imod__2exp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2876 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2Enumeral__mod2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2877 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Enumeral__bit_2Enumeral__mod2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2878 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> c_2Earithmetic_2EZERO = ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Earithmetic_2EZERO) & (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Enumeral__bit_2EiSUC,V1x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Enumeral__bit_2EiSUC,V1x))))) & (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT1,V2x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT1,V2x))))) & (all V3x (mem(V3x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT2,V3x))) = ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT2,V3x)))))) # label(conj_thm_2Enumeral__bit_2EFDUB__FDUB) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2879 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB),V0x) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiDUB,V0x)))) # label(conj_thm_2Enumeral__bit_2EFDUB__iDUB) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2880 (all V5n (mem(V5n,ty_2Enum_2Enum) -> (all V6f (mem(V6f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V7x (mem(V7x,ty_2Enum_2Enum) -> (all V8b (mem(V8b,ty_2Enum_2Enum) -> (all V9e (mem(V9e,ty_2Enum_2Enum) -> (all V10y (mem(V10y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Enum_2ESUC,V5n)),V6f),V7x),V8b),V9e),V10y) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,V5n),V6f),ap(ap(c_2Earithmetic_2EDIV,V7x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,V8b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V9e)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V6f,V8b),ap(c_2Earithmetic_2EODD,V7x))),ap(ap(c_2Earithmetic_2E_2B,V9e),V10y)),V10y)))))))))))))) # label(ax_thm_2Enumeral__bit_2EBIT__MODF__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2881 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (all V3e (mem(V3e,ty_2Enum_2Enum) -> (all V4y (mem(V4y,ty_2Enum_2Enum) -> V4y = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,c_2Enum_2E0),V0f),V1x),V2b),V3e),V4y))))))))))) # label(ax_thm_2Enumeral__bit_2EBIT__MODF__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2882 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 -> ap(c_2Ebit_2ELOWEST__SET__BIT,V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V0n)),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Ebit_2ELOWEST__SET__BIT,ap(c_2Earithmetic_2EDIV2,V0n))))))) # label(conj_thm_2Enumeral__bit_2ELOWEST__SET__BIT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2883 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4y (mem(V4y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Enum_2ESUC,V2n)),V3x),V4y) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,V2n),ap(ap(c_2Earithmetic_2EDIV,V3x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4y)),ap(ap(c_2Ebit_2ESBIT,ap(c_2Earithmetic_2EODD,V3x)),c_2Enum_2E0))))))))) # label(ax_thm_2Enumeral__bit_2EBIT__REV__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2884 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V1y = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,c_2Enum_2E0),V0x),V1y))))) # label(ax_thm_2Enumeral__bit_2EBIT__REV__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2885 (all V11b (mem(V11b,ty_2Enum_2Enum) -> (all V9opr (mem(V9opr,arr(bool,arr(bool,bool))) -> (all V10a (mem(V10a,ty_2Enum_2Enum) -> (all V12w ap(f313(V11b,V9opr,V10a),V12w) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V9opr,ap(c_2Earithmetic_2EODD,V10a)),ap(c_2Earithmetic_2EODD,V11b))),ap(c_2Earithmetic_2EBIT1,V12w)),ap(c_2Enumeral_2EiDUB,V12w))))))))) # label(lameq_f313) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2886 (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),V1y),c_2Enum_2E0) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2887 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2)),ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Enumeral__bit_2EiDIV2,V3x)) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V3x))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2888 (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5x (mem(V5x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))),V5x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2)),ap(c_2Earithmetic_2ENUMERAL,V4n)),ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiDIV2,V5x))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2889 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),c_2Enum_2E0),V0x))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2890 (all V2f (mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,V2f),ap(c_2Enum_2ESUC,V3n)),V4x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V4x),c_2Enum_2E0)),c_2Enum_2E0),ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,V2f),V3n),ap(V2f,V4x))))))))) # label(ax_thm_2Enumeral__bit_2ESFUNPOW__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2891 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> V1x = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,V0f),c_2Enum_2E0),V1x))))) # label(ax_thm_2Enumeral__bit_2ESFUNPOW__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2892 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(ty_2Enum_2Enum),c_2Earithmetic_2EDIV2),V0n),V1x) = ap(ap(c_2Ebit_2EDIV__2EXP,V0n),V1x))))) # label(conj_thm_2Enumeral__bit_2EDIV__2EXP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2893 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V3x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB)),ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Enumeral_2EiDUB,V3x)))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2894 (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5x (mem(V5x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB)),ap(c_2Earithmetic_2ENUMERAL,V4n)),ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiDUB,V5x))) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))),V5x))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2895 (all V1y (mem(V1y,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),V1y),c_2Enum_2E0))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2896 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),c_2Enum_2E0),V0x) = V0x)) # label(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2897 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2ETIMES__2EXP,V0n),c_2Enum_2E0) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2898 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2ETIMES__2EXP,V1n),ap(c_2Earithmetic_2ENUMERAL,V2x)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),V1n),V2x)))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2899 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V1y = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,c_2Enum_2E0),V0x),V1y))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2900 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Enum_2E0),ap(c_2Enumeral_2EiDUB,V3y)) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),c_2Enum_2E0),V3y))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2901 (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7x (mem(V7x,ty_2Enum_2Enum) -> (all V8y (mem(V8y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,V7x))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V7x)),ap(c_2Earithmetic_2EBIT1,V8y)),ap(c_2Enumeral_2EiDUB,V8y))) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,V7x)),V8y))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2902 (all V9n (mem(V9n,ty_2Enum_2Enum) -> (all V10x (mem(V10x,ty_2Enum_2Enum) -> (all V11y (mem(V11y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9n))),ap(c_2Earithmetic_2ENUMERAL,V10x)),V11y) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9n))),ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,V10x))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V10x)),ap(c_2Earithmetic_2EBIT1,V11y)),ap(c_2Enumeral_2EiDUB,V11y))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2903 (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5y (mem(V5y,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))),c_2Enum_2E0),ap(c_2Enumeral_2EiDUB,V5y)) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))),c_2Enum_2E0),V5y))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2904 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIV__2EXP,V0n),c_2Enum_2E0) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2905 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),V1n),V2x)) = ap(ap(c_2Ebit_2EDIV__2EXP,V1n),ap(c_2Earithmetic_2ENUMERAL,V2x)))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2906 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enumeral__bit_2EiLOG2,ap(c_2Earithmetic_2EBIT1,V1n)) = ap(c_2Ebit_2ELOG2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))))) # label(conj_thm_2Enumeral__bit_2Enumeral__log2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2907 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral__bit_2EiLOG2,ap(c_2Enumeral_2EiDUB,V0n)) = ap(c_2Ebit_2ELOG2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral__bit_2Enumeral__log2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2908 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enumeral__bit_2EiLOG2,ap(c_2Earithmetic_2EBIT2,V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Enumeral__bit_2EiLOG2,V1n)))) # label(conj_thm_2Enumeral__bit_2Enumeral__ilog2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2909 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral__bit_2EiLOG2,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Enumeral__bit_2EiLOG2,V0n)))) # label(conj_thm_2Enumeral__bit_2Enumeral__ilog2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2910 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOWEST__SET__BIT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2911 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOWEST__SET__BIT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))) = ap(c_2Enum_2ESUC,ap(c_2Ebit_2ELOWEST__SET__BIT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V0n)))))) # label(conj_thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2912 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Earithmetic_2ENUMERAL,V0m)),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,V0m)),c_2Enum_2E0),c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2913 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Earithmetic_2ENUMERAL,V2m)),ap(c_2Earithmetic_2ENUMERAL,V1n)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,ap(c_2Earithmetic_2ENUMERAL,V2m)),ap(c_2Earithmetic_2ENUMERAL,V1n)),c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2914 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> c_2Enum_2E0 = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),c_2Enum_2E0))) # label(ax_thm_2Enumeral__bit_2EFDUB__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2915 (all V1f (mem(V1f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(V1f,ap(V1f,ap(c_2Enum_2ESUC,V2n))) = ap(ap(c_2Enumeral__bit_2EFDUB,V1f),ap(c_2Enum_2ESUC,V2n)))))) # label(ax_thm_2Enumeral__bit_2EFDUB__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2916 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Earithmetic_2ENUMERAL,V0m)),V1f),c_2Enum_2E0) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,V0m)),V1f),c_2Enum_2E0),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2917 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3f (mem(V3f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,V2m)),V3f),ap(c_2Earithmetic_2ENUMERAL,V4n)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Earithmetic_2ENUMERAL,V2m)),V3f),ap(c_2Earithmetic_2ENUMERAL,V4n)))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2918 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V0m),V1f),V2n) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,V0m),V1f),V2n),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0))))))) # label(conj_thm_2Enumeral__bit_2EBIT__MODIFY__EVAL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2919 (all V5n (mem(V5n,ty_2Enum_2Enum) -> (all V6a (mem(V6a,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V5n),V6a),V6a)) <-> $T))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2920 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,ap(c_2Enum_2ESUC,V2n)),V3a),V4b)) <-> p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V2n),ap(c_2Earithmetic_2EDIV2,V3a)),ap(c_2Earithmetic_2EDIV2,V4b))) & (p(ap(c_2Earithmetic_2EODD,V4b)) <-> p(ap(c_2Earithmetic_2EODD,V3a)))))))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2921 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ($T <-> p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,c_2Enum_2E0),V0a),V1b))))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2922 (all V6b (mem(V6b,ty_2Enum_2Enum) -> (all V4opr (mem(V4opr,arr(bool,arr(bool,bool))) -> (all V5a (mem(V5a,ty_2Enum_2Enum) -> (all V7w ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V4opr,ap(c_2Earithmetic_2EODD,V5a)),ap(c_2Earithmetic_2EODD,V6b))),ap(c_2Earithmetic_2EBIT1,V7w)),ap(c_2Enumeral_2EiDUB,V7w)) = ap(f312(V6b,V4opr,V5a),V7w)))))))) # label(lameq_f312) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2923 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBIT__REVERSE,V0m),V1n) = ap(ap(ap(c_2Enumeral__bit_2EBIT__REV,V0m),V1n),c_2Enum_2E0))))) # label(conj_thm_2Enumeral__bit_2EBIT__REVERSE__EVAL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2924 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Earithmetic_2EBIT1,V0n)) = V0n & ap(c_2Enumeral__bit_2EiSUC,V0n) = ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Earithmetic_2EBIT2,V0n)) & ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,ap(c_2Earithmetic_2EBIT2,V0n))) = ap(c_2Enumeral__bit_2EiSUC,V0n) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral__bit_2EiSUC,V0n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Enumeral__bit_2EiSUC,V0n) = ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,ap(c_2Earithmetic_2EBIT1,V0n))) & ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,c_2Earithmetic_2EZERO)) = c_2Earithmetic_2EZERO & c_2Earithmetic_2EZERO = ap(c_2Enumeral__bit_2EiDIV2,c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__iDIV2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2925 (all V0base_20_3C_202_20or_20n_20_3D_200 (mem(V0base_20_3C_202_20or_20n_20_3D_200,bool) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eprim__rec_2E_3C,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0))),ap(ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),c_2Elogroot_2ELOG),V0base_20_3C_202_20or_20n_20_3D_200),V1m),V2n)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V2n),V1m)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V1m),ap(ap(c_2Earithmetic_2EDIV,V2n),V1m))))) = ap(ap(c_2Elogroot_2ELOG,V1m),V2n))))))) # label(conj_thm_2Enumeral__bit_2ELOG__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2926 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (all V3e (mem(V3e,ty_2Enum_2Enum) -> (all V4y (mem(V4y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,c_2Enum_2E0),V0f),V1x),V2b),V3e),V4y) = V4y)))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2927 (all V21n (mem(V21n,ty_2Enum_2Enum) -> (all V22f (mem(V22f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V23x (mem(V23x,ty_2Enum_2Enum) -> (all V24b (mem(V24b,ty_2Enum_2Enum) -> (all V25e (mem(V25e,ty_2Enum_2Enum) -> (all V26y (mem(V26y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V21n))),V22f),ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,V23x))),ap(ap(c_2Earithmetic_2E_2B,V24b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V25e))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V22f,V24b),ap(c_2Earithmetic_2EODD,V23x))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V25e)),V26y)),V26y)) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V21n))),V22f),ap(c_2Earithmetic_2ENUMERAL,V23x)),V24b),ap(c_2Earithmetic_2ENUMERAL,V25e)),V26y))))))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2928 (all V15n (mem(V15n,ty_2Enum_2Enum) -> (all V16f (mem(V16f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V17x (mem(V17x,ty_2Enum_2Enum) -> (all V18b (mem(V18b,ty_2Enum_2Enum) -> (all V19e (mem(V19e,ty_2Enum_2Enum) -> (all V20y (mem(V20y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V15n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V16f),ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,V17x))),ap(ap(c_2Earithmetic_2E_2B,V18b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V19e))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V16f,V18b),ap(c_2Earithmetic_2EODD,V17x))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V19e)),V20y)),V20y)) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V15n))),V16f),ap(c_2Earithmetic_2ENUMERAL,V17x)),V18b),ap(c_2Earithmetic_2ENUMERAL,V19e)),V20y))))))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2929 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11f (mem(V11f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V12b (mem(V12b,ty_2Enum_2Enum) -> (all V13e (mem(V13e,ty_2Enum_2Enum) -> (all V14y (mem(V14y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10n))),V11f),c_2Enum_2E0),V12b),ap(c_2Earithmetic_2ENUMERAL,V13e)),V14y) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10n))),V11f),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V12b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V13e))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V11f,V12b),c_2Ebool_2EF)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V13e)),V14y)),V14y)))))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2930 (all V5n (mem(V5n,ty_2Enum_2Enum) -> (all V6f (mem(V6f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V7b (mem(V7b,ty_2Enum_2Enum) -> (all V8e (mem(V8e,ty_2Enum_2Enum) -> (all V9y (mem(V9y,ty_2Enum_2Enum) -> ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V6f),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V7b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V8e))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(V6f,V7b),c_2Ebool_2EF)),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V8e)),V9y)),V9y)) = ap(ap(ap(ap(ap(ap(c_2Enumeral__bit_2EBIT__MODF,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5n))),V6f),c_2Enum_2E0),V7b),ap(c_2Earithmetic_2ENUMERAL,V8e)),V9y))))))))))) # label(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2931 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EMOD__2EXP,V0x),c_2Enum_2E0) = c_2Enum_2E0)) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2932 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EMOD__2EXP,V1x),ap(c_2Earithmetic_2ENUMERAL,V2n)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,V1x),V2n)))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2933 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V1n ap(f314(V0s),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,bool),V1n),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(c_2Epred__set_2EMIN__SET,ap(ap(c_2Epred__set_2EDELETE(ty_2Enum_2Enum),V0s),c_2Enum_2E0))))))) # label(lameq_f314) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2934 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V1e (mem(V1e,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1e),V0s)) -> p(ap(ap(c_2Edivides_2Edivides,ap(c_2Egcdset_2Egcdset,V0s)),V1e))))))) # label(conj_thm_2Egcdset_2Egcdset__divides) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2935 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V2d ap(f316(V0s),V2d) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,bool),V2d),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f315(V0s,V2d)))))) # label(lameq_f316) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2936 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,bool)),V0s),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,bool)),V0s),ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),c_2Enum_2E0),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))))),c_2Enum_2E0),ap(c_2Epred__set_2EMAX__SET,ap(ap(c_2Epred__set_2EINTER(ty_2Enum_2Enum),ap(c_2Epred__set_2EGSPEC(ty_2Enum_2Enum,ty_2Enum_2Enum),f314(V0s))),ap(c_2Epred__set_2EGSPEC(ty_2Enum_2Enum,ty_2Enum_2Enum),f316(V0s))))) = ap(c_2Egcdset_2Egcdset,V0s))) # label(ax_thm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2937 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V3e ap(f315(V0s,V2d),V3e) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3e),V0s)),ap(ap(c_2Edivides_2Edivides,V2d),V3e))))))) # label(lameq_f315) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2938 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> (all V1g (mem(V1g,ty_2Enum_2Enum) -> ((all V2e (mem(V2e,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2e),V0s)) -> p(ap(ap(c_2Edivides_2Edivides,V1g),V2e))))) -> p(ap(ap(c_2Edivides_2Edivides,V1g),ap(c_2Egcdset_2Egcdset,V0s)))))))) # label(conj_thm_2Egcdset_2Egcdset__greatest) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2939 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1s (mem(V1s,arr(ty_2Enum_2Enum,bool)) -> ap(c_2Egcdset_2Egcdset,ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),V0x),V1s)) = ap(ap(c_2Egcd_2Egcd,V0x),ap(c_2Egcdset_2Egcdset,V1s)))))) # label(conj_thm_2Egcdset_2Egcdset__INSERT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2940 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x1 (mem(V2x1,A_27a) -> (all V3x2 (mem(V3x2,A_27a) -> (p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x1),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V1s),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x1),V3x2)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V3x2),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V1s),V0r)))))))))))))) # label(conj_thm_2Eset__relation_2Eupper__bounds__lem) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2941 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Elinear__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Elinear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2942 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),V0r)) <-> p(ap(ap(ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r),V1x),V2y))))))))))))) # label(conj_thm_2Eset__relation_2Ereln__to__rel__app) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2943 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s)) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))))))) # label(conj_thm_2Eset__relation_2Errestrict__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2944 (all A_27a all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0xs)),ap(c_2Ebool_2E_21(A_27a),f353(A_27a,V1r,V0xs,V2x)))) = ap(f354(A_27a,V0xs,V1r),V2x)))))) # label(lameq_f354) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2945 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)),c_2Enum_2E0) = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)))))))) & (all V8s (mem(V8s,arr(A_27a,bool)) -> (all V9r_27 (mem(V9r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V10r (mem(V10r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V11n (mem(V11n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f379(A_27a,V11n,V10r,V8s,V9r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V8s),V10r))) = ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V8s),V10r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V11n))))))))))) & (all V3s (mem(V3s,arr(A_27a,bool)) -> (all V4r_27 (mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V5r (mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f378(A_27a,V6n,V5r,V3s,V4r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r))) = ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))))))))))))) # label(conj_thm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2946 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s))) <-> p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s))))))))) # label(conj_thm_2Eset__relation_2Ereflexive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2947 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1a0 (mem(V1a0,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V2tc_27 ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27a)),f340(A_27a,V0r,V2tc_27))),ap(V2tc_27,V1a0)) = ap(f341(A_27a,V0r,V1a0),V2tc_27)))))) # label(lameq_f341) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2948 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eper(A_27a),arr(arr(A_27a,bool),arr(arr(arr(A_27a,bool),bool),bool))))) # label(mem_c_2Eset__relation_2Eper) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2949 (all A_27a all V2e (mem(V2e,A_27a) -> (all V4es ap(f370(A_27a,V2e),V4es) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V4es),V2e)))) # label(lameq_f370) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2950 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x ap(f346(A_27b,A_27a,V0R),V1x) = f345(A_27a,A_27b,V0R,V1x)))) # label(lameq_f346) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2951 (all A_27a all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V5r (mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (all V4r_27 (mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V7min ap(f378(A_27a,V6n,V5r,V3s,V4r_27),V7min) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V7min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V3s),ap(c_2Eoption_2ETHE(A_27a),V7min))),V5r)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))))) # label(lameq_f378) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2952 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eirreflexive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Eirreflexive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2953 (all A_27b all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1x f317(A_27a,A_27b,V1x,V0r) = ap(f344(A_27b,A_27a,V0r),V1x)))) # label(lameq_f344) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2954 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3s_27 (mem(V3s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V1r),V2s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V3s_27)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s_27),V2s)) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V2s)) -> p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V1r)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefix__linear__order__has__unique__minimal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2955 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x f349(A_27a,V1s,V2x) = ap(f350(A_27a,V1s),V2x)))) # label(lameq_f350) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2956 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)))))))))))) # label(conj_thm_2Eset__relation_2Etc__domain__range) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2957 (all A_27a all V9y (mem(V9y,A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V8x (mem(V8x,A_27a) -> (all V10m (mem(V10m,ty_2Enum_2Enum) -> (all V11n ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V10m),V11n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V10m)),ap(c_2Eoption_2ESOME(A_27a),V8x))),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V11n)),ap(c_2Eoption_2ESOME(A_27a),V9y)))) = ap(f357(A_27a,V9y,V0f,V8x,V10m),V11n)))))))))) # label(lameq_f357) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2958 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V1x)),V0r))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__irreflexive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2959 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V2s_27),V1s)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V2s_27))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__subset__s) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2960 (all A_27a all A_27b all V1y (mem(V1y,A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> (all V2x ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V1y)),V0r) = ap(f319(A_27a,A_27b,V1y,V0r),V2x)))))) # label(lameq_f319) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2961 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f318(A_27b,A_27a,V0r)))))))) # label(ax_thm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2962 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f368(A_27a,V0r)) = ap(c_2Eset__relation_2Efchains(A_27a),V0r))))) # label(ax_thm_2Eset__relation_2Efchains__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2963 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),V1s))))))))) # label(conj_thm_2Eset__relation_2ERREFL__EXP__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2964 (all A_27a (ne(A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r1),V2s)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r2),V2s)) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V1r2)),V2s))))))))) # label(conj_thm_2Eset__relation_2Errestrict__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2965 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) & (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Echain(A_27a),V2t),V0r)) -> ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2t),V0r) != c_2Epred__set_2EEMPTY(A_27a)))) & V1s != c_2Epred__set_2EEMPTY(A_27a) -> (exists V3x (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V0r))) & mem(V3x,A_27a)))))))))) # label(conj_thm_2Eset__relation_2Ezorns__lemma) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2966 (all A_27a (ne(A_27a) -> (all V0rs (mem(V0rs,arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) -> ((all V3r (mem(V3r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3r),V0rs)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V3r))))) & (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2r_27 (mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V2r_27),V0rs)) & V2r_27 != V1r & p(ap(ap(c_2Ebool_2EIN(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V1r),V0rs)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V2r_27)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V2r_27))))))))) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(c_2Epred__set_2EBIGUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0rs)))))))) # label(conj_thm_2Eset__relation_2Eacyclic__bigunion) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2967 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))))))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2968 (all A_27a all V3mins ap(f376(A_27a),V3mins) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Epred__set_2ESING(A_27a),V3mins)),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V3mins))),c_2Eoption_2ENONE(A_27a))) # label(lameq_f376) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2969 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V5x ap(f334(A_27b,A_27a,V0f,V1r),V5x) = f333(A_27b,A_27a,V0f,V5x,V1r)))))) # label(lameq_f334) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2970 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),V0r)) & p(ap(ap(V1tc_27,V6z),V5y)) & mem(V6z,A_27a))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__ind__left) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2971 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> f344(A_27b,A_27a,V0r) = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r))))))) # label(ax_thm_2Eset__relation_2Ereln__to__rel__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2972 (all A_27a all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1x1 ap(f329(A_27a,V0xs),V1x1) = f328(A_27a,V0xs,V1x1)))) # label(lameq_f329) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2973 (all A_27a all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 ap(f353(A_27a,V1r,V0xs,V2x),V3x_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x_27),V0xs)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x_27),V2x)),V1r))),ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3x_27))))))))) # label(lameq_f353) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 2974 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eantisym(A_27a),V0t)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1s),V0t)) -> p(ap(c_2Eset__relation_2Eantisym(A_27a),V1s)))))))))) # label(conj_thm_2Eset__relation_2Eantisym__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2975 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (c_2Eoption_2ENONE(A_27a) != ap(V0f,V3m) & ap(V0f,V3m) = ap(V0f,V2n) -> V2n = V3m))))) & (all V6m (mem(V6m,ty_2Enum_2Enum) -> (all V7x (mem(V7x,A_27a) -> (ap(V0f,V6m) = ap(c_2Eoption_2ESOME(A_27a),V7x) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V7x),V1s))))))) & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) -> (exists V5m (mem(V5m,ty_2Enum_2Enum) & ap(c_2Eoption_2ESOME(A_27a),V4x) = ap(V0f,V5m)))))) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f360(A_27a,V0f)))),V1s)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f364(A_27a,V0f)))),V1s))))))))) # label(conj_thm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2976 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Eset__relation_2Etc(A_27a),V1s))) -> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)),ap(c_2Eset__relation_2Etc(A_27a),V1s)))))))))) # label(conj_thm_2Eset__relation_2Etc__closure) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2977 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3a0 (mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V4x ap(c_2Ebool_2E_3F(A_27a),f335(A_27a,V3a0,V4x,V0r)) = ap(f336(A_27a,V0r,V3a0),V4x)))))) # label(lameq_f336) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2978 (all A_27a all V11n (mem(V11n,ty_2Enum_2Enum) -> (all V10r (mem(V10r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V8s (mem(V8s,arr(A_27a,bool)) -> (all V9r_27 (mem(V9r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V12min ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V12min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V9r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V8s),ap(c_2Eoption_2ETHE(A_27a),V12min))),V10r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V11n)))) = ap(f379(A_27a,V11n,V10r,V8s,V9r_27),V12min)))))))))) # label(lameq_f379) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2979 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> ((exists V2x (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V0y)),V1r)) & mem(V2x,A_27b))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Eset__relation_2Erange(A_27a,A_27b),V1r)))))))))))) # label(conj_thm_2Eset__relation_2Ein__range) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2980 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))),V1s)))))))) # label(conj_thm_2Eset__relation_2Edomain__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2981 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2ERREFL__EXP(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Eset__relation_2ERREFL__EXP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2982 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (V0r = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R) <-> ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r) = V1R))))))))) # label(conj_thm_2Eset__relation_2Erel__to__reln__swap) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2983 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Echain(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool))))) # label(mem_c_2Eset__relation_2Echain) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2984 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) <-> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))))))) # label(conj_thm_2Eset__relation_2Epartial__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2985 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V12x f363(A_27a,V0f,V12x) = ap(f364(A_27a,V0f),V12x)))) # label(lameq_f364) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2986 (all A_27a all V8x (mem(V8x,A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V9y (mem(V9y,A_27a) -> (all V10m ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f357(A_27a,V9y,V0f,V8x,V10m)) = ap(f358(A_27a,V8x,V0f,V9y),V10m)))))))) # label(lameq_f358) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2987 (all A_27a all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 ap(f328(A_27a,V0xs,V1x1),V2x2) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x1),V2x2)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V1x1),V0xs)),ap(ap(c_2Ebool_2EIN(A_27a),V2x2),V0xs)))))))) # label(lameq_f328) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2988 (all A_27a (ne(A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r1)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r2))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r1))) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V1r2))))))))))))))) # label(conj_thm_2Eset__relation_2Etc__implication) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2989 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Efchains(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Efchains) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2990 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (c_2Epred__set_2EEMPTY(A_27a) != V0s & p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eset__relation_2Efinite__strict__linear__order__has__maximal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2991 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x ap(f375(A_27a,V1s,V0f),V2x) = f374(A_27a,V1s,V0f,V2x)))))) # label(lameq_f375) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2992 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2y),V3z)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),V0r))))))))) <-> p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r))))))) # label(ax_thm_2Eset__relation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2993 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V3y (mem(V3y,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),ap(c_2Eset__relation_2Etc(A_27a),V1r)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__acyclic__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2994 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) <-> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Etransitive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2995 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(ty_2Enum_2Enum,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Enum_2Enum),V0f),V1s),V2t)) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s)),V1s))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__num__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2996 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s_27),V0r))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s_27),V0r))) -> V3x = V4y))))))))))))) # label(conj_thm_2Eset__relation_2Eminimal__linear__order__unique) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2997 (all A_27a (ne(A_27a) -> (all V0lo (mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0lo)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0lo)) = V1X))))))) # label(conj_thm_2Eset__relation_2Elinear__order__dom__rg) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2998 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 2999 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2y),V1x)),V0r)) -> V1x = V2y)))))))))) # label(ax_thm_2Eset__relation_2Eantisym__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3000 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s)) -> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r) = ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),ap(c_2Eset__relation_2Etc(A_27a),V1r))))))))) # label(conj_thm_2Eset__relation_2Eminimal__TC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3001 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r))))))))))))) # label(conj_thm_2Eset__relation_2Eminimal__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3002 (all A_27a (ne(A_27a) -> (all V0xss (mem(V0xss,arr(arr(A_27a,bool),bool)) -> ap(c_2Eset__relation_2Eall__choices(A_27a),V0xss) = ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a)),f373(A_27a,V0xss)))))) # label(ax_thm_2Eset__relation_2Eall__choices__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3003 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x ap(f327(A_27a,V0r),V1x) = f326(A_27a,V0r,V1x)))) # label(lameq_f327) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3004 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f346(A_27b,A_27a,V0R))))))))) # label(ax_thm_2Eset__relation_2Erel__to__reln__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3005 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s))))))))))))) # label(conj_thm_2Eset__relation_2Epartial__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3006 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Errestrict(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)))))) # label(mem_c_2Eset__relation_2Errestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3007 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V0xs)) = ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),V1r))))))) # label(conj_thm_2Eset__relation_2Eminimal__elements__rrestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3008 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3009 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s)))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__rrestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3010 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eacyclic(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)))) # label(mem_c_2Eset__relation_2Eacyclic) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3011 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),c_2Epred__set_2EEMPTY(A_27a))) <-> V0r = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a))))))) # label(conj_thm_2Eset__relation_2Eempty__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3012 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Eset__relation_2Etc(A_27a),V0r))))))) # label(conj_thm_2Eset__relation_2Esubset__tc) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3013 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))),V1s)) & p(ap(c_2Eset__relation_2Eantisym(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) & p(ap(c_2Eset__relation_2Etransitive(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))),V1s))))))))) # label(conj_thm_2Eset__relation_2Estrict__partial__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3014 (all A_27a all V1k (mem(V1k,arr(A_27a,bool)) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2C ap(f367(A_27a,V1k,V0r),V2C) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eset__relation_2Echain(A_27a),V2C),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2C),V1k)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C)),V1k)),c_2Epred__set_2EEMPTY(A_27a)))))),ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C))),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27a),V2C),V0r)),V2C)),V1k)),V0r)))))))) # label(lameq_f367) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3015 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Eupper__bounds(A_27a,A_27b),arr(arr(A_27b,bool),arr(arr(ty_2Epair_2Eprod(A_27b,A_27a),bool),arr(A_27a,bool)))))))) # label(mem_c_2Eset__relation_2Eupper__bounds) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3016 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V1r))))))))))))) # label(conj_thm_2Eset__relation_2Emaximal__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3017 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) -> ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r) = ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),ap(c_2Eset__relation_2Etc(A_27a),V1r))))))))) # label(conj_thm_2Eset__relation_2Emaximal__TC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3018 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1xss (mem(V1xss,arr(arr(A_27a,bool),bool)) -> (all V2e (mem(V2e,A_27a) -> (p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss)) -> p(ap(ap(c_2Eset__relation_2Eper(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0xs),V2e)),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f371(A_27a,V2e,V1xss))))))))))))) # label(conj_thm_2Eset__relation_2Eper__delete) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3019 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Enth__min(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))))))) # label(mem_c_2Eset__relation_2Enth__min) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3020 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Edomain(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(A_27a,bool))))))) # label(mem_c_2Eset__relation_2Edomain) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3021 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) = ap(c_2Eset__relation_2Estrict(A_27a),V0r))))) # label(conj_thm_2Eset__relation_2Estrict__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3022 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (all V2lo (mem(V2lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1X)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V2lo),V1X)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1X),V2lo))) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V0x)),V2lo))))))))))))))) # label(conj_thm_2Eset__relation_2EIN__MIN__LO) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3023 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f356(A_27a,V1s)))),V1s))))))))) # label(conj_thm_2Eset__relation_2Elinear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3024 (all A_27a (ne(A_27a) -> (all V0lo (mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0lo)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1X)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1X)))))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__in__set) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3025 (all A_27b all A_27c all A_27a all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> (all V2x ap(f325(A_27b,A_27c,A_27a,V0r1,V1r2),V2x) = f324(A_27a,A_27c,A_27b,V0r1,V1r2,V2x)))))) # label(lameq_f325) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3026 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s)) & p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eset__relation_2Efinite__linear__order__has__minimal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3027 (all A_27a all A_27c all A_27b all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),ap(c_2Ebool_2E_3F(A_27c),f323(A_27b,A_27a,A_27c,V2x,V0r1,V3y,V1r2))) = ap(f324(A_27a,A_27c,A_27b,V0r1,V1r2,V2x),V3y)))))))) # label(lameq_f324) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3028 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)),ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)))) = ap(f321(A_27a,V1s,V0r,V2x),V3y)))))))) # label(lameq_f321) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3029 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2ESND(A_27a,A_27a),V0x)),V2s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27a),V0x)),V2s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),V1r)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s)))))))))))) # label(conj_thm_2Eset__relation_2Ein__rrestrict__alt) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3030 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),arr(ty_2Enum_2Enum,bool)))) -> ((all V4r_27 (mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V5s (mem(V5s,arr(A_27a,bool)) -> (all V6r (mem(V6r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V7n (mem(V7n,ty_2Enum_2Enum) -> ((all V8min (mem(V8min,ty_2Eoption_2Eoption(A_27a)) -> (V8min != c_2Eoption_2ENONE(A_27a) & ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V5s),V6r)) = V8min -> p(ap(ap(ap(V0P,V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V5s),ap(c_2Eoption_2ETHE(A_27a),V8min))),V6r)),V7n))))) -> p(ap(ap(ap(V0P,V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V5s),V6r)),ap(c_2Enum_2ESUC,V7n)))))))))))) & (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3r (mem(V3r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> p(ap(ap(ap(V0P,V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V2s),V3r)),c_2Enum_2E0)))))))) -> (all V9v (mem(V9v,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V10v1 (mem(V10v1,arr(A_27a,bool)) -> (all V11v2 (mem(V11v2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V12v3 (mem(V12v3,ty_2Enum_2Enum) -> p(ap(ap(ap(V0P,V9v),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V10v1),V11v2)),V12v3))))))))))))))) # label(conj_thm_2Eset__relation_2Enth__min__ind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3031 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27b,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f366(A_27b,A_27a,V1r,V0s)) = ap(ap(c_2Eset__relation_2Eupper__bounds(A_27a,A_27b),V0s),V1r))))))))) # label(ax_thm_2Eset__relation_2Eupper__bounds__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3032 (all A_27a (ne(A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r1))) -> (all V3r2 (mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V3r2))))))))))))))) # label(conj_thm_2Eset__relation_2Etc__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3033 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s)) -> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s_27)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2s_27)))))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__restrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3034 (all A_27b all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1x ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(c_2Ebool_2E_3F(A_27b),f317(A_27a,A_27b,V1x,V0r))) = ap(f318(A_27b,A_27a,V0r),V1x)))) # label(lameq_f318) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3035 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V3s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V1y),V3s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),V2r)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V2r),V3s)))))))))))))) # label(conj_thm_2Eset__relation_2Ein__rrestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3036 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (c_2Epred__set_2EEMPTY(A_27a) != V0s -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r)) -> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) & mem(V2x,A_27a)))))))))))) # label(conj_thm_2Eset__relation_2Efinite__acyclic__has__maximal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3037 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) <-> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V0r)))))))) # label(conj_thm_2Eset__relation_2Eacyclic__SWAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3038 (all A_27a all V1xs (mem(V1xs,arr(A_27a,bool)) -> (all V0xss (mem(V0xss,arr(arr(A_27a,bool),bool)) -> (all V2xs_27 ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),ap(ap(c_2Epred__set_2EINTER(A_27a),V2xs_27),V1xs)),ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs_27),V0xss)) = ap(f369(A_27a,V1xs,V0xss),V2xs_27)))))) # label(lameq_f369) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3039 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1k ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V1k),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eset__relation_2Echain(A_27a),V1k),V0r)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V1k),c_2Epred__set_2EEMPTY(A_27a)))),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f367(A_27a,V1k,V0r))))) = ap(f368(A_27a,V0r),V1k)))) # label(lameq_f368) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3040 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Epair_2ECURRY(A_27a,A_27b,bool) = c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b))))) # label(conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3041 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Enum__order(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)))))) # label(mem_c_2Eset__relation_2Enum__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3042 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(c_2Eset__relation_2Euniv__reln(A_27a),V0s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Eset__relation_2ERRUNIV(A_27a),V0s)))))) # label(conj_thm_2Eset__relation_2Euniv__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3043 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> p(ap(c_2Eset__relation_2Etransitive(A_27a),ap(c_2Eset__relation_2Etc(A_27a),V0r))))))) # label(conj_thm_2Eset__relation_2Etc__transitive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3044 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V5x (mem(V5x,A_27a) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V6y ap(f333(A_27b,A_27a,V0f,V5x,V1r),V6y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27b,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27b,A_27b),ap(V0f,V5x)),ap(V0f,V6y))),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5x),V6y)),V1r))))))))) # label(lameq_f333) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3045 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),V2r)) -> p(ap(ap(c_2Ebool_2EIN(A_27b),V1y),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V2r))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V2r)))))))))))))) # label(conj_thm_2Eset__relation_2Ein__dom__rg) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3046 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Eantisym__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3047 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V8x (mem(V8x,A_27a) -> (all V9y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V8x),V9y)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f358(A_27a,V8x,V0f,V9y))) = ap(f359(A_27a,V0f,V8x),V9y)))))) # label(lameq_f359) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3048 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f322(A_27a,V1s,V0r))))))))) # label(ax_thm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3049 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> ((exists V5z (mem(V5z,A_27a) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V5z)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5z),V4y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))))) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V4y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))))) & (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))))))))) # label(conj_thm_2Eset__relation_2Etc__rules) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3050 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)),ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V2x)),ap(V0f,V3y))))) = ap(f374(A_27a,V1s,V0f,V2x),V3y)))))))) # label(lameq_f374) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3051 (all A_27b all A_27a all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> (all V0s (mem(V0s,arr(A_27b,bool)) -> (all V2x ap(f366(A_27b,A_27a,V1r,V0s),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Erange(A_27a,A_27b),V1r))),ap(c_2Ebool_2E_21(A_27b),f365(A_27a,A_27b,V1r,V2x,V0s))))))))) # label(lameq_f366) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3052 (all A_27a all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x_27),V0xs)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3x_27)),V1r))),ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3x_27)) = ap(f351(A_27a,V1r,V0xs,V2x),V3x_27)))))))) # label(lameq_f351) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3053 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Erange(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27b,A_27a),bool),arr(A_27a,bool))))))) # label(mem_c_2Eset__relation_2Erange) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3054 (all A_27b all A_27c all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool)) -> (all V4x (mem(V4x,A_27b) -> (all V3s2 (mem(V3s2,arr(A_27c,bool)) -> (all V5y ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27c),V5y),V3s2)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27c)),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V4x),V5y)),V1r2)) = ap(f331(A_27b,A_27c,V1r2,V4x,V3s2),V5y)))))))) # label(lameq_f331) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3055 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1lo (mem(V1lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1lo)),V0s)))))))) # label(conj_thm_2Eset__relation_2Eminimal__elements__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3056 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V1r)) = ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0xs),V1r))))))) # label(conj_thm_2Eset__relation_2Eminimal__elements__SWAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3057 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (p(ap(ap(V1tc_27,V6z),V5y)) & p(ap(ap(V1tc_27,V4x),V6z)) & mem(V6z,A_27a))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__ind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3058 (all A_27a all V12x (mem(V12x,A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V13y (mem(V13y,A_27a) -> (all V14m ap(f362(A_27a,V12x,V0f,V13y),V14m) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f361(A_27a,V13y,V0f,V12x,V14m))))))))) # label(lameq_f362) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3059 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V2s (mem(V2s,arr(A_27b,bool)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V2s)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V1r_27),V0r)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V1r_27),V2s))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__subset__r) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3060 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Etransitive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)))) # label(mem_c_2Eset__relation_2Etransitive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3061 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s))))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3062 (all A_27a all A_27b all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (all V0s (mem(V0s,arr(A_27b,bool)) -> (all V3y ap(f365(A_27a,A_27b,V1r,V2x,V0s),V3y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27b),V3y),V0s)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V3y),V2x)),V1r))))))))) # label(lameq_f365) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3063 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1xss (mem(V1xss,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1xss)),V0xs)) & (all V2xs1 (mem(V2xs1,arr(A_27a,bool)) -> (all V3xs2 (mem(V3xs2,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs1),V1xss)) & V2xs1 != V3xs2 & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3xs2),V1xss)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2xs1),V3xs2))))))) & -p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),c_2Epred__set_2EEMPTY(A_27a)),V1xss))))))))) # label(ax_thm_2Eset__relation_2Eper__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3064 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s)) & c_2Epred__set_2EEMPTY(A_27a) != V0s -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r)))))))))))) # label(conj_thm_2Eset__relation_2Efinite__linear__order__has__maximal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3065 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))),V1s)))))))) # label(conj_thm_2Eset__relation_2Erange__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3066 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f329(A_27a,V0xs))) = ap(c_2Eset__relation_2Euniv__reln(A_27a),V0xs))))) # label(ax_thm_2Eset__relation_2Euniv__reln__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3067 (all A_27a all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x ap(f352(A_27a,V0xs,V1r),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0xs)),ap(c_2Ebool_2E_21(A_27a),f351(A_27a,V1r,V0xs,V2x))))))))) # label(lameq_f352) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3068 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Eset__relation_2Estrict(A_27a),V0r) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f327(A_27a,V0r))))))) # label(ax_thm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3069 (all A_27a all V0xss (mem(V0xss,arr(arr(A_27a,bool),bool)) -> (all V1choice ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),A_27a),V1choice),V0xss)),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f372(A_27a,V0xss,V1choice))) = ap(f373(A_27a,V0xss),V1choice)))) # label(lameq_f373) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3070 (all A_27a (ne(A_27a) -> (all V0lo (mem(V0lo,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1X (mem(V1X,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0lo),V1X)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1X)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0lo)))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__refl) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3071 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,arr(A_27a,bool)) -> (all V2y (mem(V2y,arr(A_27a,bool)) -> ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),ap(ap(c_2Epred__set_2EINTER(A_27a),V1x),V2y)) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1x)),V2y))))))))) # label(conj_thm_2Eset__relation_2Errestrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3072 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x ap(f322(A_27a,V1s,V0r),V2x) = f321(A_27a,V1s,V0r,V2x)))))) # label(lameq_f322) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3073 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)),V1s))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3074 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f375(A_27a,V1s,V0f))) = ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s))))))) # label(ax_thm_2Eset__relation_2Enum__order__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3075 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> V0R = ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Eset__relation_2ERREFL__EXP__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3076 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x ap(f348(A_27a,V0s),V1x) = f347(A_27a,V1x,V0s)))) # label(lameq_f348) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3077 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (V0s != c_2Epred__set_2EEMPTY(A_27a) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__acyclic__has__minimal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3078 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3079 (all A_27a (ne(A_27a) -> ap(c_2Eset__relation_2Etc(A_27a),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a))) = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)))) # label(conj_thm_2Eset__relation_2Etc__empty__eqn) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3080 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2r1 (mem(V2r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3r2 (mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V2r1),V3r2)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V3r2))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V1s),V2r1)))))))))))))) # label(conj_thm_2Eset__relation_2Emaximal__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3081 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(f355(A_27a,V1s,V2x),V3y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a)))))))))) # label(lameq_f355) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3082 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V0r),V1r_27)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V0r)),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V1r_27)))))))))))) # label(conj_thm_2Eset__relation_2Erange__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3083 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (V0r = c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a)) <-> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Eset__relation_2Eempty__strict__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3084 (all A_27a (ne(A_27a) -> f343(A_27a) = c_2Eset__relation_2Etc(A_27a))) # label(ax_thm_2Eset__relation_2Etc__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3085 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> ap(c_2Eset__relation_2Erange(A_27a,A_27b),V0r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f320(A_27b,A_27a,V0r)))))))) # label(ax_thm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3086 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1t (mem(V1t,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V1t)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V0s))))))) <-> V1t = V0s))))))))) # label(conj_thm_2Eset__relation_2Erextension) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 3087 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Estrict__linear__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Estrict__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3088 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)) | (exists V3z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),V0r)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & mem(V3z,A_27a)))))))))))) # label(conj_thm_2Eset__relation_2Etc__cases__left) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3089 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r))))) <-> p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),V1s))))))))) # label(ax_thm_2Eset__relation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3090 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))))))))) # label(conj_thm_2Eset__relation_2Epartial__order__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3091 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0xy (mem(V0xy,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (all V5r1 (mem(V5r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V6r2 (mem(V6r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V7R1 (mem(V7R1,arr(A_27a,arr(A_27b,bool))) -> (all V8R2 (mem(V8R2,arr(A_27a,arr(A_27b,bool))) -> (all V9R (mem(V9R,arr(A_27a,arr(A_27a,bool))) -> (all V10r (mem(V10r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> (all V11r (mem(V11r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V12s (mem(V12s,arr(A_27a,bool)) -> (all V13r1 (mem(V13r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V14r2 (mem(V14r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> (p(ap(ap(V1R,ap(c_2Epair_2EFST(A_27a,A_27b),V0xy)),ap(c_2Epair_2ESND(A_27a,A_27b),V0xy))) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V0xy),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)))) & (V6r2 = V5r1 <-> ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V6r2) = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V5r1)) & V9R = ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V9R),c_2Epred__set_2EUNIV(A_27a)) & ap(c_2Eset__relation_2Estrict(A_27a),V11r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) & ap(c_2Eset__relation_2Etc(A_27a),V11r) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) & (p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) <-> p(ap(c_2Eset__relation_2Etransitive(A_27a),V11r))) & (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)))) & (p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) <-> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a)))) & (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V11r),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)))) & (p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))) <-> p(ap(c_2Eset__relation_2Eantisym(A_27a),V11r))) & (p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V11r),V12s)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s)))) & (p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V11r),V12s)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s)))) & (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V11r)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r))))) & ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Eset__relation_2ERRUNIV(A_27a),V12s)) = ap(c_2Eset__relation_2Euniv__reln(A_27a),V12s) & ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27c,A_27b),V14r2)),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27c),V13r1))) = ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V13r1),V14r2) & ap(ap(c_2Eset__relation_2Errestrict(A_27a),V11r),V12s) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V11r)),V12s)) & ap(c_2Erelation_2ERRANGE(A_27b,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27b,A_27a),V10r)) = ap(c_2Eset__relation_2Erange(A_27a,A_27b),V10r) & ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V2r) = ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r)) & V9R = ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V9R),c_2Epred__set_2EUNIV(A_27a)) & (V7R1 = V8R2 <-> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V8R2) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V7R1)) & V2r = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r)) & V1R = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R)) & (p(ap(ap(ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V2r),V3x),V4y)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),V2r))))))))))))))))))))))))))))))))))))))) # label(conj_thm_2Eset__relation_2Ereln__rel__conv__thms) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3092 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (mem(V6z,A_27a) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(V1tc_27,V6z),V5y)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(V1tc_27,V4x),V6z)))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__strongind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3093 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(ty_2Enum_2Enum,bool)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,ty_2Enum_2Enum),V0f),V1s),V2t)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(ap(c_2Eset__relation_2Enum__order(A_27a),V0f),V1s)),V1s))))))))))) # label(conj_thm_2Eset__relation_2Enum__order__finite__prefix) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3094 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(V0f,V4y) = ap(V0f,V3x) -> V4y = V3x))))) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V1r),V2s)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27b,A_27b),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27b,A_27b),ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Epair_2EUNCURRY(A_27a,A_27a,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27b,A_27b),bool)),f334(A_27b,A_27a,V0f,V1r)))),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__inj__image) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3095 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s)) -> (exists V3y (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2s),V0r))) & (V1x = V3y | p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V1x)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))) & mem(V3y,A_27a))))))))))))) # label(conj_thm_2Eset__relation_2EWF__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3096 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2Eset__relation_2Efinite__prefixes) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3097 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s)),V0r)))))))) # label(conj_thm_2Eset__relation_2Errestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3098 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2ERRUNIV(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Eset__relation_2ERRUNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3099 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1xss (mem(V1xss,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Eset__relation_2Eper(A_27a),V0xs),V1xss)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V0xs)) -> p(ap(c_2Epred__set_2Ecountable(arr(A_27a,bool)),V1xss))))))))) # label(conj_thm_2Eset__relation_2Ecountable__per) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3100 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> V0R = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R)))))))) # label(conj_thm_2Eset__relation_2Erel__to__reln__inv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3101 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V2s1 (mem(V2s1,arr(A_27b,bool)) -> (all V3s2 (mem(V3s2,arr(A_27b,bool)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V1r2),V3s2)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r1),V2s1)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27b)),V0r1),V1r2)),ap(ap(c_2Epred__set_2EINTER(A_27b),V2s1),V3s2)))))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3102 (all A_27a all A_27b all V1x (mem(V1x,A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V2y ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),V0r) = ap(f317(A_27a,A_27b,V1x,V0r),V2y)))))) # label(lameq_f317) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3103 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1s)) -> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)),ap(c_2Eset__relation_2Etc(A_27a),V1s)))))))))) # label(conj_thm_2Eset__relation_2Etc__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3104 (all A_27a all V3a0 (mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V4x (mem(V4x,A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V5y ap(f335(A_27a,V3a0,V4x,V0r),V5y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Epair_2Eprod(A_27a,A_27a)),V3a0),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y))),ap(V0r,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V5y)))))))))) # label(lameq_f335) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3105 (all A_27a all V0xss (mem(V0xss,arr(arr(A_27a,bool),bool)) -> (all V1choice (mem(V1choice,arr(arr(A_27a,bool),A_27a)) -> (all V2xs ap(f372(A_27a,V0xss,V1choice),V2xs) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V2xs),V0xss)),ap(ap(c_2Ebool_2EIN(A_27a),ap(V1choice,V2xs)),V2xs))))))) # label(lameq_f372) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3106 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xy (mem(V0xy,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V0xy),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R))) <-> p(ap(ap(V1R,ap(c_2Epair_2EFST(A_27a,A_27b),V0xy)),ap(c_2Epair_2ESND(A_27a,A_27b),V0xy)))))))))))) # label(conj_thm_2Eset__relation_2Ein__rel__to__reln) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3107 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Euniv__reln(A_27a),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))))) # label(mem_c_2Eset__relation_2Euniv__reln) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3108 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2tc_27 (mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3a0 ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f336(A_27a,V0r,V3a0))),ap(c_2Ebool_2E_3F(A_27a),f339(A_27a,V2tc_27,V3a0)))),ap(V2tc_27,V3a0)) = ap(f340(A_27a,V0r,V2tc_27),V3a0)))))) # label(lameq_f340) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3109 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s)) & p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s)) & p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) & p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s)) <-> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s))))))))) # label(ax_thm_2Eset__relation_2Epartial__order__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3110 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s)) & p(ap(c_2Epred__set_2Ecountable(A_27a),V1s)) -> (exists V2r_27 (mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V2r_27),V1s)) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V2r_27)) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V2r_27),V1s))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__of__countable__po) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3111 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r)))))))))))) # label(ax_thm_2Eset__relation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3112 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s)) & p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) & (all V2x (mem(V2x,A_27a) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),V0r)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (V3x != V4y & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V4y)),V0r)) | p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4y),V3x)),V0r))))))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s)) <-> p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s))))))))) # label(ax_thm_2Eset__relation_2Estrict__linear__order__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3113 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) <-> (all V1x (mem(V1x,A_27a) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V1x)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))))))) # label(ax_thm_2Eset__relation_2Eacyclic__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3114 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27c),bool),arr(arr(ty_2Epair_2Eprod(A_27c,A_27b),bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))))))))) # label(mem_c_2Eset__relation_2Ercomp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3115 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),c_2Epred__set_2EUNIV(A_27a)) = V0R)))) # label(conj_thm_2Eset__relation_2EREL__RESTRICT__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3116 (all A_27a all V3a0 (mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V2tc_27 (mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V6x (mem(V6x,A_27a) -> (all V7y ap(f338(A_27a,V3a0,V2tc_27,V6x),V7y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Epair_2Eprod(A_27a,A_27a)),V3a0),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V7y))),ap(c_2Ebool_2E_3F(A_27a),f337(A_27a,V6x,V7y,V2tc_27)))))))))) # label(lameq_f338) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3117 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V1r),V0s)) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s_27)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2s_27)))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__restrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3118 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Etc(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))))) # label(mem_c_2Eset__relation_2Etc) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3119 (all A_27a all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V2tc_27 (mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V8z ap(ap(c_2Ebool_2E_2F_5C,ap(V2tc_27,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V8z))),ap(V2tc_27,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V8z),V7y))) = ap(f337(A_27a,V6x,V7y,V2tc_27),V8z)))))))) # label(lameq_f337) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3120 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,arr(A_27a,bool)) -> (all V2e (mem(V2e,A_27a) -> (all V3e_27 (mem(V3e_27,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2e),V3e_27)),ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1x)))) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2e),V3e_27)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))))))))))) # label(conj_thm_2Eset__relation_2Errestrict__tc) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3121 (all A_27c all A_27b all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool)) -> (all V3s2 (mem(V3s2,arr(A_27c,bool)) -> (all V4x ap(f332(A_27c,A_27b,V1r2,V3s2),V4x) = ap(ap(c_2Epair_2E_2C(A_27b,bool),V4x),ap(c_2Ebool_2E_3F(A_27c),f331(A_27b,A_27c,V1r2,V4x,V3s2)))))))) # label(lameq_f332) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3122 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r)),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r)),V0s)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V1r)))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__WF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3123 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),ap(c_2Eset__relation_2Etc(A_27a),V0r)) = ap(c_2Eset__relation_2Etc(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27a),ty_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP(A_27a,A_27a)),V0r)))))) # label(conj_thm_2Eset__relation_2Etc__SWAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3124 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27))))))))))) # label(conj_thm_2Eset__relation_2Elinear__order__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3125 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)))))))))) # label(conj_thm_2Eset__relation_2Estrict__partial__order__acyclic) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3126 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(arr(A_27a,bool),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Eper(A_27a),V1s),V0r)) -> p(ap(ap(c_2Eset__relation_2Eper(A_27a),V2s_27),ap(ap(c_2Eset__relation_2Eper__restrict(A_27a),V0r),V2s_27)))))))))))) # label(conj_thm_2Eset__relation_2Eper__restrict__per) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3127 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27c,A_27b),V1r2)),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27c),V0r1))) = ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V0r1),V1r2))))))))))) # label(conj_thm_2Eset__relation_2Ercomp__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3128 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)),c_2Enum_2E0) = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V1r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V0s),V2r)))))))) & (all V3s (mem(V3s,arr(A_27a,bool)) -> (all V4r_27 (mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V5r (mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)),f377(A_27a,V6n,V5r,V3s,V4r_27)),ap(ap(c_2Eset__relation_2Eget__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r))) = ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V3s),V5r)),ap(c_2Enum_2ESUC,V6n)))))))))))) # label(conj_thm_2Eset__relation_2Enth__min__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3129 (all A_27b all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V2e (mem(V2e,A_27b) -> (all V3e_27 ap(f330(A_27b,A_27a,V0r,V2e),V3e_27) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3e_27),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3e_27),V2e)),V0r))))))) # label(lameq_f330) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3130 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V1r),V0s)) & V0s != c_2Epred__set_2EEMPTY(A_27a) -> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0s),V1r))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eset__relation_2Efinite__strict__linear__order__has__minimal) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3131 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Eset__relation_2Etc(A_27a),V0r) = ap(c_2Eset__relation_2Etc(A_27a),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))) # label(conj_thm_2Eset__relation_2Etc__idemp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3132 (all A_27a all A_27b all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f345(A_27a,A_27b,V0R,V1x),V2y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),ap(ap(V0R,V1x),V2y))))))) # label(lameq_f345) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3133 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r) = ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r)))))))) # label(conj_thm_2Eset__relation_2Edomain__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3134 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (p(ap(ap(V1tc_27,V4x),V6z)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),V0r)) & mem(V6z,A_27a))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__ind__right) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3135 (all A_27a (ne(A_27a) -> (all V0xss (mem(V0xss,arr(arr(A_27a,bool),bool)) -> (all V1xs (mem(V1xs,arr(A_27a,bool)) -> ap(ap(c_2Eset__relation_2Eper__restrict(A_27a),V0xss),V1xs) = ap(ap(c_2Epred__set_2EDELETE(arr(A_27a,bool)),ap(c_2Epred__set_2EGSPEC(arr(A_27a,bool),arr(A_27a,bool)),f369(A_27a,V1xs,V0xss))),c_2Epred__set_2EEMPTY(A_27a)))))))) # label(ax_thm_2Eset__relation_2Eper__restrict__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3136 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f326(A_27a,V0r,V1x),V2y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y))))))))) # label(lameq_f326) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3137 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Emaximal__elements(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(A_27a,bool)))))) # label(mem_c_2Eset__relation_2Emaximal__elements) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3138 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) <-> (all V2e (mem(V2e,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V2e),V1s)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f330(A_27b,A_27a,V0r,V2e)))))))))))))))) # label(ax_thm_2Eset__relation_2Efinite__prefixes__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3139 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r))) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r)) -> (exists V3y (mem(V3y,A_27a) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),ap(c_2Eset__relation_2Etc(A_27a),V1r))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0s),V1r)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__acyclic__has__maximal__path) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3140 (all A_27a all V2e (mem(V2e,A_27a) -> (all V1xss (mem(V1xss,arr(arr(A_27a,bool),bool)) -> (all V3es ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),bool),V3es),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3es),ap(ap(c_2Epred__set_2EIMAGE(arr(A_27a,bool),arr(A_27a,bool)),f370(A_27a,V2e)),V1xss))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V3es),c_2Epred__set_2EEMPTY(A_27a))))) = ap(f371(A_27a,V2e,V1xss),V3es)))))) # label(lameq_f371) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3141 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> ((exists V5z (mem(V5z,A_27a) & p(ap(ap(V1tc_27,V3x),V5z)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V5z),V4y)),V0r)))) -> p(ap(ap(V1tc_27,V3x),V4y))))))) & (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r))) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r))) -> p(ap(ap(V1tc_27,V2x),V2x))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6x),V7y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V6x),V7y)))))))))))))) # label(conj_thm_2Eset__relation_2Ertc__ind__right) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3142 (all A_27b all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> (all V1y ap(f320(A_27b,A_27a,V0r),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1y),ap(c_2Ebool_2E_3F(A_27b),f319(A_27a,A_27b,V1y,V0r)))))) # label(lameq_f320) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3143 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2r1 (mem(V2r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3r2 (mem(V3r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V2r1),V3r2)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V2r1))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V3r2)))))))))))))) # label(conj_thm_2Eset__relation_2Eminimal__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3144 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) <-> p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a)))))))) # label(conj_thm_2Eset__relation_2Ereflexive__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3145 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eget__min(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ty_2Eoption_2Eoption(A_27a)))))) # label(mem_c_2Eset__relation_2Eget__min) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3146 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x ap(f356(A_27a,V1s),V2x) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s))))) # label(lameq_f356) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3147 (all A_27a all V2tc_27 (mem(V2tc_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3a0 (mem(V3a0,ty_2Epair_2Eprod(A_27a,A_27a)) -> (all V6x ap(f339(A_27a,V2tc_27,V3a0),V6x) = ap(c_2Ebool_2E_3F(A_27a),f338(A_27a,V3a0,V2tc_27,V6x))))))) # label(lameq_f339) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3148 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (V0R1 = V1R2 <-> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R1) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V1R2)))))))))) # label(conj_thm_2Eset__relation_2Erel__to__reln__11) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3149 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f352(A_27a,V0xs,V1r)) = ap(ap(c_2Eset__relation_2Emaximal__elements(A_27a),V0xs),V1r))))))) # label(ax_thm_2Eset__relation_2Emaximal__elements__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3150 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V2s_27)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3151 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f355(A_27a,V1s,V2x)))),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),c_2Epred__set_2EEMPTY(A_27a)))))))))))))) # label(conj_thm_2Eset__relation_2Eextend__linear__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3152 (all A_27a all V13y (mem(V13y,A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V12x (mem(V12x,A_27a) -> (all V14m (mem(V14m,ty_2Enum_2Enum) -> (all V15n ap(f361(A_27a,V13y,V0f,V12x,V14m),V15n) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,V14m),V15n)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V14m)),ap(c_2Eoption_2ESOME(A_27a),V12x))),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),ap(V0f,V15n)),ap(c_2Eoption_2ESOME(A_27a),V13y))))))))))))) # label(lameq_f361) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3153 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2r_27 (mem(V2r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V3s_27 (mem(V3s_27,arr(A_27b,bool)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V2r_27),V0r)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V3s_27),V1s)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V2r_27),V3s_27))))))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__subset__rs) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3154 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Estrict(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool))))) # label(mem_c_2Eset__relation_2Estrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3155 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27b)),V0r),V1r_27)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r)),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V1r_27)))))))))))) # label(conj_thm_2Eset__relation_2Edomain__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3156 (all A_27a (ne(A_27a) -> (all V0r_27 (mem(V0r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2r (mem(V2r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(c_2Ebool_2ELET(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a)),f376(A_27a)),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V1s),V2r)),V0r_27)) = ap(ap(c_2Eset__relation_2Eget__min(A_27a),V0r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),V1s),V2r)))))))))) # label(ax_thm_2Eset__relation_2Eget__min__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3157 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27b,A_27a),bool)) -> ap(c_2Eset__relation_2Erange(A_27a,A_27b),V0r) = ap(c_2Erelation_2ERRANGE(A_27b,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27b,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Erange__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3158 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))))) # label(mem_c_2Eset__relation_2Erel__to__reln) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3159 (all A_27a (ne(A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1r2),V0r1)) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r1)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r2))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3160 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eminimal__elements(A_27a),arr(arr(A_27a,bool),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(A_27a,bool)))))) # label(mem_c_2Eset__relation_2Eminimal__elements) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3161 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),bool),arr(A_27a,arr(A_27b,bool)))))))) # label(mem_c_2Eset__relation_2Ereln__to__rel) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3162 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eantisym(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)))) # label(mem_c_2Eset__relation_2Eantisym) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3163 (all A_27b all A_27a all A_27c all V2x (mem(V2x,A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V3y (mem(V3y,A_27b) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> (all V4z ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27c)),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V4z)),V0r1)),ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27c,A_27b)),ap(ap(c_2Epair_2E_2C(A_27c,A_27b),V4z),V3y)),V1r2)) = ap(f323(A_27b,A_27a,A_27c,V2x,V0r1,V3y,V1r2),V4z)))))))))) # label(lameq_f323) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3164 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3s_27 (mem(V3s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V0r),V1s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V0r))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s_27),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V3s_27)) -> (exists V4x_27 (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x_27),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V3s_27),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x_27),V2x)),V0r)) & mem(V4x_27,A_27a)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefix__po__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3165 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0x),V1y)),ap(c_2Eset__relation_2Etc(A_27a),c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(A_27a,A_27a))))))))))) # label(conj_thm_2Eset__relation_2Etc__empty) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3166 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(c_2Eset__relation_2ERRUNIV(A_27a),V0s) = f348(A_27a,V0s))))) # label(ax_thm_2Eset__relation_2ERRUNIV__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3167 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(arr(A_27a,bool),bool)) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0x)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V0x),ap(c_2Eset__relation_2Eall__choices(A_27a),V1s))) -> (exists V3z (mem(V3z,arr(A_27a,bool)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V3z)) & p(ap(ap(c_2Ebool_2EIN(arr(A_27a,bool)),V3z),V1s))))))))))))) # label(conj_thm_2Eset__relation_2Eall__choices__thm) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3168 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),V0r)) & p(ap(ap(V1tc_27,V4x),V6z)) & mem(V6z,A_27a))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__strongind__right) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3169 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1a0 ap(c_2Ebool_2E_21(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f341(A_27a,V0r,V1a0)) = ap(f342(A_27a,V0r),V1a0)))) # label(lameq_f342) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3170 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eper__restrict(A_27a),arr(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))))) # label(mem_c_2Eset__relation_2Eper__restrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3171 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V1r)) | p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V1r))))))) <-> p(ap(ap(c_2Eset__relation_2Echain(A_27a),V0s),V1r))))))))) # label(ax_thm_2Eset__relation_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3172 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V12x (mem(V12x,A_27a) -> (all V13y ap(f363(A_27a,V0f,V12x),V13y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V12x),V13y)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f362(A_27a,V12x,V0f,V13y)))))))) # label(lameq_f363) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3173 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V1r))) <-> (exists V2y (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V2y)),V1r)) & mem(V2y,A_27b)))))))))))) # label(conj_thm_2Eset__relation_2Ein__domain) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3174 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),c_2Epred__set_2EUNIV(A_27a))) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)))))))) # label(conj_thm_2Eset__relation_2Elinear__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3175 (all A_27a all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V5r (mem(V5r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V3s (mem(V3s,arr(A_27a,bool)) -> (all V4r_27 (mem(V4r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V7min ap(f377(A_27a,V6n,V5r,V3s,V4r_27),V7min) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(A_27a)),V7min),c_2Eoption_2ENONE(A_27a))),c_2Eoption_2ENONE(A_27a)),ap(ap(ap(c_2Eset__relation_2Enth__min(A_27a),V4r_27),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V3s),ap(c_2Eoption_2ETHE(A_27a),V7min))),V5r)),V6n))))))))))) # label(lameq_f377) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3176 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2xs (mem(V2xs,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1r_27)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2xs),V1r_27)),ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V2xs),V0r)))))))))))) # label(conj_thm_2Eset__relation_2Eminimal__elements__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3177 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) -> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3y),V2x)),V0r)) | p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r))))))) & p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) & p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),V1s))))))))) # label(ax_thm_2Eset__relation_2Elinear__order__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3178 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Eset__relation_2Errestrict(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r)),V1s) = ap(c_2Eset__relation_2Estrict(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s)))))))) # label(conj_thm_2Eset__relation_2Estrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3179 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r_27 (mem(V1r_27,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V0r)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r))),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r_27)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r_27)))) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V1r_27)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r),V1r_27)))))))))) # label(conj_thm_2Eset__relation_2Eacyclic__union) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3180 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),ap(c_2Eset__relation_2ERRUNIV(A_27a),V1s))) & p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s)))))))))) # label(conj_thm_2Eset__relation_2Epartial__order__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3181 (all A_27a (ne(A_27a) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r1),V2s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Eset__relation_2Edomain(A_27a,A_27a),V1r2)),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V1r2))),V2s)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(A_27a,A_27a)),V1r2),V0r1)) <-> p(ap(c_2Eset__relation_2Eacyclic(A_27a),ap(ap(c_2Epred__set_2EUNION(ty_2Epair_2Eprod(A_27a,A_27a)),V0r1),V1r2))))))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__union__acyclic) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3182 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Ereflexive(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Ereflexive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3183 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),V1s) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27a),V0R),f350(A_27a,V1s)))))))) # label(ax_thm_2Eset__relation_2ERREFL__EXP__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27c),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27c,A_27b),bool)) -> ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V0r1),V1r2) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f325(A_27b,A_27c,A_27a,V0r1,V1r2))))))))))))) # label(ax_thm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3185 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> V0r = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r)))))))) # label(conj_thm_2Eset__relation_2Ereln__to__rel__inv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3186 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) <-> (exists V3z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & mem(V3z,A_27a))) | p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r))))))))))) # label(conj_thm_2Eset__relation_2Etc__cases) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3187 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Epair_2EUNCURRY(A_27a,A_27b,bool) = c_2Eset__relation_2Erel__to__reln(A_27a,A_27b))))) # label(conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3188 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Eoption_2Eoption(A_27a))) -> (all V8x ap(f360(A_27a,V0f),V8x) = f359(A_27a,V0f,V8x)))) # label(lameq_f360) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3189 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2s_27 (mem(V2s_27,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),V1s)) & p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Epartial__order(A_27a),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V2s_27)),V2s_27))))))))))) # label(conj_thm_2Eset__relation_2Epartial__order__subset) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3190 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2t (mem(V2t,arr(A_27b,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),V2t),ap(c_2Eset__relation_2Erange(A_27b,A_27a),V0r))) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),ap(ap(c_2Epred__set_2EUNION(A_27b),V1s),V2t)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__range) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3191 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Epartial__order(A_27a),arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Epartial__order) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 3192 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Eirreflexive(A_27a),V0r),V1s)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r)),V1s)))))))))) # label(conj_thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3193 (all A_27a all V1x (mem(V1x,A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2y ap(f347(A_27a,V1x,V0s),V2y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0s))))))) # label(lameq_f347) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3194 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(f349(A_27a,V1s,V2x),V3y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2x),V3y)),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)))))))) # label(lameq_f349) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3195 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Eset__relation_2Estrict__linear__order(A_27a),V0r),V1s)) -> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__acyclic) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3196 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V1r2) = ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27b),V0r1) <-> V1r2 = V0r1))))))))) # label(conj_thm_2Eset__relation_2Ereln__to__rel__11) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3197 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (p(ap(c_2Eset__relation_2Etransitive(A_27a),V0r)) -> ap(c_2Eset__relation_2Etc(A_27a),V0r) = V0r))))) # label(conj_thm_2Eset__relation_2Etransitive__tc) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3198 (all A_27a all V0r f342(A_27a,V0r) = ap(f343(A_27a),V0r)) # label(lameq_f343) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3199 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0r1 (mem(V0r1,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1r2 (mem(V1r2,arr(ty_2Epair_2Eprod(A_27b,A_27c),bool)) -> (all V2s1 (mem(V2s1,arr(A_27b,bool)) -> (all V3s2 (mem(V3s2,arr(A_27c,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(c_2Epred__set_2EGSPEC(A_27b,A_27b),f332(A_27c,A_27b,V1r2,V3s2))),V2s1)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27b,A_27c),V1r2),V3s2)) & p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r1),V2s1)) -> p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27c),ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27c,A_27b),V0r1),V1r2)),V3s2))))))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__comp) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3200 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(ap(c_2Eset__relation_2Eminimal__elements(A_27a),V0xs),V1r) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f354(A_27a,V0xs,V1r)))))))) # label(ax_thm_2Eset__relation_2Eminimal__elements__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3201 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V2y)),V0r)) | (exists V3z (mem(V3z,A_27a) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V1x),V3z)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3z),V2y)),V0r))))))))))))) # label(conj_thm_2Eset__relation_2Etc__cases__right) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3202 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Eset__relation_2Ereln__to__rel(A_27a,A_27a),V0r))) = ap(c_2Eset__relation_2Etc(A_27a),V0r))))) # label(conj_thm_2Eset__relation_2Etc__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3203 (all A_27a (ne(A_27a) -> mem(c_2Eset__relation_2Eall__choices(A_27a),arr(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eset__relation_2Eall__choices) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3204 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1tc_27 (mem(V1tc_27,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ((exists V6z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V6z),V5y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(V1tc_27,V6z),V5y)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4x),V6z)),V0r)) & mem(V6z,A_27a))) -> p(ap(ap(V1tc_27,V4x),V5y))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V3y)),V0r)) -> p(ap(ap(V1tc_27,V2x),V3y))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V7x),V8y)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) -> p(ap(ap(V1tc_27,V7x),V8y)))))))))))))) # label(conj_thm_2Eset__relation_2Etc__strongind__left) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3205 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EZIP(A_27a,A_27b),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))))) # label(mem_c_2Elist_2EZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3206 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2P (mem(V2P,arr(A_27b,bool)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (p(ap(ap(c_2Elist_2EEVERY(A_27b),V2P),V1l2)) <-> p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),f459(A_27a,A_27b,V2P)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))))))) # label(conj_thm_2Elist_2Eevery__zip__snd) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3207 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)))))))))))) # label(conj_thm_2Elist_2EMAP__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3208 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ps (mem(V0ps,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))) -> (all V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps)) = ap(c_2Elist_2ELENGTH(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps)) & p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V1p),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),V0ps)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps)))) & p(ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V1p)),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps))))))))))))) # label(conj_thm_2Elist_2EMEM__ZIP__MEM__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3209 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> ((exists V2h (mem(V2h,A_27a) & (exists V3t (p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) & mem(V3t,ty_2Elist_2Elist(A_27a)))))) | p(ap(V0P,c_2Elist_2ENIL(A_27a))) <-> (exists V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) & p(ap(V0P,V1l))))))))) # label(conj_thm_2Elist_2EEXISTS__LIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3210 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> (ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0l1) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V1l2) & ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1l2) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0l1) -> V0l1 = V1l2))))))))) # label(conj_thm_2Elist_2ELIST__EQ__MAP__PAIR) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3211 (all A_27a all A_27c all A_27b all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27c,A_27a)) -> (all V6x (mem(V6x,A_27c) -> (all V7y ap(ap(V0P,ap(V1f,V6x)),V7y) = ap(f455(A_27a,A_27c,A_27b,V0P,V1f,V6x),V7y)))))))) # label(lameq_f455) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3212 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1n1 (mem(V1n1,ty_2Enum_2Enum) -> (all V2n2 (mem(V2n2,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V0a)),V1n1)),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V1n1),V0a))),V2n2)) = ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V0a)),ap(ap(c_2Earithmetic_2E_2B,V1n1),V2n2)))))))) # label(conj_thm_2Elist_2EGENLIST__PLUS__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3213 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3e ap(ap(c_2Earithmetic_2E_2B,V2a),ap(V0f,V3e)) = ap(f427(A_27a,V0f,V2a),V3e)))))) # label(lameq_f427) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3214 (all V0l1 (mem(V0l1,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),V0l1),V1l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V0l1)),ap(c_2Elist_2ESUM,V1l2)))))) # label(conj_thm_2Elist_2ESUM__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3215 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),f400(A_27a))))) # label(conj_thm_2Elist_2EWF__LIST__PRED) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3216 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0h (mem(V0h,A_27b) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27b)) -> ap(c_2Eoption_2ESOME(A_27b),V0h) = ap(c_2Elist_2EoHD(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) & c_2Eoption_2ENONE(A_27a) = ap(c_2Elist_2EoHD(A_27a),c_2Elist_2ENIL(A_27a)))))))))) # label(conj_thm_2Elist_2EoHD__thm) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3217 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Elist_2Elist(A_27a)) -> (V0x != c_2Elist_2ENIL(A_27a) -> ap(c_2Elist_2ELAST(A_27a),V0x) = ap(c_2Elist_2EHD(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0x))))))) # label(conj_thm_2Elist_2EHD__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3218 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(c_2Elist_2ELENGTH(A_27a),V2l2))) -> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l1),V2l2))))))))))) # label(conj_thm_2Elist_2ELENGTH__LT__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3219 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l))) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Elist_2EEL(A_27a),V0n),V1l) = ap(ap(c_2Elist_2EEL(A_27a),V0n),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V1l))))))))))) # label(conj_thm_2Elist_2EEL__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3220 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))))))) # label(conj_thm_2Elist_2EFINITE__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3221 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Enum_2Enum),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(c_2Eoption_2EOPTION__MAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),ty_2Enum_2Enum),c_2Epair_2EFST(ty_2Enum_2Enum,A_27a))),ap(ap(c_2Elist_2EINDEX__FIND(A_27a),c_2Enum_2E0),ap(c_2Emin_2E_3D(A_27a),V0x))) = ap(c_2Elist_2EINDEX__OF(A_27a),V0x))))) # label(ax_thm_2Elist_2EINDEX__OF__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3222 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l)) & p(ap(V0P,V1x)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)))))))))))) # label(conj_thm_2Elist_2EEVERY__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3223 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f1 (mem(V0f1,arr(A_27a,A_27c)) -> (all V1g1 (mem(V1g1,arr(A_27b,A_27c)) -> (all V2f2 (mem(V2f2,arr(A_27a,A_27c)) -> (all V3g2 (mem(V3g2,arr(A_27b,A_27c)) -> (all V4xs (mem(V4xs,ty_2Elist_2Elist(A_27a)) -> (all V5ys (mem(V5ys,ty_2Elist_2Elist(A_27b)) -> (ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f2),V4xs) = ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V0f1),V4xs) & ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V1g1),V5ys) = ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V3g2),V5ys) <-> ap(ap(c_2Elist_2EAPPEND(A_27c),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f2),V4xs)),ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V3g2),V5ys)) = ap(ap(c_2Elist_2EAPPEND(A_27c),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V0f1),V4xs)),ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V1g1),V5ys))))))))))))))))))))) # label(conj_thm_2Elist_2EMAP__APPEND__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3224 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2ELIST__IGNORE__BIND(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))))) # label(mem_c_2Elist_2ELIST__IGNORE__BIND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3225 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,A_27a) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Elist_2EDROP(A_27a),V0n),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2xs)) = ap(ap(c_2Elist_2EDROP(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2xs)))))))))) # label(conj_thm_2Elist_2EDROP__cons) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3226 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ((exists V2pfx ((exists V3sfx (ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2pfx),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3sfx) = V1l & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2pfx))) & mem(V3sfx,ty_2Elist_2Elist(A_27a)))) & mem(V2pfx,ty_2Elist_2Elist(A_27a)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))))))))) # label(conj_thm_2Elist_2EMEM__SPLIT__APPEND__first) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3227 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1ls)))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3228 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1l_27 (mem(V1l_27,ty_2Elist_2Elist(A_27a)) -> (all V2b (mem(V2b,A_27b) -> (all V3b_27 (mem(V3b_27,A_27b) -> (all V4f (mem(V4f,arr(A_27a,arr(A_27b,A_27b))) -> (all V5f_27 (mem(V5f_27,arr(A_27a,arr(A_27b,A_27b))) -> (V0l = V1l_27 & (all V6x (mem(V6x,A_27a) -> (all V7a (mem(V7a,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l_27))) -> ap(ap(V5f_27,V6x),V7a) = ap(ap(V4f,V6x),V7a)))))) & V2b = V3b_27 -> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V4f),V2b),V0l) = ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V5f_27),V3b_27),V1l_27)))))))))))))))))) # label(conj_thm_2Elist_2EFOLDR__CONG) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3229 (all A_27a all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V3h1 (mem(V3h1,A_27a) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V6h2 f447(A_27a,V4t1,V3h1,V2R,V6h2) = ap(f448(A_27a,V4t1,V3h1,V2R),V6h2)))))))) # label(lameq_f448) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3230 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EDROP(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))) # label(conj_thm_2Elist_2EDROP__nil) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3231 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> ap(ap(c_2Elist_2Elist__size(A_27a),V0f),c_2Elist_2ENIL(A_27a)) = c_2Enum_2E0)) & (all V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2a0 (mem(V2a0,A_27a) -> (all V3a1 (mem(V3a1,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,ap(V1f,V2a0)),ap(ap(c_2Elist_2Elist__size(A_27a),V1f),V3a1))) = ap(ap(c_2Elist_2Elist__size(A_27a),V1f),ap(ap(c_2Elist_2ECONS(A_27a),V2a0),V3a1)))))))))) # label(ax_thm_2Elist_2Elist__size__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3232 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27a),V0l),f443(A_27a)) = V0l)))) # label(conj_thm_2Elist_2ESINGL__LIST__APPLY__R) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3233 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1h1 (mem(V1h1,A_27a) -> (all V2t1 (mem(V2t1,ty_2Elist_2Elist(A_27a)) -> (all V3h2 (mem(V3h2,A_27a) -> (all V4t2 (mem(V4t2,ty_2Elist_2Elist(A_27a)) -> -p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),c_2Elist_2ENIL(A_27a))) & p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2))) & (ap(c_2Elist_2ELENGTH(A_27a),V4t2) = ap(c_2Elist_2ELENGTH(A_27a),V2t1) & (p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V2t1),V4t2)) & V1h1 = V3h2 | p(ap(ap(V0R,V1h1),V3h2))) | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V2t1)),ap(c_2Elist_2ELENGTH(A_27a),V4t2))) <-> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))) & -p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))))))))))))))) # label(conj_thm_2Elist_2ESHORTLEX__THM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3234 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (all V2f (mem(V2f,arr(A_27a,arr(A_27b,A_27c))) -> ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V2f),V0l1),V1l2)))))))))))))) # label(conj_thm_2Elist_2EMAP2__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3235 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (V0l = c_2Elist_2ENIL(A_27a) <-> ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0))) & (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n)) = ap(c_2Elist_2ELENGTH(A_27a),V1l) <-> (exists V3h (mem(V3h,A_27a) & (exists V4l_27 (ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4l_27) = V1l & ap(c_2Elist_2ELENGTH(A_27a),V4l_27) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & mem(V4l_27,ty_2Elist_2Elist(A_27a))))))))))) & (all V9l (mem(V9l,ty_2Elist_2Elist(A_27a)) -> (all V10n1 (mem(V10n1,ty_2Enum_2Enum) -> (all V11n2 (mem(V11n2,ty_2Enum_2Enum) -> ((exists V12l1 ((exists V13l2 (V9l = ap(ap(c_2Elist_2EAPPEND(A_27a),V12l1),V13l2) & V11n2 = ap(c_2Elist_2ELENGTH(A_27a),V13l2) & V10n1 = ap(c_2Elist_2ELENGTH(A_27a),V12l1) & mem(V13l2,ty_2Elist_2Elist(A_27a)))) & mem(V12l1,ty_2Elist_2Elist(A_27a)))) <-> ap(ap(c_2Earithmetic_2E_2B,V10n1),V11n2) = ap(c_2Elist_2ELENGTH(A_27a),V9l)))))))) & (all V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> ((exists V7h ((exists V8l_27 (mem(V8l_27,ty_2Elist_2Elist(A_27a)) & ap(ap(c_2Elist_2ECONS(A_27a),V7h),V8l_27) = V5l & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n)) = ap(c_2Elist_2ELENGTH(A_27a),V8l_27))) & mem(V7h,A_27a))) <-> ap(c_2Elist_2ELENGTH(A_27a),V5l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))))))))) # label(conj_thm_2Elist_2ELENGTH__EQ__NUM__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3236 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> -p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l),c_2Elist_2ENIL(A_27a))))))))) # label(conj_thm_2Elist_2ESHORTLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3237 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)))))) # label(conj_thm_2Elist_2ELENGTH__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3238 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELIST__TO__SET(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(A_27a,bool))))) # label(mem_c_2Elist_2ELIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3239 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> (all V2ys (mem(V2ys,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Earithmetic_2EMIN,ap(c_2Elist_2ELENGTH(A_27a),V1xs)),ap(c_2Elist_2ELENGTH(A_27b),V2ys)) = ap(c_2Elist_2ELENGTH(A_27c),ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),V1xs),V2ys)))))))))))))) # label(conj_thm_2Elist_2ELENGTH__MAP2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3240 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2Enub(A_27a),V0l))))))) # label(conj_thm_2Elist_2Eall__distinct__nub) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3241 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Elist_2Elist(A_27a)) -> (V0x != c_2Elist_2ENIL(A_27a) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0x)))))))) # label(conj_thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3242 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EEVERY(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),bool))))) # label(mem_c_2Elist_2EEVERY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3243 (all A_27a all A_27b all V3k (mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V4h (mem(V4h,A_27b) -> (all V6p f438(A_27a,A_27b,V3k,V4h,V6p) = ap(f439(A_27a,A_27b,V3k,V4h),V6p)))))) # label(lameq_f439) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3244 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2ETAKE(A_27a),V1n),V2l)) = ap(ap(c_2Elist_2ETAKE(A_27b),V1n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l)))))))))))) # label(conj_thm_2Elist_2EMAP__TAKE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3245 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EFLAT(A_27a),ap(c_2Elist_2EREVERSE(ty_2Elist_2Elist(A_27a)),V0xs)))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0xs)))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3246 (all A_27a (ne(A_27a) -> (all V0L1 (mem(V0L1,ty_2Elist_2Elist(A_27a)) -> (all V1L2 (mem(V1L2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0L1)),V1L2) = ap(ap(c_2Elist_2EREV(A_27a),V0L1),V1L2))))))) # label(conj_thm_2Elist_2EREV__REVERSE__LEM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3247 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1ys (mem(V1ys,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),c_2Elist_2ENIL(A_27a)),V1ys)) <-> c_2Elist_2ENIL(A_27b) = V1ys))))) & (all V2P (mem(V2P,arr(A_27c,arr(A_27d,bool))) -> (all V3yys (mem(V3yys,ty_2Elist_2Elist(A_27d)) -> (all V4x (mem(V4x,A_27c) -> (all V5xs (mem(V5xs,ty_2Elist_2Elist(A_27c)) -> ((exists V6y (mem(V6y,A_27d) & (exists V7ys (mem(V7ys,ty_2Elist_2Elist(A_27d)) & ap(ap(c_2Elist_2ECONS(A_27d),V6y),V7ys) = V3yys & p(ap(ap(V2P,V4x),V6y)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V2P),V5xs),V7ys)))))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V2P),ap(ap(c_2Elist_2ECONS(A_27c),V4x),V5xs)),V3yys))))))))))) & (all V8P (mem(V8P,arr(A_27e,arr(A_27f,bool))) -> (all V9xs (mem(V9xs,ty_2Elist_2Elist(A_27e)) -> (V9xs = c_2Elist_2ENIL(A_27e) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27e,A_27f),V8P),V9xs),c_2Elist_2ENIL(A_27f)))))))) & (all V10P (mem(V10P,arr(A_27g,arr(A_27h,bool))) -> (all V11xxs (mem(V11xxs,ty_2Elist_2Elist(A_27g)) -> (all V12y (mem(V12y,A_27h) -> (all V13ys (mem(V13ys,ty_2Elist_2Elist(A_27h)) -> ((exists V14x ((exists V15xs (mem(V15xs,ty_2Elist_2Elist(A_27g)) & p(ap(ap(V10P,V14x),V12y)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27g,A_27h),V10P),V15xs),V13ys)) & V11xxs = ap(ap(c_2Elist_2ECONS(A_27g),V14x),V15xs))) & mem(V14x,A_27g))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27g,A_27h),V10P),V11xxs),ap(ap(c_2Elist_2ECONS(A_27h),V12y),V13ys)))))))))))))))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__THM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3248 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)))) <-> (exists V3m (mem(V3m,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V2n)) & V0x = ap(V1f,V3m)))))))))))) # label(conj_thm_2Elist_2EMEM__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3249 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27a))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3h (mem(V3h,A_27a) -> ap(ap(c_2Elist_2EMAP(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f)),ap(ap(ap(c_2Elist_2ELUPDATE(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V3h)),V1n),V0xs)) = ap(ap(ap(c_2Elist_2ELUPDATE(ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2ESOME(A_27b),ap(V2f,V3h))),V1n),ap(ap(c_2Elist_2EMAP(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f)),V0xs)))))))))))))) # label(conj_thm_2Elist_2ELUPDATE__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3250 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (p(ap(ap(V0R1,V4x),V5y)) -> p(ap(ap(V1R2,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V2l1),V3l2)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1R2),V2l1),V3l2)))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3251 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EDROP(A_27a),c_2Enum_2E0),V0l) = V0l)))) # label(conj_thm_2Elist_2EDROP__0) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3252 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EUNIQUE(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),bool))))) # label(mem_c_2Elist_2EUNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3253 (all A_27a (ne(A_27a) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z)))))))) & (all V0x (mem(V0x,A_27a) -> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) = V0x)))) # label(conj_thm_2Elist_2ELAST__CONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3254 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((exists V2h (mem(V2h,A_27a) & (exists V3l_27 (mem(V3l_27,ty_2Elist_2Elist(A_27a)) & ap(c_2Elist_2ELENGTH(A_27a),V3l_27) = V1n & V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3l_27))))) <-> ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Elist_2ELENGTH__CONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3255 (all A0 (ne(A0) -> ne(ty_2Elist_2Elist(A0)))) # label(ne_ty_2Elist_2Elist) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3256 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))) # label(conj_thm_2Elist_2ETAKE__nil) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3257 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EOPT__MMAP(A_27a,A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(ty_2Elist_2Elist(A_27b),ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27a))))))))) # label(mem_c_2Elist_2EOPT__MMAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3258 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EAPPEND(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EAPPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3259 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0t2 (mem(V0t2,ty_2Elist_2Elist(A_27c)) -> (all V1t1 (mem(V1t1,ty_2Elist_2Elist(A_27b)) -> (all V2h2 (mem(V2h2,A_27c) -> (all V3h1 (mem(V3h1,A_27b) -> (all V4f (mem(V4f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V4f),ap(ap(c_2Elist_2ECONS(A_27b),V3h1),V1t1)),ap(ap(c_2Elist_2ECONS(A_27c),V2h2),V0t2)) = ap(ap(c_2Elist_2ECONS(A_27a),ap(ap(V4f,V3h1),V2h2)),ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V4f),V1t1),V0t2)))))))))))) & (all V5y (mem(V5y,ty_2Elist_2Elist(A_27c)) -> (all V6f (mem(V6f,arr(A_27b,arr(A_27c,A_27a))) -> c_2Elist_2ENIL(A_27a) = ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V6f),c_2Elist_2ENIL(A_27b)),V5y))))) & (all V7v5 (mem(V7v5,ty_2Elist_2Elist(A_27b)) -> (all V8v4 (mem(V8v4,A_27b) -> (all V9f (mem(V9f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V9f),ap(ap(c_2Elist_2ECONS(A_27b),V8v4),V7v5)),c_2Elist_2ENIL(A_27c)) = c_2Elist_2ENIL(A_27a))))))))))))) # label(conj_thm_2Elist_2EMAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3260 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> ((exists V4l3 (mem(V4l3,ty_2Elist_2Elist(A_27a)) & (exists V5l4 (mem(V5l4,ty_2Elist_2Elist(A_27a)) & V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l3),V5l4) & ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V5l4) = V3l2 & ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V4l3) = V2l1)))) <-> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2)))))))))))) # label(conj_thm_2Elist_2EFILTER__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3261 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f466(A_27b,A_27a) = c_2Elist_2Elist__CASE(A_27a,A_27b))))) # label(conj_thm_2Elist_2Elazy__list__case__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3262 (all A_27a (ne(A_27a) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2) <-> V2l1 = c_2Elist_2ENIL(A_27a) & c_2Elist_2ENIL(A_27a) = V3l2))))) & (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (V0l1 = c_2Elist_2ENIL(A_27a) & V1l2 = c_2Elist_2ENIL(A_27a) <-> c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)))))))) # label(conj_thm_2Elist_2EAPPEND__eq__NIL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3263 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),f391(A_27b,A_27a,V1f,V0P)),V2l)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V2l)))))))))))))) # label(conj_thm_2Elist_2EEVERY__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3264 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2f1 (mem(V2f1,arr(A_27a,A_27c)) -> (all V3f2 (mem(V3f2,arr(A_27b,A_27d)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) -> ap(c_2Elist_2EZIP(A_27a,A_27d),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27d)),V0l1),ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V3f2),V1l2))) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27d)),f414(A_27d,A_27a,A_27b,V3f2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) & ap(c_2Elist_2EZIP(A_27c,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f1),V0l1)),V1l2)) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27b)),f413(A_27c,A_27a,A_27b,V2f1)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))))))))))) # label(conj_thm_2Elist_2EZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3265 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27b))) -> (all V2a (mem(V2a,A_27b) -> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),V0s),V2a) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),ap(c_2Ecombin_2EC(A_27a,A_27b,A_27b),V1f)),V2a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s))))))))))))) # label(conj_thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3266 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V1f2 (mem(V1f2,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V2x1 (mem(V2x1,ty_2Elist_2Elist(A_27a)) -> (all V3x2 (mem(V3x2,ty_2Elist_2Elist(A_27a)) -> ((all V4a (mem(V4a,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3x2))) -> ap(V1f2,V4a) = ap(V0f1,V4a)))) & V2x1 = V3x2 -> ap(ap(c_2Elist_2EOPT__MMAP(A_27b,A_27a),V1f2),V3x2) = ap(ap(c_2Elist_2EOPT__MMAP(A_27b,A_27a),V0f1),V2x1)))))))))))))) # label(conj_thm_2Elist_2EOPT__MMAP__cong) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3267 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),V0h),ap(c_2Elist_2ELAST(A_27a),V1t)) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))))) # label(ax_thm_2Elist_2ELAST__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3268 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (-p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l))))))))) # label(conj_thm_2Elist_2ENOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3269 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(c_2Elist_2EREVERSE(A_27a),V1l1)),ap(c_2Elist_2EREVERSE(A_27b),V2l2)))))))))))))) # label(conj_thm_2Elist_2EEVERY2__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3270 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V3s f430(A_27b,A_27a,V0f,V3s) = ap(f431(A_27a,A_27b,V0f),V3s)))) # label(lameq_f431) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3271 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))) & (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EFILTER(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(V1P,V2h)),ap(ap(c_2Elist_2ECONS(A_27a),V2h),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V3t))),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V3t)))))))))) # label(ax_thm_2Elist_2EFILTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3272 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),A_27a))))) # label(mem_c_2Elist_2EEL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3273 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2l3 (mem(V2l3,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V2l3)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)),V2l3))))))))) # label(conj_thm_2Elist_2EAPPEND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3274 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1h1 (mem(V1h1,A_27a) -> (all V2h2 (mem(V2h2,A_27b) -> (all V3t1 (mem(V3t1,ty_2Elist_2Elist(A_27a)) -> (all V4t2 (mem(V4t2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(V0R,V1h1),V2h2)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V3t1),V4t2)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V4t2)))))))))))) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))))))))) # label(conj_thm_2Elist_2ELIST__REL__rules) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3275 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EINDEX__OF(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Enum_2Enum)))))) # label(mem_c_2Elist_2EINDEX__OF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3276 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls))),ap(c_2Elist_2ELENGTH(A_27a),V0ls))))))) # label(conj_thm_2Elist_2ECARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3277 (all A_27c all A_27a all A_27b all V2f1 (mem(V2f1,arr(A_27a,A_27c)) -> (all V4p ap(f413(A_27c,A_27a,A_27b,V2f1),V4p) = ap(ap(c_2Epair_2E_2C(A_27c,A_27b),ap(V2f1,ap(c_2Epair_2EFST(A_27a,A_27b),V4p))),ap(c_2Epair_2ESND(A_27a,A_27b),V4p))))) # label(lameq_f413) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3278 (all A_27a (ne(A_27a) -> (all V0L (mem(V0L,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ELEN(A_27a),V0L),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V0L)),V1n))))))) # label(conj_thm_2Elist_2ELEN__LENGTH__LEM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3279 (all A_27b all A_27a all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V3L1 ap(f412(A_27b,A_27a,V0x,V1y),V3L1) = f411(A_27a,A_27b,V0x,V3L1,V1y)))))) # label(lameq_f412) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3280 (all A_27a (ne(A_27a) -> c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2ETL(A_27a),c_2Elist_2ENIL(A_27a)) & (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> V1t = ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))))) # label(ax_thm_2Elist_2ETL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3281 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R)))))))) # label(conj_thm_2Elist_2ESHORTLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3282 (all A_27b all A_27a all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3x ap(f460(A_27b,A_27a,V2P),V3x) = ap(V2P,ap(c_2Epair_2EFST(A_27a,A_27b),V3x))))) # label(lameq_f460) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3283 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0ls)))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__DROP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3284 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))) & ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27b,A_27a)),ap(c_2Elist_2EZIP(A_27b,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),V1l2),V0l1))))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__ZIP__SWAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3285 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> ((exists V2n (mem(V2n,ty_2Enum_2Enum) & V1x = ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l))))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))))))))) # label(conj_thm_2Elist_2EMEM__EL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3286 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),V1n)) -> ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0l) = c_2Elist_2ENIL(A_27a)))))))) # label(conj_thm_2Elist_2EDROP__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3287 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1LIST__REL_27 (mem(V1LIST__REL_27,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool))) -> ((all V2h1 (mem(V2h1,A_27a) -> (all V3h2 (mem(V3h2,A_27b) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V5t2 (mem(V5t2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(V0R,V2h1),V3h2)) & p(ap(ap(V1LIST__REL_27,V4t1),V5t2)) -> p(ap(ap(V1LIST__REL_27,ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27b),V3h2),V5t2)))))))))))) & p(ap(ap(V1LIST__REL_27,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))) -> (all V6a0 (mem(V6a0,ty_2Elist_2Elist(A_27a)) -> (all V7a1 (mem(V7a1,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V6a0),V7a1)) -> p(ap(ap(V1LIST__REL_27,V6a0),V7a1)))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__ind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3288 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0R)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),V2l2)))) & ap(c_2Elist_2ELENGTH(A_27b),V2l2) = ap(c_2Elist_2ELENGTH(A_27a),V1l1) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__EVERY__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3289 (all A_27a (ne(A_27a) -> (all V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) -> (all V6n1 (mem(V6n1,ty_2Enum_2Enum) -> (all V7n2 (mem(V7n2,ty_2Enum_2Enum) -> ((exists V8l1 ((exists V9l2 (mem(V9l2,ty_2Elist_2Elist(A_27a)) & ap(c_2Elist_2ELENGTH(A_27a),V8l1) = V6n1 & V7n2 = ap(c_2Elist_2ELENGTH(A_27a),V9l2) & ap(ap(c_2Elist_2EAPPEND(A_27a),V8l1),V9l2) = V5l)) & mem(V8l1,ty_2Elist_2Elist(A_27a)))) <-> ap(ap(c_2Earithmetic_2E_2B,V6n1),V7n2) = ap(c_2Elist_2ELENGTH(A_27a),V5l)))))))) & (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((exists V3h ((exists V4l_27 (ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4l_27) = V1l & V2n = ap(c_2Elist_2ELENGTH(A_27a),V4l_27) & mem(V4l_27,ty_2Elist_2Elist(A_27a)))) & mem(V3h,A_27a))) <-> ap(c_2Enum_2ESUC,V2n) = ap(c_2Elist_2ELENGTH(A_27a),V1l)))))) & (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 <-> V0l = c_2Elist_2ENIL(A_27a)))))) # label(conj_thm_2Elist_2ELENGTH__EQ__NUM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3290 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,A_27b) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V2l),V0b),V1f) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Elist_2ENULL(A_27a),V2l)),V0b),ap(ap(V1f,ap(c_2Elist_2EHD(A_27a),V2l)),ap(c_2Elist_2ETL(A_27a),V2l))))))))))))) # label(conj_thm_2Elist_2Elist__case__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3291 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1e (mem(V1e,A_27b) -> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V0f),V1e),c_2Elist_2ENIL(A_27a)) = V1e)))) & (all V2f (mem(V2f,arr(A_27a,arr(A_27b,A_27b))) -> (all V3e (mem(V3e,A_27b) -> (all V4x (mem(V4x,A_27a) -> (all V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V2f),V3e),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5l)) = ap(ap(V2f,V4x),ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V2f),V3e),V5l)))))))))))))) # label(ax_thm_2Elist_2EFOLDR) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3292 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EoEL(A_27a),V0n),ap(ap(c_2Elist_2EDROP(A_27a),V1m),V2xs)) = ap(ap(c_2Elist_2EoEL(A_27a),ap(ap(c_2Earithmetic_2E_2B,V1m),V0n)),V2xs))))))))) # label(conj_thm_2Elist_2EoEL__DROP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3293 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V4a ap(f402(A_27b,A_27a,V0P,V1Q),V4a) = f401(A_27a,A_27b,V0P,V4a,V1Q)))))) # label(lameq_f402) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3294 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EPAD__RIGHT(A_27a),V0c),V1n),V2s) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2s),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Enum_2Enum),V0c)),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2s)))))))))))) # label(ax_thm_2Elist_2EPAD__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3295 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool))) -> (all V1k (mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Enum_2Enum,A_27a),ap(c_2Ewhile_2EOLEAST,f441(A_27b,V0P,V2l))),ap(ap(V1k,V2l),c_2Elist_2ENIL(A_27b))),f442(A_27b,A_27a,V1k,V2l)) = ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V0P),V1k),V2l))))))))))) # label(conj_thm_2Elist_2EsplitAtPki__EQN) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3296 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> ((exists V2n ((exists V3f (p(ap(V0P,ap(ap(c_2Elist_2EGENLIST(A_27a),V3f),V2n))) & mem(V3f,arr(ty_2Enum_2Enum,A_27a)))) & mem(V2n,ty_2Enum_2Enum))) <-> (exists V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) & p(ap(V0P,V1ls))))))))) # label(conj_thm_2Elist_2Eexists__list__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3297 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1xs))) = ap(c_2Elist_2ELENGTH(A_27a),V1xs))))))) # label(conj_thm_2Elist_2ELENGTH__FRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3298 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),bool)))) -> ((all V1f (mem(V1f,arr(A_27b,arr(A_27c,A_27a))) -> (all V2h1 (mem(V2h1,A_27b) -> (all V3t1 (mem(V3t1,ty_2Elist_2Elist(A_27b)) -> (all V4h2 (mem(V4h2,A_27c) -> (all V5t2 (mem(V5t2,ty_2Elist_2Elist(A_27c)) -> (p(ap(ap(ap(V0P,V1f),V3t1),V5t2)) -> p(ap(ap(ap(V0P,V1f),ap(ap(c_2Elist_2ECONS(A_27b),V2h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27c),V4h2),V5t2)))))))))))))) & (all V6f (mem(V6f,arr(A_27b,arr(A_27c,A_27a))) -> (all V7y (mem(V7y,ty_2Elist_2Elist(A_27c)) -> p(ap(ap(ap(V0P,V6f),c_2Elist_2ENIL(A_27b)),V7y)))))) & (all V8f (mem(V8f,arr(A_27b,arr(A_27c,A_27a))) -> (all V9v4 (mem(V9v4,A_27b) -> (all V10v5 (mem(V10v5,ty_2Elist_2Elist(A_27b)) -> p(ap(ap(ap(V0P,V8f),ap(ap(c_2Elist_2ECONS(A_27b),V9v4),V10v5)),c_2Elist_2ENIL(A_27c))))))))) -> (all V11v (mem(V11v,arr(A_27b,arr(A_27c,A_27a))) -> (all V12v1 (mem(V12v1,ty_2Elist_2Elist(A_27b)) -> (all V13v2 (mem(V13v2,ty_2Elist_2Elist(A_27c)) -> p(ap(ap(ap(V0P,V11v),V12v1),V13v2))))))))))))))))) # label(conj_thm_2Elist_2EMAP2__ind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3299 (all A_27a all V6h2 (mem(V6h2,A_27a) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V3h1 (mem(V3h1,A_27a) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V7t2 ap(f445(A_27a,V6h2,V2R,V3h1,V4t1),V7t2) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V4t1)),ap(c_2Elist_2ELENGTH(A_27a),V7t2))),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Elist_2ELENGTH(A_27a),V4t1)),ap(c_2Elist_2ELENGTH(A_27a),V7t2))),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(V2R,V3h1),V6h2)),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(A_27a),V3h1),V6h2)),ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V2R),V4t1),V7t2)),c_2Ebool_2EF))),c_2Ebool_2EF))))))))))) # label(lameq_f445) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 3300 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(c_2Elist_2EdropWhile(A_27a),V0P) = ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(c_2Ecombin_2EC(A_27a,ty_2Enum_2Enum,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(ty_2Enum_2Enum,bool),bool),c_2Ecombin_2EK(bool,ty_2Enum_2Enum)),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)))),ap(c_2Ecombin_2EK(arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))))))) # label(conj_thm_2Elist_2EdropWhile__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3301 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1e (mem(V1e,A_27a) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (all V3m1 (mem(V3m1,ty_2Elist_2Elist(A_27a)) -> (all V4m2 (mem(V4m2,ty_2Elist_2Elist(A_27a)) -> (ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V2l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V3m1),V4m2) <-> (exists V6l (mem(V6l,ty_2Elist_2Elist(A_27a)) & V4m2 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V6l),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V2l2) & ap(ap(c_2Elist_2EAPPEND(A_27a),V3m1),V6l) = V0l1)) | (exists V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) & V2l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V5l),V4m2) & V3m1 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V5l)))))))))))))))) # label(conj_thm_2Elist_2EAPPEND__EQ__APPEND__MID) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3302 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1L (mem(V1L,ty_2Elist_2Elist(A_27a)) -> ((exists V2L1 (mem(V2L1,ty_2Elist_2Elist(A_27a)) & (exists V3L2 (mem(V3L2,ty_2Elist_2Elist(A_27a)) & ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2L1),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3L2) = V1L & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3L2))) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2L1))))))) <-> p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L))))))))) # label(ax_thm_2Elist_2EUNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3303 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V2y),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(V0R,V1x),V3z))))))))) -> (all V4x (mem(V4x,ty_2Elist_2Elist(A_27a)) -> (all V5y (mem(V5y,ty_2Elist_2Elist(A_27a)) -> (all V6z (mem(V6z,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V4x),V5y)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V5y),V6z)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V4x),V6z)))))))))))))) # label(conj_thm_2Elist_2EEVERY2__trans) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3304 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EoEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a)))))) # label(mem_c_2Elist_2EoEL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3305 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2s (mem(V2s,arr(A_27b,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27b),V2s),ap(c_2Epred__set_2EBIGUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,arr(A_27b,bool)),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)))) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,arr(A_27b,bool)),f431(A_27a,A_27b,V0f)),V2s),V1ls))))))))))) # label(conj_thm_2Elist_2EFOLDL__UNION__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3306 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27a) -> (all V3lr (mem(V3lr,ty_2Elist_2Elist(A_27a)) -> ((exists V4l1 ((exists V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27a)) & ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V4l1) = c_2Elist_2ENIL(A_27a) & ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V5l2) = V3lr & p(ap(V0P,V2h)) & V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),ap(ap(c_2Elist_2ECONS(A_27a),V2h),c_2Elist_2ENIL(A_27a)))),V5l2))) & mem(V4l1,ty_2Elist_2Elist(A_27a)))) <-> ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3lr) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))))))))))) # label(conj_thm_2Elist_2EFILTER__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3307 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R)))))))) # label(conj_thm_2Elist_2ELLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3308 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2f (mem(V2f,arr(A_27a,A_27c)) -> (all V3g (mem(V3g,arr(A_27b,A_27d)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) -> V0l1 = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) & ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = V1l2 & ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V3g),V1l2) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27d),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27b),V3g),c_2Epair_2ESND(A_27a,A_27b))),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) & ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a),V2f),c_2Epair_2EFST(A_27a,A_27b))),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f),V0l1)))))))))))))))))) # label(conj_thm_2Elist_2EMAP__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3309 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V1f2 (mem(V1f2,arr(A_27c,A_27b)) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27c)) -> (ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f1),V2l1) = ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V1f2),V3l2) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27c),f417(A_27c,A_27b,A_27a,V0f1,V1f2)),V2l1),V3l2)) & ap(c_2Elist_2ELENGTH(A_27c),V3l2) = ap(c_2Elist_2ELENGTH(A_27a),V2l1)))))))))))))))) # label(conj_thm_2Elist_2EMAP__EQ__EVERY2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3310 (all A_27a all V1h k(ty_2Elist_2Elist(A_27a),ap(c_2Eoption_2ESOME(A_27a),V1h)) = ap(f463(A_27a),V1h)) # label(lameq_f463) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3311 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,ty_2Elist_2Elist(A_27a)) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,ty_2Elist_2Elist(A_27a)) -> (V3b = V1y & V2a = V0x <-> ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1y) = ap(ap(c_2Elist_2ESNOC(A_27a),V2a),V3b)))))))))))) # label(conj_thm_2Elist_2ESNOC__11) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3312 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V1t)))))) # label(conj_thm_2Elist_2ETL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3313 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (c_2Elist_2ENIL(A_27a) = V0l <-> c_2Elist_2ENIL(A_27b) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) & (c_2Elist_2ENIL(A_27a) = V0l <-> c_2Elist_2ENIL(A_27b) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)))))))))) # label(conj_thm_2Elist_2EMAP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3314 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l)) <-> (all V1n1 (mem(V1n1,ty_2Enum_2Enum) -> (all V2n2 (mem(V2n2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n2),ap(c_2Elist_2ELENGTH(A_27a),V0l))) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n1),ap(c_2Elist_2ELENGTH(A_27a),V0l))) -> (ap(ap(c_2Elist_2EEL(A_27a),V1n1),V0l) = ap(ap(c_2Elist_2EEL(A_27a),V2n2),V0l) <-> V1n1 = V2n2))))))))))) # label(conj_thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3315 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (p(ap(ap(V0R1,V4x),V5y)) -> p(ap(ap(V1R2,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V2l1),V3l2)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1R2),V2l1),V3l2)))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__mono) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3316 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0x1 (mem(V0x1,A_27a) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2x2 (mem(V2x2,A_27b) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V0x1),V1l1)),ap(ap(c_2Elist_2ECONS(A_27b),V2x2),V3l2))) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x1),V2x2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),V3l2))))))))))) & ap(c_2Elist_2EZIP(A_27c,A_27d),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27d)),c_2Elist_2ENIL(A_27c)),c_2Elist_2ENIL(A_27d))) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27c,A_27d)))))))))) # label(conj_thm_2Elist_2EZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3317 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1)) & p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l2)) & (all V2e (mem(V2e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3318 (all A_27a all V2b (mem(V2b,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V3t ap(V0f,ap(ap(c_2Earithmetic_2E_2B,V3t),V2b)) = ap(f425(A_27a,V2b,V0f),V3t)))))) # label(lameq_f425) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3319 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ((all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) -> ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V1x)),V0l)))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3320 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1LIST__REL_27 (mem(V1LIST__REL_27,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool))) -> ((all V2h1 (mem(V2h1,A_27a) -> (all V3h2 (mem(V3h2,A_27b) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V5t2 (mem(V5t2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V4t1),V5t2)) & p(ap(ap(V1LIST__REL_27,V4t1),V5t2)) & p(ap(ap(V0R,V2h1),V3h2)) -> p(ap(ap(V1LIST__REL_27,ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27b),V3h2),V5t2)))))))))))) & p(ap(ap(V1LIST__REL_27,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))) -> (all V6a0 (mem(V6a0,ty_2Elist_2Elist(A_27a)) -> (all V7a1 (mem(V7a1,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V6a0),V7a1)) -> p(ap(ap(V1LIST__REL_27,V6a0),V7a1)))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__strongind) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3321 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls))) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1ls))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3322 (all A_27a all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (all V4l ap(f394(A_27a,V0P),V4l) = ap(c_2Ebool_2E_21(A_27a),f393(A_27a,V4l,V0P))))) # label(lameq_f394) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3323 (all A_27a all A_27b all V1f (mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b))) -> (all V3x f435(A_27b,A_27a,V3x,V1f) = ap(f436(A_27a,A_27b,V1f),V3x)))) # label(lameq_f436) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3324 (all A_27a (ne(A_27a) -> (all V0a1 (mem(V0a1,ty_2Elist_2Elist(A_27a)) -> (all V1a0 (mem(V1a0,A_27a) -> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1))))))) # label(conj_thm_2Elist_2ENOT__CONS__NIL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3325 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,A_27b) -> (all V2ls (mem(V2ls,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0) = c_2Elist_2EHD(A_27a) & ap(ap(c_2Elist_2EEL(A_27b),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Elist_2ECONS(A_27b),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27b),V0n),V2ls))))))))))) # label(conj_thm_2Elist_2EEL__restricted) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3326 (all A_27a all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V3h1 (mem(V3h1,A_27a) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V6h2 (mem(V6h2,A_27a) -> (all V7t2 ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(V2R,V3h1),V6h2)),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(A_27a),V3h1),V6h2)),ap(ap(ap(c_2Elist_2ELLEX(A_27a),V2R),V4t1),V7t2)),c_2Ebool_2EF)) = ap(f447(A_27a,V4t1,V3h1,V2R,V6h2),V7t2)))))))))) # label(lameq_f447) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3327 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27b),ap(V3f,V0x)),V1n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f),V2l)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2l)))))))))))))) # label(conj_thm_2Elist_2ELUPDATE__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3328 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(c_2Elist_2EREVERSE(A_27a),V1l)) = ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)))))))) # label(conj_thm_2Elist_2EREVERSE__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3329 (all A_27a all V1x ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) = ap(f443(A_27a),V1x)) # label(lameq_f443) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3330 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3331 (all A_27b all A_27a all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27b)) -> (all V3x ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V3x),V0l)),ap(V1f,V3x)) = ap(f426(A_27b,A_27a,V0l,V1f),V3x)))))) # label(lameq_f426) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3332 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ETL(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2ETL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3333 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0ls)) = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(arr(A_27a,bool)),ap(ap(c_2Elist_2EMAP(ty_2Elist_2Elist(A_27a),arr(A_27a,bool)),c_2Elist_2ELIST__TO__SET(A_27a)),V0ls))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__FLAT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3334 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EREVERSE(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2EREVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3335 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (V0l1 = c_2Elist_2ENIL(A_27a) & V1l2 = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t) | (exists V4lt (mem(V4lt,ty_2Elist_2Elist(A_27a)) & ap(ap(c_2Elist_2ECONS(A_27a),V2h),V4lt) = V0l1 & ap(ap(c_2Elist_2EAPPEND(A_27a),V4lt),V1l2) = V3t)) <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))))))))))) # label(conj_thm_2Elist_2EAPPEND__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3336 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l) <-> V0l = c_2Elist_2ENIL(A_27a)) & (c_2Elist_2ENIL(A_27a) = V0l <-> c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))))) # label(conj_thm_2Elist_2ELIST__TO__SET__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3337 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27a,A_27b))) -> (all V1e (mem(V1e,A_27b) -> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),c_2Elist_2ENIL(A_27a)) = V1e)))) & (all V2f (mem(V2f,arr(A_27b,arr(A_27a,A_27b))) -> (all V3e (mem(V3e,A_27b) -> (all V4x (mem(V4x,A_27a) -> (all V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V2f),V3e),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5l)) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V2f),ap(ap(V2f,V3e),V4x)),V5l))))))))))))) # label(ax_thm_2Elist_2EFOLDL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3338 (all A_27a all V0L1 (mem(V0L1,ty_2Elist_2Elist(A_27a)) -> (all V1L2 ap(f399(A_27a,V0L1),V1L2) = ap(c_2Ebool_2E_3F(A_27a),f398(A_27a,V0L1,V1L2))))) # label(lameq_f399) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3339 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ESNOC(A_27a),V1x),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l2)))))))))) # label(conj_thm_2Elist_2EAPPEND__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3340 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Elist_2Elist(A_27a)) -> (all V1y (mem(V1y,A_27a) -> (all V2ys (mem(V2ys,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V0x),ap(ap(c_2Elist_2ECONS(A_27a),V1y),V2ys))) <-> c_2Elist_2ENIL(A_27a) = V0x | (exists V3xs (p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V3xs),V2ys)) & ap(ap(c_2Elist_2ECONS(A_27a),V1y),V3xs) = V0x & mem(V3xs,ty_2Elist_2Elist(A_27a))))))))))))) # label(conj_thm_2Elist_2EisPREFIX__CONSR) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3341 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2ETAKE(A_27a),c_2Enum_2E0),V0l))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4h (mem(V4h,A_27c) -> (all V5t (mem(V5t,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2Elist_2ECONS(A_27c),V4h),ap(ap(c_2Elist_2ETAKE(A_27c),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V5t)) = ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(ap(c_2Elist_2ECONS(A_27c),V4h),V5t)))))))) & (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7h (mem(V7h,A_27c) -> (all V8t (mem(V8t,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2Elist_2ECONS(A_27c),V7h),ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),V8t)) = ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),ap(ap(c_2Elist_2ECONS(A_27c),V7h),V8t)))))))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ETAKE(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b))) & (all V1n (mem(V1n,ty_2Enum_2Enum) -> c_2Elist_2ENIL(A_27b) = ap(ap(c_2Elist_2ETAKE(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),c_2Elist_2ENIL(A_27b)))))))))) # label(conj_thm_2Elist_2ETAKE__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3342 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27a))))))))))) # label(mem_c_2Elist_2EMAP2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3343 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (p(ap(V0P,c_2Elist_2ENIL(A_27a))) & (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> (p(ap(V0P,V1t)) -> (all V2h (mem(V2h,A_27a) -> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t)))))))) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,V3l))))))))) # label(conj_thm_2Elist_2Elist__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3344 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls))),ap(c_2Elist_2ELENGTH(A_27a),V1ls))))))))) # label(conj_thm_2Elist_2ELENGTH__dropWhile__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3345 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> ((all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> (p(ap(V0P,V1t)) -> (all V2h (mem(V2h,A_27a) -> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t)))))))) & p(ap(V0P,c_2Elist_2ENIL(A_27a))) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,V3l))))))))) # label(conj_thm_2Elist_2Elist__induction) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3346 (all A_27a (ne(A_27a) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4h (mem(V4h,A_27a) -> (all V5t (mem(V5t,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(V3P,V4h)),ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),V2i),V4h))),ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),ap(c_2Enum_2ESUC,V2i)),V3P),V5t)) = ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),V2i),V3P),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t)))))))))) & (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),V0i),V1P),c_2Elist_2ENIL(A_27a)) = c_2Eoption_2ENONE(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))))))) # label(ax_thm_2Elist_2EINDEX__FIND__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3347 (all A_27a (ne(A_27a) -> ap(c_2Elist_2ESET__TO__LIST(A_27a),c_2Epred__set_2EEMPTY(A_27a)) = c_2Elist_2ENIL(A_27a))) # label(conj_thm_2Elist_2ESET__TO__LIST__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3348 (all A_27b all A_27a all A_27c all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V4x (mem(V4x,A_27a) -> (all V1f2 (mem(V1f2,arr(A_27c,A_27b)) -> (all V5y ap(f416(A_27b,A_27a,A_27c,V0f1,V4x,V1f2),V5y) = ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f1,V4x)),ap(V1f2,V5y))))))))) # label(lameq_f416) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3349 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V1ls)) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,ty_2Enum_2Enum),f428(A_27a,V0f)),c_2Enum_2E0),V1ls))))))) # label(conj_thm_2Elist_2ESUM__MAP__FOLDL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3350 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27a),V1l),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))))))))) # label(conj_thm_2Elist_2ESNOC__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3351 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V3x ap(f390(A_27a,V0P,V1Q),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V3x)),ap(V1Q,V3x))))))) # label(lameq_f390) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3352 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ESNOC(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2ESNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3353 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V3x ap(f453(A_27a,V0f,V1g),V3x) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V3x)),ap(V1g,V3x))))))) # label(lameq_f453) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3354 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EGENLIST(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EGENLIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3355 (all A_27c all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool)))) -> (all V4x (mem(V4x,A_27a) -> (all V3s (mem(V3s,arr(A_27c,bool)) -> (all V5y ap(f432(A_27c,A_27a,A_27b,V0f,V4x,V3s),V5y) = ap(ap(c_2Epred__set_2EUNION(A_27c),V3s),ap(ap(V0f,V4x),V5y))))))))) # label(lameq_f432) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3356 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls) = ap(ap(c_2Elist_2EGENLIST(A_27b),f454(A_27a,A_27b,V1ls,V0f)),ap(c_2Elist_2ELENGTH(A_27a),V1ls)))))))))) # label(conj_thm_2Elist_2EGENLIST__EL__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3357 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)),V2l) = ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V0f),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1g),V2l)))))))))))))) # label(conj_thm_2Elist_2EMAP__MAP__o) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3358 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) -> ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2) = ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))) # label(conj_thm_2Elist_2EUNZIP__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3359 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(c_2Epred__set_2ECARD(A_27a),V0s) = ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s))))))) # label(conj_thm_2Elist_2ESET__TO__LIST__CARD) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3360 (all A_27a (ne(A_27a) -> (all V3l1 (mem(V3l1,ty_2Elist_2Elist(A_27a)) -> (all V4l2 (mem(V4l2,ty_2Elist_2Elist(A_27a)) -> (all V5l3 (mem(V5l3,ty_2Elist_2Elist(A_27a)) -> (V4l2 = V5l3 <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V5l3),V3l1) = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l2),V3l1)))))))) & (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2l3 (mem(V2l3,ty_2Elist_2Elist(A_27a)) -> (V2l3 = V1l2 <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l3) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)))))))))) # label(conj_thm_2Elist_2EAPPEND__11) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3361 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2EREVERSE(A_27a),V1l2) = V0l1 <-> V1l2 = ap(c_2Elist_2EREVERSE(A_27a),V0l1)))))))) # label(conj_thm_2Elist_2ESWAP__REVERSE__SYM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3362 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3i (mem(V3i,ty_2Enum_2Enum) -> ((exists V4j (mem(V4j,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V4j),ap(c_2Elist_2ELENGTH(A_27a),V0l))) & V4j != V3i & ap(ap(c_2Elist_2EEL(A_27a),V4j),V0l) = V1x)) | p(ap(ap(c_2Eprim__rec_2E_3C,V3i),ap(c_2Elist_2ELENGTH(A_27a),V0l))) & V2y = V1x <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2y),V3i),V0l))))))))))))))) # label(conj_thm_2Elist_2EMEM__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3363 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(arr(A_27a,bool),bool)) -> ((all V1s (mem(V1s,arr(A_27a,bool)) -> ((p(ap(c_2Epred__set_2EFINITE(A_27a),V1s)) & V1s != c_2Epred__set_2EEMPTY(A_27a) -> p(ap(V0P,ap(c_2Epred__set_2EREST(A_27a),V1s)))) -> p(ap(V0P,V1s))))) -> (all V2v (mem(V2v,arr(A_27a,bool)) -> p(ap(V0P,V2v))))))))) # label(conj_thm_2Elist_2ESET__TO__LIST__IND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3364 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (p(ap(V0P,c_2Elist_2ENIL(A_27a))) & (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))))))) <-> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,V1l))))))))) # label(conj_thm_2Elist_2EFORALL__LIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3365 (all A_27a (ne(A_27a) -> (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3x)) <-> V1h = V3x | p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),V2t),V3x))))))))) & (all V0x (mem(V0x,A_27a) -> (p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)),V0x)) <-> $F))))) # label(ax_thm_2Elist_2ELIST__TO__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3366 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27b))) & (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V1f,V2h)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V3t)))))))))))) # label(ax_thm_2Elist_2EMAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3367 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1x),V2y)) <-> V2y = V1x))))))) & (all V3R (mem(V3R,arr(A_27a,arr(A_27a,bool))) -> (all V4h (mem(V4h,A_27a) -> (all V5t (mem(V5t,ty_2Elist_2Elist(A_27a)) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V3R),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t)),V6x),V7y)) <-> (exists V8z (mem(V8z,A_27a) & p(ap(ap(V3R,V6x),V8z)) & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V3R),V5t),V8z),V7y)))) & V4h = V6x))))))))))))) # label(ax_thm_2Elist_2ELRC__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3368 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1)) & ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3369 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,ty_2Elist_2Elist(A_27c))) -> ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Enum_2Enum,ty_2Elist_2Elist(A_27c)),c_2Elist_2ELENGTH(A_27c)),V0f) = ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Enum_2Enum,ty_2Elist_2Elist(A_27c)),c_2Elist_2ELENGTH(A_27c)),ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27c)),c_2Elist_2EREVERSE(A_27c)),V0f)) & ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum,ty_2Elist_2Elist(A_27a)),c_2Elist_2ELENGTH(A_27a)),c_2Elist_2EREVERSE(A_27a)) = c_2Elist_2ELENGTH(A_27a))))))))) # label(conj_thm_2Elist_2ELENGTH__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3370 (all A_27a (ne(A_27a) -> (all V0h1 (mem(V0h1,A_27a) -> (all V1h2 (mem(V1h2,A_27a) -> (V0h1 = V1h2 -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> (V3l2 = V2l1 -> ap(ap(c_2Elist_2ECONS(A_27a),V0h1),V2l1) = ap(ap(c_2Elist_2ECONS(A_27a),V1h2),V3l2))))))))))))) # label(conj_thm_2Elist_2EEQ__LIST) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3371 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) != V0ls -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Elist_2ELENGTH(A_27a),V0ls))),V0ls) = ap(c_2Elist_2ELAST(A_27a),V0ls)))))) # label(conj_thm_2Elist_2ELAST__EL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3372 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = V1l)))))) # label(conj_thm_2Elist_2EFRONT__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3373 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EPAD__RIGHT(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) # label(mem_c_2Elist_2EPAD__RIGHT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3374 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) -> (p(ap(V2P,V4x)) <-> p(ap(V3P_27,V4x)))))) & V1l2 = V0l1 -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V2P),V0l1)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V3P_27),V1l2)))))))))))))) # label(conj_thm_2Elist_2EEVERY__CONG) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3375 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),V2n)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),V1l2)) = ap(ap(c_2Elist_2ETAKE(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2))))))))))) # label(conj_thm_2Elist_2ETAKE__APPEND2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3376 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(c_2Ebool_2E_7E,ap(V0P,V2x)) = ap(f392(A_27a,V0P),V2x)))) # label(lameq_f392) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3377 (all A_27a all A_27b all V6a (mem(V6a,A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V7b ap(ap(V0P,V6a),V7b) = ap(f403(A_27a,A_27b,V6a,V0P),V7b)))))) # label(lameq_f403) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3378 (all A_27d all A_27a all A_27b all V3f2 (mem(V3f2,arr(A_27b,A_27d)) -> (all V5p ap(f414(A_27d,A_27a,A_27b,V3f2),V5p) = ap(ap(c_2Epair_2E_2C(A_27a,A_27d),ap(c_2Epair_2EFST(A_27a,A_27b),V5p)),ap(V3f2,ap(c_2Epair_2ESND(A_27a,A_27b),V5p)))))) # label(lameq_f414) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3379 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((exists V1a (mem(V1a,A_27a) & (exists V2b (p(ap(ap(V0R,V1a),V2b)) & mem(V2b,A_27a))))) -> -p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R)))))))) # label(conj_thm_2Elist_2ELLEX__not__WF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3380 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ECONS(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2ECONS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3381 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EoHD(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Elist_2EoHD) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3382 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Elist_2ELENGTH(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)))))))))) # label(conj_thm_2Elist_2ELENGTH__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3383 (all A_27c all A_27b all A_27a all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V1f2 (mem(V1f2,arr(A_27c,A_27b)) -> (all V4x ap(f417(A_27c,A_27b,A_27a,V0f1,V1f2),V4x) = f416(A_27b,A_27a,A_27c,V0f1,V4x,V1f2)))))) # label(lameq_f417) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3384 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27a),i(A_27a)),V0l) = V0l & V0l = ap(ap(c_2Elist_2EMAP(A_27a,A_27a),c_2Ecombin_2EI(A_27a)),V0l))))) # label(conj_thm_2Elist_2EMAP__ID) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3385 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (V1l2 = V0l1 & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) -> (p(ap(V2P,V4x)) <-> p(ap(V3P_27,V4x)))))) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V3P_27),V1l2)) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V2P),V0l1)))))))))))))) # label(conj_thm_2Elist_2EEXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3386 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2l (mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V2l))) -> (exists V3z (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V3z),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V2l))) & ap(c_2Epair_2EFST(A_27a,A_27b),V3z) = V0x & mem(V3z,ty_2Epair_2Eprod(A_27a,A_27b))))))))))))))) # label(conj_thm_2Elist_2Emem__exists__set) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3387 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1h1 (mem(V1h1,A_27a) -> (all V2t1 (mem(V2t1,ty_2Elist_2Elist(A_27a)) -> (all V3h2 (mem(V3h2,A_27a) -> (all V4t2 (mem(V4t2,ty_2Elist_2Elist(A_27a)) -> -p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) & (V1h1 = V3h2 & p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V2t1),V4t2)) | p(ap(ap(V0R,V1h1),V3h2)) <-> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))) & p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2))) & -p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),c_2Elist_2ENIL(A_27a))))))))))))))) # label(conj_thm_2Elist_2ELLEX__THM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3388 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1ts (mem(V1ts,ty_2Elist_2Elist(A_27a)) -> (all V2tt (mem(V2tt,ty_2Elist_2Elist(A_27b)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2EMIN,ap(c_2Elist_2ELENGTH(A_27a),V1ts)),ap(c_2Elist_2ELENGTH(A_27b),V2tt)))) -> ap(ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1ts)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V2tt)) = ap(ap(c_2Elist_2EEL(A_27c),V3n),ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),V1ts),V2tt))))))))))))))))) # label(conj_thm_2Elist_2EEL__MAP2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3389 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,A_27a) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2xs)) = ap(ap(c_2Elist_2ETAKE(A_27a),V0n),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2xs))))))))))) # label(conj_thm_2Elist_2ETAKE__cons) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3390 (all A_27a all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (all V5x ap(f393(A_27a,V4l,V0P),V5x) = ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V5x),V4l))))))) # label(lameq_f393) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3391 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v_27 (mem(V0v_27,A_27b) -> (all V1f_27 (mem(V1f_27,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> (all V2M (mem(V2M,ty_2Elist_2Elist(A_27a)) -> (all V3M_27 (mem(V3M_27,ty_2Elist_2Elist(A_27a)) -> (all V4v (mem(V4v,A_27b) -> (all V5f (mem(V5f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> (V2M = V3M_27 & (V3M_27 = c_2Elist_2ENIL(A_27a) -> V4v = V0v_27) & (all V6a0 (mem(V6a0,A_27a) -> (all V7a1 (mem(V7a1,ty_2Elist_2Elist(A_27a)) -> (V3M_27 = ap(ap(c_2Elist_2ECONS(A_27a),V6a0),V7a1) -> ap(ap(V1f_27,V6a0),V7a1) = ap(ap(V5f,V6a0),V7a1)))))) -> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V2M),V4v),V5f) = ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V3M_27),V0v_27),V1f_27)))))))))))))))))) # label(conj_thm_2Elist_2Elist__case__cong) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3392 (all A_27a (ne(A_27a) -> (all V0list (mem(V0list,arr(ty_2Elist_2Elist(A_27a),arr(arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),bool))) -> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0list,c_2Elist_2ENIL(A_27a)),c_2Elist_2ECONS(A_27a)))))))) # label(conj_thm_2Elist_2Edatatype__list) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3393 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),f437(A_27b,A_27a,V1f)),V0ls) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f),ap(c_2Elist_2EZIP(A_27a,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V0ls),V0ls))))))))))) # label(conj_thm_2Elist_2EMAP__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3394 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EMAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))))))) # label(mem_c_2Elist_2EMAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3395 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EDROP(A_27a),c_2Enum_2E0),V0l) = V0l)) & (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EDROP(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> c_2Elist_2ENIL(A_27b) = ap(ap(c_2Elist_2EDROP(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),c_2Elist_2ENIL(A_27b)))) & (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7h (mem(V7h,A_27c) -> (all V8t (mem(V8t,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),ap(ap(c_2Elist_2ECONS(A_27c),V7h),V8t)) = ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),V8t))))))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4h (mem(V4h,A_27c) -> (all V5t (mem(V5t,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(ap(c_2Elist_2ECONS(A_27c),V4h),V5t)) = ap(ap(c_2Elist_2EDROP(A_27c),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V5t))))))))))))) # label(conj_thm_2Elist_2EDROP__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3396 (all A_27a all A_27b all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2n ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V2n),V1ls)) = ap(f454(A_27a,A_27b,V1ls,V0f),V2n)))))) # label(lameq_f454) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3397 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v (mem(V0v,A_27a) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> (all V4l3 (mem(V4l3,A_27b) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0v),ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V2x),c_2Elist_2ENIL(A_27a)))),V3l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V0v),c_2Elist_2ENIL(A_27a)))),V3l2))))))))))))))) # label(conj_thm_2Elist_2Elupdate__append2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3398 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0t (mem(V0t,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27b))) -> (all V1h (mem(V1h,A_27c) -> (all V2t1 (mem(V2t1,ty_2Elist_2Elist(A_27c)) -> (all V3t2 (mem(V3t2,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27c))) -> ap(c_2Elist_2EFLAT(A_27c),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27c)),ap(ap(c_2Elist_2ECONS(A_27c),V1h),V2t1)),V3t2)) = ap(ap(c_2Elist_2ECONS(A_27c),V1h),ap(c_2Elist_2EFLAT(A_27c),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27c)),V2t1),V3t2))) & ap(c_2Elist_2EFLAT(A_27b),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)),V0t)) = ap(c_2Elist_2EFLAT(A_27b),V0t) & ap(c_2Elist_2EFLAT(A_27a),c_2Elist_2ENIL(ty_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL(A_27a))))))))))))))) # label(conj_thm_2Elist_2EFLAT__compute) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3399 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ENULL(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))) # label(mem_c_2Elist_2ENULL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3400 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m1 (mem(V0m1,ty_2Elist_2Elist(A_27b)) -> (all V1m2 (mem(V1m2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ELIST__IGNORE__BIND(A_27a,A_27b),V0m1),V1m2) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0m1),ap(c_2Ecombin_2EK(ty_2Elist_2Elist(A_27a),A_27b),V1m2)))))))))) # label(ax_thm_2Elist_2ELIST__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3401 (all A_27a all V2SET__TO__LIST ap(f422(A_27a),V2SET__TO__LIST) = f421(A_27a,V2SET__TO__LIST)) # label(lameq_f422) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3402 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (p(ap(V0P,c_2Elist_2ENIL(A_27a))) & (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(V0P,V1l)) -> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V1l)))))))) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,V3l))))))))) # label(conj_thm_2Elist_2ESNOC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3403 (all A_27a all V2_27list_27 (mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool)) -> (all V3a0_27 (mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a)) -> (all V5a0 ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f382(A_27a,V5a0,V3a0_27,V2_27list_27)) = ap(f383(A_27a,V2_27list_27,V3a0_27),V5a0)))))) # label(lameq_f383) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3404 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))),c_2Epred__set_2EUNIV(A_27b))) -> (V1l1 = V2l2 <-> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1))))))))))))) # label(conj_thm_2Elist_2EINJ__MAP__EQ__IFF) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3405 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0L (mem(V0L,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0L)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0L)) = ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0L))))))) # label(conj_thm_2Elist_2EUNZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3406 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ENIL(A_27a),ty_2Elist_2Elist(A_27a)))) # label(mem_c_2Elist_2ENIL) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3407 (all A_27a all V1h (mem(V1h,A_27a) -> (all V4h_27 (mem(V4h_27,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V5t_27 ap(f423(A_27a,V1h,V4h_27,V2t),V5t_27) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V1h),V4h_27)),ap(ap(c_2Elist_2EisPREFIX(A_27a),V2t),V5t_27))))))))) # label(lameq_f423) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3408 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2))) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l1)) | p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l2))))))))))) # label(conj_thm_2Elist_2EEXISTS__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3409 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l2)) & p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l1)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)))))))))))) # label(conj_thm_2Elist_2EEVERY__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3410 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V2h (mem(V2h,arr(A_27b,ty_2Enum_2Enum)) -> (all V3ls1 (mem(V3ls1,ty_2Elist_2Elist(A_27a)) -> (all V4ls2 (mem(V4ls2,ty_2Elist_2Elist(A_27b)) -> ((all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27b) -> ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)) = ap(ap(c_2Earithmetic_2E_2B,ap(V1g,V5x)),ap(V2h,V6y)))))) & ap(c_2Elist_2ELENGTH(A_27a),V3ls1) = ap(c_2Elist_2ELENGTH(A_27b),V4ls2) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1g),V3ls1))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27b,ty_2Enum_2Enum),V2h),V4ls2))) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum),V0f),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V3ls1),V4ls2))))))))))))))))))) # label(conj_thm_2Elist_2ESUM__MAP__PLUS__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3411 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f418(A_27a,V0P))),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3412 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l1)) -> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1l1)),V2l2)))))))))) # label(conj_thm_2Elist_2EdropWhile__APPEND__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3413 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,ty_2Elist_2Elist(A_27a)) -> (all V3y (mem(V3y,ty_2Elist_2Elist(A_27a)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R1,V4x),V5y)) -> p(ap(ap(V1R2,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R1),V2x),V3y)) -> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V1R2),V2x),V3y)))))))))))))) # label(conj_thm_2Elist_2ELLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3414 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) <-> V0l = c_2Elist_2ENIL(A_27a)))))) # label(conj_thm_2Elist_2ELENGTH__NIL__SYM) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3415 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l)) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))))))))) # label(conj_thm_2Elist_2EFILTER__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3416 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2p (mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> ((exists V3n (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V3n),V0l1)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V1l2)) = V2p & p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) & mem(V3n,ty_2Enum_2Enum))) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V2p),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))))))))))))))))) # label(conj_thm_2Elist_2EMEM__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3417 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> V0l != ap(ap(c_2Elist_2ECONS(A_27a),V1x),V0l) & ap(ap(c_2Elist_2ECONS(A_27a),V1x),V0l) != V0l)))))) # label(conj_thm_2Elist_2ECONS__ACYCLIC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3418 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1l2)),ap(c_2Elist_2EREVERSE(A_27a),V0l1)))))))) # label(conj_thm_2Elist_2EREVERSE__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3419 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> (all V1x (mem(V1x,A_27a) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) | V0y = V1x <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l))))))))))))) # label(conj_thm_2Elist_2EMEM__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3420 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1Q,V3x))))) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l)) -> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l)))))))))))) # label(conj_thm_2Elist_2EMONO__EVERY) # label(axiom) # label(non_clause). [assumption]. 6.36/6.36 3421 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (V1l2 != c_2Elist_2ENIL(A_27a) <-> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1l2))))))) & (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V3h1 (mem(V3h1,A_27a) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),V5l2)) <-> p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V5l2),c_2Ebool_2EF),f448(A_27a,V4t1,V3h1,V2R)))))))))))))) # label(ax_thm_2Elist_2ELLEX__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3422 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EGENLIST__AUX(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) # label(mem_c_2Elist_2EGENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3423 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l1),V2l2)) <-> (exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1))) -> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V3n),V2l2)))) & ap(ap(c_2Elist_2ETAKE(A_27a),V3n),V1l1) = ap(ap(c_2Elist_2ETAKE(A_27a),V3n),V2l2) & p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V2l2)))))))))))))) # label(conj_thm_2Elist_2ELLEX__EL__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3424 (all V0b (mem(V0b,bool) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Eone_2Eone)),V0b),ap(ap(c_2Elist_2ECONS(ty_2Eone_2Eone),c_2Eone_2Eone),c_2Elist_2ENIL(ty_2Eone_2Eone))),c_2Elist_2ENIL(ty_2Eone_2Eone)) = ap(c_2Elist_2ELIST__GUARD,V0b))) # label(ax_thm_2Elist_2ELIST__GUARD__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3425 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V0h)))))) # label(ax_thm_2Elist_2EHD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3426 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EFOLDL(A_27a,A_27b),arr(arr(A_27b,arr(A_27a,A_27b)),arr(A_27b,arr(ty_2Elist_2Elist(A_27a),A_27b)))))))) # label(mem_c_2Elist_2EFOLDL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3427 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))),c_2Epred__set_2EUNIV(A_27b))) & ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1) -> V2l2 = V1l1))))))))))) # label(conj_thm_2Elist_2EINJ__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3428 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0h (mem(V0h,A_27b) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1t)) & ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Epred__set_2EEMPTY(A_27a))))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3429 (all A_27b all A_27a all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2x ap(f452(A_27b,A_27a,V1f),V2x) = ap(c_2Ebool_2E_3F(A_27b),f451(A_27a,A_27b,V1f,V2x))))) # label(lameq_f452) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3430 (all A_27a all A_27b all V2P (mem(V2P,arr(A_27b,bool)) -> (all V3x ap(f459(A_27a,A_27b,V2P),V3x) = ap(V2P,ap(c_2Epair_2ESND(A_27a,A_27b),V3x))))) # label(lameq_f459) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3431 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V2b)),ap(ap(c_2Elist_2EGENLIST(A_27a),f425(A_27a,V2b,V0f)),V1a)))))))))) # label(conj_thm_2Elist_2EGENLIST__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3432 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Elist_2Elist(A_27a)) -> (all V1b (mem(V1b,ty_2Elist_2Elist(A_27b)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(c_2Elist_2ELENGTH(A_27a),V0a) = ap(c_2Elist_2ELENGTH(A_27b),V1b) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0a))) -> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EDROP(A_27a),V2n),V0a)),ap(ap(c_2Elist_2EDROP(A_27b),V2n),V1b))) = ap(ap(c_2Elist_2EDROP(ty_2Epair_2Eprod(A_27a,A_27b)),V2n),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0a),V1b)))))))))))))) # label(conj_thm_2Elist_2EZIP__DROP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3433 (all A_27a all V5a0 (mem(V5a0,A_27a) -> (all V3a0_27 (mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a)) -> (all V2_27list_27 (mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool)) -> (all V6a1 ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(f381(A_27a),V5a0),V6a1))),ap(V2_27list_27,V6a1)) = ap(f382(A_27a,V5a0,V3a0_27,V2_27list_27),V6a1)))))))) # label(lameq_f382) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3434 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3435 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (c_2Enum_2E0 = V0n <-> p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n)))))))))) # label(conj_thm_2Elist_2ENULL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3436 (all A_27a all A_27b all V1x (mem(V1x,A_27b) -> (all V2f ap(f444(A_27a,A_27b,V1x),V2f) = ap(V2f,V1x)))) # label(lameq_f444) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3437 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27b) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27b)) -> (ap(ap(c_2Elist_2ECONS(A_27b),V2h),V3t) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l) <-> (exists V4x0 ((exists V5t0 (mem(V5t0,ty_2Elist_2Elist(A_27a)) & ap(ap(c_2Elist_2ECONS(A_27a),V4x0),V5t0) = V1l & V3t = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V5t0) & V2h = ap(V0f,V4x0))) & mem(V4x0,A_27a)))))))))))))))) # label(conj_thm_2Elist_2EMAP__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3438 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n1 (mem(V1n1,ty_2Enum_2Enum) -> (all V2n2 (mem(V2n2,ty_2Enum_2Enum) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n1),ap(c_2Elist_2ELENGTH(A_27a),V0l))) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n2),ap(c_2Elist_2ELENGTH(A_27a),V0l))) -> (ap(ap(c_2Elist_2EEL(A_27a),V2n2),V0l) = ap(ap(c_2Elist_2EEL(A_27a),V1n1),V0l) <-> V1n1 = V2n2)))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3439 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1e (mem(V1e,A_27a) -> (V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)) <-> ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)) = ap(c_2Elist_2EREVERSE(A_27a),V0l)))))))) # label(conj_thm_2Elist_2EREVERSE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3440 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1L (mem(V1L,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0e)),V1L)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) <-> p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L))))))))) # label(conj_thm_2Elist_2EUNIQUE__LENGTH__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3441 (all A_27a (ne(A_27a) -> (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ELEN(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3n) = ap(ap(c_2Elist_2ELEN(A_27a),V2t),ap(ap(c_2Earithmetic_2E_2B,V3n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) & (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Elist_2ELEN(A_27a),c_2Elist_2ENIL(A_27a)),V0n))))) # label(ax_thm_2Elist_2ELEN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3442 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27b)) -> (all V2ys (mem(V2ys,ty_2Elist_2Elist(A_27c)) -> ap(ap(ap(c_2Elist_2ELIST__LIFT2(A_27a,A_27b,A_27c),V0f),V1xs),V2ys) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27c),ap(ap(c_2Elist_2EMAP(A_27b,arr(A_27c,A_27a)),V0f),V1xs)),V2ys))))))))))))) # label(ax_thm_2Elist_2ELIST__LIFT2__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3443 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0fs (mem(V0fs,ty_2Elist_2Elist(arr(A_27b,A_27a))) -> (all V1x (mem(V1x,A_27b) -> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),V0fs),ap(ap(c_2Elist_2ECONS(A_27b),V1x),c_2Elist_2ENIL(A_27b))) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,arr(A_27b,A_27a)),ap(ap(c_2Elist_2ECONS(arr(arr(A_27b,A_27a),A_27a)),f444(A_27a,A_27b,V1x)),c_2Elist_2ENIL(arr(arr(A_27b,A_27a),A_27a)))),V0fs))))))))) # label(conj_thm_2Elist_2ESINGL__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3444 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l)) | p(ap(V0P,V1x)) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)))))))))))) # label(conj_thm_2Elist_2EEXISTS__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3445 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1Q,V3x))))) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l)) -> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1Q),V2l)))))))))))) # label(conj_thm_2Elist_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3446 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V2l2))) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V2l2)))))))))) # label(conj_thm_2Elist_2ELAST__APPEND__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3447 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELUPDATE(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) # label(mem_c_2Elist_2ELUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3448 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l)) & p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l)) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),f390(A_27a,V0P,V1Q)),V2l))))))))))) # label(conj_thm_2Elist_2EEVERY__CONJ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3449 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(A_27a),V1l)))))))) # label(conj_thm_2Elist_2ELENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3450 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ($F <-> p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))))) & (p(ap(c_2Elist_2ENULL(A_27a),c_2Elist_2ENIL(A_27a))) <-> $T))) # label(ax_thm_2Elist_2ENULL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3451 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27a)),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27b)))) & (all V1f (mem(V1f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V2h0 (mem(V2h0,A_27b) -> (all V3t0 (mem(V3t0,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V1f),ap(ap(c_2Elist_2ECONS(A_27b),V2h0),V3t0)) = ap(ap(c_2Eoption_2EOPTION__BIND(ty_2Elist_2Elist(A_27a),A_27a),ap(V1f,V2h0)),f462(A_27b,A_27a,V1f,V3t0)))))))))))) # label(ax_thm_2Elist_2EOPT__MMAP__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3452 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) -> (ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) <-> V0l1 = c_2Elist_2ENIL(A_27a) & c_2Elist_2ENIL(A_27b) = V1l2)))))))))) # label(conj_thm_2Elist_2EZIP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3453 (all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2a ap(f428(A_27a,V0f),V2a) = f427(A_27a,V0f,V2a)))) # label(lameq_f428) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3454 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V3h (mem(V3h,A_27a) -> (-p(ap(V0P,V3h)) -> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1l)) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))) & (all V2h (mem(V2h,A_27a) -> (p(ap(V0P,V2h)) -> ap(ap(c_2Elist_2ECONS(A_27a),V2h),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1l))))) & ap(ap(c_2Elist_2EFILTER(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))))) # label(conj_thm_2Elist_2EFILTER__COND__REWRITE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3455 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,arr(A_27c,A_27a))),arr(A_27a,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),A_27a))))))))))) # label(mem_c_2Elist_2EFOLDL2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3456 (all A_27a all V7a0 (mem(V7a0,A_27a) -> (all V8a1 ap(f380(A_27a,V7a0),V8a1) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,c_2Enum_2E0)),V7a0),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V8a1),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))))) # label(lameq_f380) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3457 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27a,bool))) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27b)) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(A_27b,arr(A_27a,bool)),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1ls)))),V2s)) <-> (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1ls))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V3x)),V2s)))))))))))))))) # label(conj_thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3458 (all A_27a (ne(A_27a) -> (all V3e (mem(V3e,A_27a) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) -> (all V6p (mem(V6p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V6p),ap(c_2Elist_2ELENGTH(A_27a),V5l))) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6p),V4n)),V3e),ap(ap(c_2Elist_2EEL(A_27a),V6p),V5l)) = ap(ap(c_2Elist_2EEL(A_27a),V6p),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3e),V4n),V5l))))))))))) & (all V0e (mem(V0e,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),V2l) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),V2l)))))))))) # label(conj_thm_2Elist_2ELUPDATE__SEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3459 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2y (mem(V2y,A_27a) -> (V2y = ap(ap(c_2Elist_2EEL(A_27a),V1n),V0xs) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0xs))) <-> ap(c_2Eoption_2ESOME(A_27a),V2y) = ap(ap(c_2Elist_2EoEL(A_27a),V1n),V0xs)))))))))) # label(conj_thm_2Elist_2EoEL__EQ__EL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3460 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)) = ap(c_2Elist_2EUNZIP(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) & (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V0x),V1l)) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V0x)),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V1l)))),ap(ap(c_2Elist_2ECONS(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V0x)),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V1l)))))))))))) # label(ax_thm_2Elist_2EUNZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3461 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (V0ls != c_2Elist_2ENIL(A_27a) -> ap(c_2Elist_2ELAST(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0ls)) = ap(c_2Elist_2EHD(A_27a),V0ls)))))) # label(conj_thm_2Elist_2ELAST__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3462 (all A_27a all A_27b all V3k (mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V4h (mem(V4h,A_27b) -> (all V6p (mem(V6p,ty_2Elist_2Elist(A_27b)) -> (all V7s ap(ap(V3k,ap(ap(c_2Elist_2ECONS(A_27b),V4h),V6p)),V7s) = ap(f438(A_27a,A_27b,V3k,V4h,V6p),V7s)))))))) # label(lameq_f438) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3463 (all V0x (mem(V0x,arr(ty_2Enum_2Enum,bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V1n)),ap(ap(c_2Earithmetic_2E_2B,V2a),V3b))))) -> p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V1n),V2a))),V3b)))) & p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V1n)),V2a))))))))))))) # label(conj_thm_2Elist_2EDISJOINT__GENLIST__PLUS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3464 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((all V2m1 (mem(V2m1,ty_2Enum_2Enum) -> (all V3m2 (mem(V3m2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m2),V1n)) & ap(V0f,V2m1) = ap(V0f,V3m2) & p(ap(ap(c_2Eprim__rec_2E_3C,V2m1),V1n)) -> V3m2 = V2m1))))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3465 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> -p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t))))))) & p(ap(c_2Elist_2ENULL(A_27a),c_2Elist_2ENIL(A_27a))))) # label(conj_thm_2Elist_2ENULL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3466 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l1_27 (mem(V1l1_27,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V1l1_27) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (all V3l2_27 (mem(V3l2_27,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V3l2_27) = ap(c_2Elist_2ELENGTH(A_27a),V2l2) -> (V3l2_27 = V2l2 & V0l1 = V1l1_27 <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1_27),V3l2_27) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l2)))))))))))))) # label(conj_thm_2Elist_2EAPPEND__LENGTH__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3467 (all A_27a (ne(A_27a) -> (all V0a0 (mem(V0a0,A_27a) -> (all V1a1 (mem(V1a1,ty_2Elist_2Elist(A_27a)) -> (all V2a0_27 (mem(V2a0_27,A_27a) -> (all V3a1_27 (mem(V3a1_27,ty_2Elist_2Elist(A_27a)) -> (V0a0 = V2a0_27 & V1a1 = V3a1_27 <-> ap(ap(c_2Elist_2ECONS(A_27a),V2a0_27),V3a1_27) = ap(ap(c_2Elist_2ECONS(A_27a),V0a0),V1a1)))))))))))) # label(conj_thm_2Elist_2Elist__11) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3468 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EINDEX__FIND(A_27a),arr(ty_2Enum_2Enum,arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))))))) # label(mem_c_2Elist_2EINDEX__FIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3469 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> ap(c_2Elist_2EFLAT(A_27a),V0l) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,ty_2Elist_2Elist(A_27a)),V0l),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))) & ap(c_2Elist_2EFLAT(A_27a),V0l) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,ty_2Elist_2Elist(A_27a)),V0l),i(ty_2Elist_2Elist(A_27a))))))) # label(conj_thm_2Elist_2ELIST__BIND__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3470 (all A_27b all A_27a all V2fn1 (mem(V2fn1,arr(ty_2Elist_2Elist(A_27a),A_27b)) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))) -> (all V3h ap(f388(A_27b,A_27a,V2fn1,V1f),V3h) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27a)),f387(A_27b,A_27a,V1f,V2fn1,V3h))))))) # label(lameq_f388) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3471 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V3l) = V1n -> p(ap(f394(A_27a,V0P),V3l))))) <-> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Enum_2ESUC,V1n) = ap(c_2Elist_2ELENGTH(A_27a),V2l) -> p(ap(V0P,V2l)))))))))))) # label(conj_thm_2Elist_2ELENGTH__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3472 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1L (mem(V1L,ty_2Elist_2Elist(A_27a)) -> (all V2M (mem(V2M,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1L)),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V2M)) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1L),V2M)))))))))) # label(conj_thm_2Elist_2EFILTER__APPEND__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3473 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),f392(A_27a,V0P)),V1l)) <-> c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))))))) # label(conj_thm_2Elist_2EFILTER__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3474 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3ys (mem(V3ys,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),V0xs),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V3ys)) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V1x),ap(c_2Elist_2ELENGTH(A_27a),V0xs)),ap(ap(c_2Elist_2EAPPEND(A_27a),V0xs),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3ys))))))))))))) # label(conj_thm_2Elist_2ELUPDATE__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3475 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = ap(ap(c_2Elist_2EGENLIST(A_27a),f429(A_27a,V1n,V0f)),V1n))))))) # label(conj_thm_2Elist_2EREVERSE__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3476 (all A_27a (ne(A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3xs (mem(V3xs,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ETAKE(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs))))))))) & (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))) # label(ax_thm_2Elist_2ETAKE__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3477 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,A_27a) -> (all V2ls (mem(V2ls,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),V2ls) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(ap(c_2Elist_2ECONS(A_27a),V1l),V2ls)) & ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(ap(c_2Elist_2ECONS(A_27a),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))),V2ls))))))))) # label(conj_thm_2Elist_2EEL__simp__restricted) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3478 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ESET__TO__LIST(A_27a),arr(arr(A_27a,bool),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2ESET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3479 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ((exists V2e (p(ap(V0P,V2e)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) & mem(V2e,A_27a))) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l))))))))) # label(conj_thm_2Elist_2EEXISTS__MEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3480 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,A_27b) -> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(arr(A_27b,A_27a)),V0f),c_2Elist_2ENIL(arr(A_27b,A_27a)))),ap(ap(c_2Elist_2ECONS(A_27b),V1x),c_2Elist_2ENIL(A_27b))) = ap(ap(c_2Elist_2ECONS(A_27a),ap(V0f,V1x)),c_2Elist_2ENIL(A_27a)))))))))) # label(conj_thm_2Elist_2ESINGL__SINGL__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3481 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EFLAT(A_27a),arr(ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2EFLAT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3482 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELENGTH(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum)))) # label(mem_c_2Elist_2ELENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3483 (all A_27b all A_27a all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b)) -> (all V2x ap(f437(A_27b,A_27a,V1f),V2x) = ap(V1f,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x))))) # label(lameq_f437) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3484 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27b)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2f (mem(V2f,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2EAPPEND(A_27b),V0l1),V1l2)),V2f) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0l1),V2f)),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V1l2),V2f)))))))))))) # label(conj_thm_2Elist_2ELIST__BIND__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3485 (all A_27a (ne(A_27a) -> (all V2e (mem(V2e,A_27a) -> (all V3x (mem(V3x,A_27a) -> (all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2e),c_2Enum_2E0),ap(ap(c_2Elist_2ECONS(A_27a),V3x),V4l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2e),V4l))))))) & (all V5e (mem(V5e,A_27a) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7x (mem(V7x,A_27a) -> (all V8l (mem(V8l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V7x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),V6n),V8l)) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(c_2Enum_2ESUC,V6n)),ap(ap(c_2Elist_2ECONS(A_27a),V7x),V8l)))))))))) & (all V0e (mem(V0e,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> c_2Elist_2ENIL(A_27a) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),c_2Elist_2ENIL(A_27a)))))))) # label(ax_thm_2Elist_2ELUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3486 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) -> V1ls = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),ap(ap(c_2Elist_2EEL(A_27a),V0n),V1ls)),V0n),V1ls)))))))) # label(conj_thm_2Elist_2ELUPDATE__SAME) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3487 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (-p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l)) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l))))))))) # label(conj_thm_2Elist_2ENOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3488 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> -p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l),c_2Elist_2ENIL(A_27a))))))))) # label(conj_thm_2Elist_2ELLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3489 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ((all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2x),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) -> ap(ap(c_2Elist_2EEL(A_27a),V2x),V1l2) = ap(ap(c_2Elist_2EEL(A_27a),V2x),V0l1)))) & ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l2) <-> V0l1 = V1l2))))))) # label(conj_thm_2Elist_2ELIST__EQ__REWRITE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3490 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),c_2Elist_2ENIL(A_27a)) = V0l)))) # label(conj_thm_2Elist_2EAPPEND__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3491 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),f452(A_27b,A_27a,V1f)),V0ls)) -> (exists V4l (ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V1f),V4l) = V0ls & mem(V4l,ty_2Elist_2Elist(A_27b))))))))))))) # label(conj_thm_2Elist_2EEXISTS__LIST__EQ__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3492 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27b) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27b)) -> ((exists V4h_27 ((exists V5t_27 (p(ap(ap(V0R,V4h_27),V2h)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V5t_27),V3t)) & V1xs = ap(ap(c_2Elist_2ECONS(A_27a),V4h_27),V5t_27) & mem(V5t_27,ty_2Elist_2Elist(A_27a)))) & mem(V4h_27,A_27a))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1xs),ap(ap(c_2Elist_2ECONS(A_27b),V2h),V3t)))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__CONS2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3493 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))) -> -p(ap(V0P,V2x))))) <-> p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1ls)))))))))) # label(conj_thm_2Elist_2ENULL__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3494 (all A_27a all A_27b all A_27c all V2f (mem(V2f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c)))) -> (all V4a ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(V2f,V4a)) = ap(f415(A_27a,A_27b,A_27c,V2f),V4a)))) # label(lameq_f415) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3495 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2s (mem(V2s,arr(ty_2Elist_2Elist(A_27a),bool)) -> ((exists V4a (mem(V4a,ty_2Elist_2Elist(A_27a)) & p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V4a),V2s)))) & (all V3d (mem(V3d,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V3d),V2s)) -> V1l = ap(c_2Elist_2ELENGTH(A_27a),V3d)))) -> (exists V5b (mem(V5b,ty_2Elist_2Elist(A_27a)) & (all V6c (mem(V6c,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V6c),V5b)) -> -p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V6c),V2s))))) & p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V5b),V2s)))))))))))))) # label(conj_thm_2Elist_2EWF__SHORTLEX__same__lengths) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3496 (all A_27a (ne(A_27a) -> (all V0h1 (mem(V0h1,A_27a) -> (all V1h2 (mem(V1h2,A_27a) -> (V0h1 != V1h2 -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V1h2),V3l2) != ap(ap(c_2Elist_2ECONS(A_27a),V0h1),V2l1)))))))))))) # label(conj_thm_2Elist_2ENOT__EQ__LIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3497 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l1_27 (mem(V1l1_27,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (all V3l2_27 (mem(V3l2_27,ty_2Elist_2Elist(A_27b)) -> (all V4a (mem(V4a,A_27c) -> (all V5a_27 (mem(V5a_27,A_27c) -> (all V6f (mem(V6f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c)))) -> (all V7f_27 (mem(V7f_27,arr(A_27c,arr(A_27a,arr(A_27b,A_27c)))) -> (V3l2_27 = V2l2 & (all V8z (mem(V8z,A_27c) -> (all V9b (mem(V9b,A_27a) -> (all V10c (mem(V10c,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V10c),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V9b),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27))) -> ap(ap(ap(V7f_27,V8z),V9b),V10c) = ap(ap(ap(V6f,V8z),V9b),V10c)))))))) & V5a_27 = V4a & V1l1_27 = V0l1 -> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V6f),V4a),V0l1),V2l2) = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V7f_27),V5a_27),V1l1_27),V3l2_27)))))))))))))))))))))))) # label(conj_thm_2Elist_2EFOLDL2__cong) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3498 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27b)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (V2n = ap(c_2Elist_2ELENGTH(A_27a),V0l) -> ap(ap(c_2Elist_2EGENLIST(ty_2Epair_2Eprod(A_27a,A_27b)),f426(A_27b,A_27a,V0l,V1f)),V2n) = ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l),ap(ap(c_2Elist_2EGENLIST(A_27b),V1f),V2n)))))))))))))) # label(conj_thm_2Elist_2EZIP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3499 (all A_27a (ne(A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3xs (mem(V3xs,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(c_2Eoption_2ESOME(A_27a),V2x)),ap(ap(c_2Elist_2EoEL(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs)) = ap(ap(c_2Elist_2EoEL(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)))))))) & (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EoEL(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Eoption_2ENONE(A_27a))))) # label(ax_thm_2Elist_2EoEL__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3500 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V1f2 (mem(V1f2,arr(A_27a,A_27b)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ((all V3e (mem(V3e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) -> ap(V0f1,V3e) = ap(V1f2,V3e)))) <-> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f1),V2l) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f2),V2l)))))))))))) # label(conj_thm_2Elist_2EMAP__EQ__f) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3501 (all A_27b all A_27d all A_27c all V4Q (mem(V4Q,arr(A_27c,arr(A_27d,bool))) -> (all V5g (mem(V5g,arr(A_27b,A_27d)) -> (all V8x f457(A_27d,A_27c,A_27b,V8x,V4Q,V5g) = ap(f458(A_27b,A_27d,A_27c,V4Q,V5g),V8x)))))) # label(lameq_f458) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3502 (all A_27a (ne(A_27a) -> (all V4l1 (mem(V4l1,ty_2Elist_2Elist(A_27a)) -> (all V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27a)) -> (all V6l1_27 (mem(V6l1_27,ty_2Elist_2Elist(A_27a)) -> (all V7l2_27 (mem(V7l2_27,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V5l2) = ap(c_2Elist_2ELENGTH(A_27a),V7l2_27) -> (V4l1 = V6l1_27 & V5l2 = V7l2_27 <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V5l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V6l1_27),V7l2_27))))))))))) & (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2l1_27 (mem(V2l1_27,ty_2Elist_2Elist(A_27a)) -> (all V3l2_27 (mem(V3l2_27,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2ELENGTH(A_27a),V2l1_27) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1_27),V3l2_27) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) <-> V1l2 = V3l2_27 & V0l1 = V2l1_27)))))))))))) # label(conj_thm_2Elist_2EAPPEND__11__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3503 (all A_27a (ne(A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3xs (mem(V3xs,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)),ap(ap(c_2Elist_2EDROP(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs)) = ap(ap(c_2Elist_2EDROP(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)))))))) & (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EDROP(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))) # label(ax_thm_2Elist_2EDROP__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3504 (all A_27a (ne(A_27a) -> (all V0L (mem(V0L,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),V0L) = ap(ap(c_2Elist_2ELEN(A_27a),V0L),c_2Enum_2E0))))) # label(conj_thm_2Elist_2ELENGTH__LEN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3505 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l))) -> V0n = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l))))))))) # label(conj_thm_2Elist_2ELENGTH__TAKE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3506 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)))))))) # label(conj_thm_2Elist_2EUNION__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3507 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))))))))) # label(conj_thm_2Elist_2EMEM__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3508 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V2n),V1ls)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),ap(c_2Enum_2ESUC,V2n)),V1ls)))) | p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) & ap(ap(c_2Elist_2EEL(A_27a),V2n),V1ls) = V0x))))))))) # label(conj_thm_2Elist_2EMEM__DROP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3509 (all A_27a all V0L1 ap(f400(A_27a),V0L1) = f399(A_27a,V0L1)) # label(lameq_f400) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3510 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27a),V1l1) = ap(c_2Elist_2ELENGTH(A_27b),V2l2) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1))) -> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1l1)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V2l2)))))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__EL__EQN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3511 (all A_27a (ne(A_27a) -> (all V0a1 (mem(V0a1,ty_2Elist_2Elist(A_27a)) -> (all V1a0 (mem(V1a0,A_27a) -> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1))))))) # label(conj_thm_2Elist_2ENOT__NIL__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3512 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)))))))))) # label(conj_thm_2Elist_2ESET__TO__LIST__IN__MEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3513 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3xs (mem(V3xs,ty_2Elist_2Elist(A_27b)) -> ((exists V4h_27 (mem(V4h_27,A_27b) & (exists V5t_27 (mem(V5t_27,ty_2Elist_2Elist(A_27b)) & V3xs = ap(ap(c_2Elist_2ECONS(A_27b),V4h_27),V5t_27) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2t),V5t_27)) & p(ap(ap(V0R,V1h),V4h_27)))))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3xs))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__CONS1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3514 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)) = ap(ap(c_2Elist_2ESNOC(A_27a),V0x),ap(c_2Elist_2EREVERSE(A_27a),V1l)))))) & c_2Elist_2ENIL(A_27b) = ap(c_2Elist_2EREVERSE(A_27b),c_2Elist_2ENIL(A_27b)))))) # label(conj_thm_2Elist_2EREVERSE__SNOC__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3515 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0fs (mem(V0fs,ty_2Elist_2Elist(arr(A_27b,A_27a))) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,arr(A_27b,A_27a)),V0fs),ap(ap(c_2Ecombin_2EC(arr(A_27b,A_27a),ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),c_2Elist_2EMAP(A_27b,A_27a)),V1xs)) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),V0fs),V1xs))))))))) # label(ax_thm_2Elist_2ELIST__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3516 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,bool) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),k(A_27a,V0c)),V1l)) <-> c_2Elist_2ENIL(A_27a) = V1l | p(V0c)))))))) # label(conj_thm_2Elist_2EEVERY__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3517 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EHD(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)))) # label(mem_c_2Elist_2EHD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3518 (all V0L (mem(V0L,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V0L)),V1n) = ap(ap(c_2Elist_2ESUM__ACC,V0L),V1n))))) # label(conj_thm_2Elist_2ESUM__ACC__SUM__LEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3519 (all A_27a all A_27b all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V4a (mem(V4a,A_27a) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V5b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0P,V4a),V5b)),ap(ap(V1Q,V4a),V5b)) = ap(f401(A_27a,A_27b,V0P,V4a,V1Q),V5b)))))))) # label(lameq_f401) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3520 (all V0L (mem(V0L,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> ap(c_2Elist_2ESUM,V0L) = ap(ap(c_2Elist_2ESUM__ACC,V0L),c_2Enum_2E0))) # label(conj_thm_2Elist_2ESUM__SUM__ACC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3521 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),bool),c_2Ecombin_2EK(bool,A_27a)),ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n))),c_2Ecombin_2EK(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),V1l) = ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l))))))) # label(conj_thm_2Elist_2ETAKE__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3522 (all A_27b all A_27a all V3x (mem(V3x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b))) -> (all V4y ap(f435(A_27b,A_27a,V3x,V1f),V4y) = ap(ap(V1f,V3x),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4y),V4y))))))) # label(lameq_f435) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3523 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool)))) -> (all V3s (mem(V3s,arr(A_27c,bool)) -> (all V4x f432(A_27c,A_27a,A_27b,V0f,V4x,V3s) = ap(f433(A_27b,A_27c,A_27a,V0f,V3s),V4x)))))) # label(lameq_f433) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3524 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(c_2Eoption_2EOPTION__MAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27a),c_2Epair_2ESND(ty_2Enum_2Enum,A_27a))),ap(ap(c_2Elist_2EINDEX__FIND(A_27a),c_2Enum_2E0),V0P)) = ap(c_2Elist_2EFIND(A_27a),V0P))))) # label(ax_thm_2Elist_2EFIND__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3525 (all A_27a all V2SET__TO__LIST (mem(V2SET__TO__LIST,arr(arr(A_27a,bool),ty_2Elist_2Elist(A_27a))) -> (all V3a ap(f421(A_27a,V2SET__TO__LIST),V3a) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(c_2Epred__set_2EFINITE(A_27a),V3a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V3a),c_2Epred__set_2EEMPTY(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V3a)),ap(V2SET__TO__LIST,ap(c_2Epred__set_2EREST(A_27a),V3a))))),c_2Ebool_2EARB(ty_2Elist_2Elist(A_27a))))))) # label(lameq_f421) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3526 (all A_27a (ne(A_27a) -> (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Elist_2Elist(A_27a)),f386(A_27a)),V0rep)) & mem(V0rep,arr(ty_2Elist_2Elist(A_27a),ty_2Eind__type_2Erecspace(A_27a))))))) # label(ax_thm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3527 (all A_27a all V0L1 (mem(V0L1,ty_2Elist_2Elist(A_27a)) -> (all V1L2 (mem(V1L2,ty_2Elist_2Elist(A_27a)) -> (all V2h ap(f398(A_27a,V0L1,V1L2),V2h) = ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1L2),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V0L1))))))) # label(lameq_f398) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3528 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2l1))) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2l1)),V3l2)))))))))))) # label(conj_thm_2Elist_2Elupdate__append) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3529 (all A_27a (ne(A_27a) -> (all V5e (mem(V5e,A_27a) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7x (mem(V7x,A_27a) -> (all V8l (mem(V8l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V7x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V8l)) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(ap(c_2Elist_2ECONS(A_27a),V7x),V8l)))))))))) & (all V9e (mem(V9e,A_27a) -> (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11x (mem(V11x,A_27a) -> (all V12l (mem(V12l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V9e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10n))),ap(ap(c_2Elist_2ECONS(A_27a),V11x),V12l)) = ap(ap(c_2Elist_2ECONS(A_27a),V11x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V9e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10n))),V12l)))))))))) & (all V2e (mem(V2e,A_27a) -> (all V3x (mem(V3x,A_27a) -> (all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V2e),V4l) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2e),c_2Enum_2E0),ap(ap(c_2Elist_2ECONS(A_27a),V3x),V4l)))))))) & (all V0e (mem(V0e,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))))) # label(conj_thm_2Elist_2ELUPDATE__compute) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3530 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELAST(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)))) # label(mem_c_2Elist_2ELAST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3531 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27a) -> (all V3i (mem(V3i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1xs)) & p(ap(V0P,V2h)) -> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2h),V3i),V1xs)))))))))))))) # label(conj_thm_2Elist_2EIMP__EVERY__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3532 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),V1n)) -> ap(ap(c_2Elist_2ETAKE(A_27a),V1n),V0l) = V0l))))))) # label(conj_thm_2Elist_2ETAKE__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3533 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,ty_2Elist_2Elist(A_27a)) -> (all V2y (mem(V2y,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1x),V2y)) -> ap(c_2Elist_2ELENGTH(A_27a),V1x) = ap(c_2Elist_2ELENGTH(A_27b),V2y)))))))))))) # label(conj_thm_2Elist_2ELIST__REL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3534 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27a,ty_2Enum_2Enum),V0f),c_2Enum_2ESUC)),V1n) = ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n))))))))) # label(conj_thm_2Elist_2ETL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3535 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2Enub(A_27a),V0l)))))) # label(conj_thm_2Elist_2Enub__set) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3536 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0l))) -> ap(c_2Elist_2ELAST(A_27a),V0l) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0l))))))))) # label(conj_thm_2Elist_2Elast__drop) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3537 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELEN(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))))) # label(mem_c_2Elist_2ELEN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3538 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(c_2Elist_2EEL(A_27b),V0n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V2f),V1l)) = ap(V2f,ap(ap(c_2Elist_2EEL(A_27a),V0n),V1l))))))))))))) # label(conj_thm_2Elist_2EEL__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3539 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3540 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f402(A_27b,A_27a,V0P,V1Q)),V2l1),V3l2)) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f406(A_27b,A_27a,V1Q)),V2l1),V3l2)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f404(A_27b,A_27a,V0P)),V2l1),V3l2))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3541 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0h (mem(V0h,A_27b) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Epred__set_2EEMPTY(A_27a) & ap(ap(c_2Epred__set_2EINSERT(A_27b),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1t)) = ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)))))))))) # label(conj_thm_2Elist_2ELIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3542 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EALL__DISTINCT(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))) # label(mem_c_2Elist_2EALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3543 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27b))) -> ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),ap(c_2Elist_2EFLAT(A_27b),V1l)) = ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2EMAP(A_27b,A_27a),V0f)),V1l)))))))))) # label(conj_thm_2Elist_2EMAP__FLAT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3544 (all A_27a (ne(A_27a) -> (all V0ll (mem(V0ll,ty_2Elist_2Elist(A_27a)) -> V0ll = c_2Elist_2ENIL(A_27a) | (exists V1x (mem(V1x,A_27a) & (exists V2l (V0ll = ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l) & mem(V2l,ty_2Elist_2Elist(A_27a)))))))))) # label(conj_thm_2Elist_2ESNOC__CASES) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3545 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0pl (mem(V0pl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0pl) = ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0pl))) & ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0pl) = ap(c_2Elist_2ELENGTH(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0pl))))))))) # label(conj_thm_2Elist_2ELENGTH__UNZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3546 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V2a0 (mem(V2a0,A_27a) -> (all V3a1 (mem(V3a1,ty_2Elist_2Elist(A_27a)) -> (all V4v (mem(V4v,A_27b) -> (all V5f (mem(V5f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> ap(ap(V5f,V2a0),V3a1) = ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27a),V2a0),V3a1)),V4v),V5f))))))))) & (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),c_2Elist_2ENIL(A_27a)),V0v),V1f) = V0v)))))))) # label(ax_thm_2Elist_2Elist__case__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3547 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2k),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(c_2Elist_2EREVERSE(A_27a),V1ls)))),V2k)) -> p(ap(V0P,ap(ap(c_2Elist_2EEL(A_27a),V2k),V1ls)))))))))))) # label(conj_thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3548 (all A_27a (ne(A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Elist_2ESNOC(A_27a),ap(V1f,V2n)),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)))))) & (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),c_2Enum_2E0))))) # label(ax_thm_2Elist_2EGENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3549 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27c)) -> (all V2g (mem(V2g,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V0f),V1l)),V2g) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V1l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),A_27b),V2g),V0f)))))))))))))) # label(conj_thm_2Elist_2ELIST__BIND__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3550 (all A_27a (ne(A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),V3t)) & p(ap(V1P,V2h))))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> ($T <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),c_2Elist_2ENIL(A_27a)))))))) # label(ax_thm_2Elist_2EEVERY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3551 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2f (mem(V2f,arr(A_27c,A_27b)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27c)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f408(A_27b,A_27a,V0R)),V1l1),ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V2f),V3l2))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27c),f410(A_27c,A_27b,A_27a,V0R,V2f)),V1l1),V3l2))))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__MAP2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3552 (all A_27a (ne(A_27a) -> (all V0ys (mem(V0ys,ty_2Elist_2Elist(A_27a)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1k),ap(ap(c_2Elist_2ESNOC(A_27a),V3y),V0ys)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1k),ap(c_2Elist_2ELENGTH(A_27a),V0ys))),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V0ys)),ap(ap(c_2Elist_2ESNOC(A_27a),V3y),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1k),V0ys))))))))))))) # label(conj_thm_2Elist_2ELUPDATE__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3553 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) -> p(ap(c_2Erelation_2Etotal(ty_2Elist_2Elist(A_27a)),ap(c_2Erelation_2ERC(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R))))))))) # label(conj_thm_2Elist_2ESHORTLEX__total) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3554 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2x (mem(V2x,A_27b) -> ((exists V3x0 (ap(V0f,V3x0) = V2x & ap(ap(c_2Elist_2ECONS(A_27a),V3x0),c_2Elist_2ENIL(A_27a)) = V1l & mem(V3x0,A_27a))) <-> ap(ap(c_2Elist_2ECONS(A_27b),V2x),c_2Elist_2ENIL(A_27b)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l)))))))))))) # label(conj_thm_2Elist_2EMAP__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3555 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Elist_2Elist(A_27a)) -> (all V1v (mem(V1v,A_27b) -> (all V2f (mem(V2f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))) -> (all V3v_27 (mem(V3v_27,A_27b) -> (c_2Elist_2ENIL(A_27a) = V0x & V1v = V3v_27 | (exists V4a ((exists V5l (ap(ap(V2f,V4a),V5l) = V3v_27 & ap(ap(c_2Elist_2ECONS(A_27a),V4a),V5l) = V0x & mem(V5l,ty_2Elist_2Elist(A_27a)))) & mem(V4a,A_27a))) <-> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V0x),V1v),V2f) = V3v_27))))))))))))) # label(conj_thm_2Elist_2Elist__case__eq) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3556 (all A_27a (ne(A_27a) -> ap(c_2Elist_2ELENGTH(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Enum_2E0 & (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(A_27a),V1t)) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))))) # label(ax_thm_2Elist_2ELENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3557 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2ELIST__APPLY(A_27a,A_27b),arr(ty_2Elist_2Elist(arr(A_27b,A_27a)),arr(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)))))))) # label(mem_c_2Elist_2ELIST__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3558 (all A_27a (ne(A_27a) -> (all V0P1 (mem(V0P1,arr(A_27a,bool)) -> (all V1P2 (mem(V1P2,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),V2l)) -> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),ap(ap(c_2Elist_2EFILTER(A_27a),V1P2),V2l)))))))))))) # label(conj_thm_2Elist_2EEVERY__FILTER__IMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3559 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Elist_2Elist(A_27a),A_27b)),f389(A_27b,A_27a,V0x,V1f))))))))))) # label(conj_thm_2Elist_2Elist__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3560 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,ty_2Elist_2Elist(A_27a)) -> (all V3y (mem(V3y,ty_2Elist_2Elist(A_27a)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R1,V4x),V5y)) -> p(ap(ap(V1R2,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R1),V2x),V3y)) -> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V1R2),V2x),V3y)))))))))))))) # label(conj_thm_2Elist_2ESHORTLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3561 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> c_2Elist_2ENIL(A_27a) = V0l | (exists V1h ((exists V2t (V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t) & mem(V2t,ty_2Elist_2Elist(A_27a)))) & mem(V1h,A_27a))))))) # label(conj_thm_2Elist_2Elist__nchotomy) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3562 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))))) & (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))) = ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))))))))))) # label(conj_thm_2Elist_2EFRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3563 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (c_2Elist_2ENIL(A_27a) != V0l -> ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) = ap(V1f,ap(c_2Elist_2ELAST(A_27a),V0l))))))))))) # label(conj_thm_2Elist_2ELAST__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.37 3564 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n1 (mem(V1n1,ty_2Enum_2Enum) -> (all V2n2 (mem(V2n2,ty_2Enum_2Enum) -> ((exists V3l1 (mem(V3l1,ty_2Elist_2Elist(A_27a)) & (exists V4l2 (mem(V4l2,ty_2Elist_2Elist(A_27a)) & V2n2 = ap(c_2Elist_2ELENGTH(A_27a),V4l2) & V0l = ap(ap(c_2Elist_2EAPPEND(A_27a),V3l1),V4l2) & ap(c_2Elist_2ELENGTH(A_27a),V3l1) = V1n1)))) <-> ap(ap(c_2Earithmetic_2E_2B,V1n1),V2n2) = ap(c_2Elist_2ELENGTH(A_27a),V0l)))))))))) # label(conj_thm_2Elist_2ELENGTH__EQ__SUM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3565 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> (all V1h (mem(V1h,A_27b) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(V0f,V1h)),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V2t),V0f)) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V1h),V2t)),V0f) & ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),c_2Elist_2ENIL(A_27b)),V0f) = c_2Elist_2ENIL(A_27a))))))))))) # label(conj_thm_2Elist_2ELIST__BIND__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3566 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V1ls)))))))))) # label(conj_thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3567 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),V0l1))),ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f450(A_27a,V0l1)),V1l2)))))))))) # label(conj_thm_2Elist_2Elength__nub__append) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3568 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)) = ap(ap(c_2Elist_2ESNOC(A_27b),ap(V0f,V1x)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l)))))))))))) # label(conj_thm_2Elist_2EMAP__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3569 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0fs (mem(V0fs,ty_2Elist_2Elist(arr(A_27c,A_27a))) -> (all V1gs (mem(V1gs,ty_2Elist_2Elist(arr(A_27b,A_27c))) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27c),V0fs),ap(ap(c_2Elist_2ELIST__APPLY(A_27c,A_27b),V1gs),V2xs)) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ELIST__APPLY(arr(A_27b,A_27a),arr(A_27b,A_27c)),ap(ap(c_2Elist_2ELIST__APPLY(arr(arr(A_27b,A_27c),arr(A_27b,A_27a)),arr(A_27c,A_27a)),ap(ap(c_2Elist_2ECONS(arr(arr(A_27c,A_27a),arr(arr(A_27b,A_27c),arr(A_27b,A_27a)))),c_2Ecombin_2Eo(A_27b,A_27a,A_27c)),c_2Elist_2ENIL(arr(arr(A_27c,A_27a),arr(arr(A_27b,A_27c),arr(A_27b,A_27a)))))),V0fs)),V1gs)),V2xs))))))))))))) # label(conj_thm_2Elist_2ELIST__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3570 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2x),V1n)) -> ap(ap(c_2Elist_2EEL(A_27a),V2x),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = ap(V0f,V2x)))))))))) # label(conj_thm_2Elist_2EEL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3571 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0x),c_2Elist_2ENIL(A_27b))),V1f) = ap(V1f,V0x))))))))) # label(conj_thm_2Elist_2ESINGL__LIST__APPLY__L) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3572 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V0l)) = ap(ap(c_2Elist_2EFILTER(A_27a),V1P),ap(c_2Elist_2EREVERSE(A_27a),V0l)))))))) # label(conj_thm_2Elist_2EFILTER__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3573 (all A_27a all A_27b all V4a (mem(V4a,A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V5b ap(f407(A_27a,A_27b,V4a,V0R),V5b) = ap(ap(V0R,V4a),V5b)))))) # label(lameq_f407) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3574 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1xs))),V0n),ap(c_2Elist_2ELENGTH(A_27a),V1xs)))))))) # label(conj_thm_2Elist_2ELENGTH__TAKE__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3575 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) -> ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)) = ap(c_2Elist_2ELENGTH(A_27a),V0ls)))))) # label(conj_thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3576 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1x (mem(V1x,ty_2Elist_2Elist(A_27b)) -> c_2Elist_2ENIL(A_27a) = ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V0f),V1x),c_2Elist_2ENIL(A_27c)))))))))))) # label(conj_thm_2Elist_2EMAP2__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3577 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((exists V3i (p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n)) & p(ap(V0P,ap(V1f,V3i))) & mem(V3i,ty_2Enum_2Enum))) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)))))))))))) # label(conj_thm_2Elist_2EEXISTS__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3578 (all A_27a all V1a0_27 ap(f386(A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f385(A_27a,V1a0_27))) # label(lameq_f386) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3579 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l))) -> p(ap(V1P,ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l)))))) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),V0l))))))))) # label(conj_thm_2Elist_2EEVERY__EL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3580 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EUNZIP(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))))))) # label(mem_c_2Elist_2EUNZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3581 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,V1n)),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,V1n)) & ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),c_2Enum_2E0) = c_2Elist_2ENIL(A_27a))))))) # label(conj_thm_2Elist_2EGENLIST__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3582 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27b)) -> (all V1f (mem(V1f,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EMAP(A_27b,ty_2Elist_2Elist(A_27a)),V1f),V0l)) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0l),V1f))))))))) # label(ax_thm_2Elist_2ELIST__BIND__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3583 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1l1),V2l2)) -> ap(c_2Elist_2ELENGTH(A_27a),V1l1) = ap(c_2Elist_2ELENGTH(A_27b),V2l2)))))))))))) # label(conj_thm_2Elist_2EEVERY2__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3584 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool)))) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> (all V2s (mem(V2s,arr(A_27c,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27c),V2s),ap(c_2Epred__set_2EBIGUNION(A_27c),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27c,bool)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27c,bool)),V0f)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V1ls)))) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27c,bool)),f434(A_27a,A_27b,A_27c,V0f)),V2s),V1ls))))))))))))) # label(conj_thm_2Elist_2EFOLDL__UNION__BIGUNION__paired) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3585 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27a),V0f),ap(c_2Epred__set_2Ecount,V1n)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3586 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EoEL(A_27a),V1n),V0xs) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0xs))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(c_2Elist_2EEL(A_27a),V1n),V0xs))),c_2Eoption_2ENONE(A_27a)))))))) # label(conj_thm_2Elist_2EoEL__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3587 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) != V0l -> V0l = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EFRONT(A_27a),V0l)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Elist_2ELAST(A_27a),V0l)),c_2Elist_2ENIL(A_27a)))))))) # label(conj_thm_2Elist_2EAPPEND__FRONT__LAST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3588 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)),V2l) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V2l)),ap(ap(c_2Elist_2ETAKE(A_27a),V1m),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V2l))))))))))) # label(conj_thm_2Elist_2ETAKE__SUM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3589 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)) = ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l)))))))))) # label(conj_thm_2Elist_2ELIST__TO__SET__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3590 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27b) -> ((exists V3y (mem(V3y,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) & V2x = ap(V1f,V3y))) <-> p(ap(ap(c_2Ebool_2EIN(A_27b),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l))))))))))))))) # label(conj_thm_2Elist_2EMEM__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3591 (all A_27b all A_27a all V1f (mem(V1f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V3t0 (mem(V3t0,ty_2Elist_2Elist(A_27b)) -> (all V4h ap(ap(c_2Eoption_2EOPTION__BIND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V1f),V3t0)),f461(A_27a,V4h)) = ap(f462(A_27b,A_27a,V1f,V3t0),V4h)))))) # label(lameq_f462) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3592 (all A_27a (ne(A_27a) -> mem(c_2Elist_2Elist__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum))))) # label(mem_c_2Elist_2Elist__size) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3593 (all A_27a (ne(A_27a) -> (all V0M (mem(V0M,ty_2Elist_2Elist(A_27a)) -> (all V1N (mem(V1N,ty_2Elist_2Elist(A_27a)) -> (all V2f (mem(V2f,arr(A_27a,ty_2Enum_2Enum)) -> (all V3f_27 (mem(V3f_27,arr(A_27a,ty_2Enum_2Enum)) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1N))) -> ap(V2f,V4x) = ap(V3f_27,V4x)))) & V0M = V1N -> ap(ap(c_2Elist_2Elist__size(A_27a),V2f),V0M) = ap(ap(c_2Elist_2Elist__size(A_27a),V3f_27),V1N)))))))))))) # label(conj_thm_2Elist_2Elist__size__cong) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3594 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0l)) = V0l)))))) # label(conj_thm_2Elist_2EZIP__UNZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3595 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l1)) -> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V2l2) = ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2))))))))))) # label(conj_thm_2Elist_2EdropWhile__APPEND__EVERY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3596 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EFILTER(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EFILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3597 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) = V0x <-> p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V0x),c_2Elist_2ENIL(A_27a)))))))) # label(conj_thm_2Elist_2EisPREFIX__NILR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3598 (all A_27a all A_27b all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(f451(A_27a,A_27b,V1f,V2x),V3y) = ap(ap(c_2Emin_2E_3D(A_27a),V2x),ap(V1f,V3y))))))) # label(lameq_f451) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3599 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2g (mem(V2g,arr(ty_2Enum_2Enum,A_27a)) -> (ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n) = ap(ap(c_2Elist_2EGENLIST(A_27a),V2g),V0n) <-> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3x),V0n)) -> ap(V1f,V3x) = ap(V2g,V3x))))))))))))) # label(conj_thm_2Elist_2EGENLIST__FUN__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3600 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EFRONT(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2EFRONT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3601 (all A_27a all V2_27list_27 (mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool)) -> (all V3a0_27 ap(f384(A_27a,V2_27list_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),c_2Enum_2E0),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))),ap(c_2Ebool_2E_3F(A_27a),f383(A_27a,V2_27list_27,V3a0_27)))),ap(V2_27list_27,V3a0_27))))) # label(lameq_f384) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3602 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> V0l = ap(c_2Elist_2EREVERSE(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)))))) # label(conj_thm_2Elist_2EREVERSE__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3603 (all V0acc (mem(V0acc,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ESUM__ACC,c_2Elist_2ENIL(ty_2Enum_2Enum)),V0acc) = V0acc)) # label(ax_thm_2Elist_2ESUM__ACC__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3604 (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> (all V3acc (mem(V3acc,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ESUM__ACC,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V1h),V2t)),V3acc) = ap(ap(c_2Elist_2ESUM__ACC,V2t),ap(ap(c_2Earithmetic_2E_2B,V1h),V3acc)))))))) # label(ax_thm_2Elist_2ESUM__ACC__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3605 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),V1n),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n))))))) # label(conj_thm_2Elist_2EGENLIST__GENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3606 (all A_27a all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V4h_27 f423(A_27a,V1h,V4h_27,V2t) = ap(f424(A_27a,V1h,V2t),V4h_27)))))) # label(lameq_f424) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3607 (all A_27b all A_27a all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V3x ap(V0P,ap(V1f,V3x)) = ap(f391(A_27b,A_27a,V1f,V0P),V3x)))))) # label(lameq_f391) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3608 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ETAKE(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2ETAKE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3609 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n))) <-> (all V3i (mem(V3i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n)) -> p(ap(V0P,ap(V1f,V3i))))))))))))))) # label(conj_thm_2Elist_2EEVERY__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3610 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EFIND(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a)))))) # label(mem_c_2Elist_2EFIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3611 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l)) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) -> p(ap(V1Q,V3x))))) -> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l))))))))))) # label(conj_thm_2Elist_2EEVERY__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3612 (all A_27b all A_27a all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V8a f405(A_27a,A_27b,V8a,V1Q) = ap(f406(A_27b,A_27a,V1Q),V8a)))) # label(lameq_f406) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3613 (all A_27a (ne(A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(V1P,V2h)),ap(ap(c_2Elist_2EdropWhile(A_27a),V1P),V3t)),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(c_2Elist_2EdropWhile(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a))))) # label(ax_thm_2Elist_2EdropWhile__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3614 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1L (mem(V1L,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L)) <-> ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0e)),V1L) = ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a))))))))) # label(conj_thm_2Elist_2EUNIQUE__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3615 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2Elist__CASE(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),arr(A_27b,arr(arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)),A_27b)))))))) # label(mem_c_2Elist_2Elist__CASE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3616 (all A_27a all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2x ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) = ap(f449(A_27a,V1l2),V2x)))) # label(lameq_f449) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3617 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3h1 (mem(V3h1,A_27a) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V5h2 (mem(V5h2,A_27a) -> (all V6t2 (mem(V6t2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),c_2Elist_2ENIL(A_27a))) <-> $F) & (p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V4t1),V6t2)) & V3h1 = V5h2 <-> p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27a),V5h2),V6t2)))) & (p(ap(ap(c_2Elist_2EisPREFIX(A_27a),c_2Elist_2ENIL(A_27a)),V0l)) <-> $T))))))))))))))))) # label(conj_thm_2Elist_2EisPREFIX__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3618 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ((all V2e (mem(V2e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) -> p(ap(V0P,V2e))))) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l))))))))) # label(conj_thm_2Elist_2EEVERY__MEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3619 (all A_27a all A_27b all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1b ap(f465(A_27a,A_27b,V0l),V1b) = f464(A_27b,A_27a,V1b,V0l)))) # label(lameq_f465) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3620 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1a0 (mem(V1a0,ty_2Elist_2Elist(A_27a)) -> (all V2a1 (mem(V2a1,ty_2Elist_2Elist(A_27b)) -> (c_2Elist_2ENIL(A_27a) = V1a0 & c_2Elist_2ENIL(A_27b) = V2a1 | (exists V3h1 (mem(V3h1,A_27a) & (exists V4h2 ((exists V5t1 ((exists V6t2 (mem(V6t2,ty_2Elist_2Elist(A_27b)) & ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V5t1) = V1a0 & V2a1 = ap(ap(c_2Elist_2ECONS(A_27b),V4h2),V6t2) & p(ap(ap(V0R,V3h1),V4h2)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V5t1),V6t2)))) & mem(V5t1,ty_2Elist_2Elist(A_27a)))) & mem(V4h2,A_27b))))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1a0),V2a1))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__cases) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3621 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)) = ap(c_2Elist_2ELENGTH(A_27a),V0ls) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls))))))) # label(conj_thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3622 (all A_27a all V0R ap(f420(A_27a),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(arr(A_27a,bool)),V0R)),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f419(A_27a,V0R)))) # label(lameq_f420) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3623 (all A_27a (ne(A_27a) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Elist_2ECONS(A_27a),ap(V2f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V4l)) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4l))))))) & (all V5f (mem(V5f,arr(ty_2Enum_2Enum,A_27a)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7l (mem(V7l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V5f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),V7l) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V5f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(ap(c_2Elist_2ECONS(A_27a),ap(V5f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n)))),V7l)))))))) & (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> V1l = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),c_2Enum_2E0),V1l))))))) # label(conj_thm_2Elist_2EGENLIST__AUX__compute) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3624 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) <-> (exists V2pfx (mem(V2pfx,ty_2Elist_2Elist(A_27a)) & (exists V3sfx (ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2pfx),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3sfx) = V1l & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3sfx))) & mem(V3sfx,ty_2Elist_2Elist(A_27a))))))))))))) # label(conj_thm_2Elist_2EMEM__SPLIT__APPEND__last) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3625 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R)))))))) # label(conj_thm_2Elist_2EWF__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3626 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EFOLDR(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(A_27b,arr(ty_2Elist_2Elist(A_27a),A_27b)))))))) # label(mem_c_2Elist_2EFOLDR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3627 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),arr(A_27b,A_27b)))) -> (exists V2fn ((all V3x (mem(V3x,A_27a) -> (all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> ap(V2fn,ap(ap(c_2Elist_2ESNOC(A_27a),V3x),V4l)) = ap(ap(ap(V1f,V3x),V4l),ap(V2fn,V4l)))))) & ap(V2fn,c_2Elist_2ENIL(A_27a)) = V0e & mem(V2fn,arr(ty_2Elist_2Elist(A_27a),A_27b)))))))))))) # label(conj_thm_2Elist_2ESNOC__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3628 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2e (mem(V2e,A_27a) -> (ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) <-> ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a)) = V0l1 & V1l2 = c_2Elist_2ENIL(A_27a) | ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a)) = V1l2 & c_2Elist_2ENIL(A_27a) = V0l1))))))))) # label(conj_thm_2Elist_2EAPPEND__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3629 (all A_27a (ne(A_27a) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (all V3h (mem(V3h,A_27a) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1l1)),V2l2) = ap(ap(c_2Elist_2ECONS(A_27a),V3h),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)))))))) & (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> V0l = ap(ap(c_2Elist_2EAPPEND(A_27a),c_2Elist_2ENIL(A_27a)),V0l))))) # label(ax_thm_2Elist_2EAPPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3630 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3i (mem(V3i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2y),V3i),V0l)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) | V2y = V1x))))))))))) # label(conj_thm_2Elist_2EMEM__LUPDATE__E) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3631 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> (all V3ls (mem(V3ls,ty_2Elist_2Elist(A_27a)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V3ls))),ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V1Q),V3ls))))))))))))) # label(conj_thm_2Elist_2ELENGTH__FILTER__LEQ__MONO) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3632 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27c,A_27a)) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27c)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27c,arr(A_27b,bool),A_27a),V0R),V1f)),V2l1),V3l2)) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2EMAP(A_27c,A_27a),V1f),V2l1)),V3l2))))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__MAP1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3633 (all A_27a all V1P2 (mem(V1P2,arr(A_27a,bool)) -> (all V0P1 (mem(V0P1,arr(A_27a,bool)) -> (all V3x ap(f397(A_27a,V1P2,V0P1),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P2,V3x)),ap(V0P1,V3x))))))) # label(lameq_f397) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3634 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l))) -> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2ETL(A_27a),V0l)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(conj_thm_2Elist_2ELENGTH__TL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3635 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1L (mem(V1L,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EFLAT(A_27a),V1L)))) <-> (exists V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) & p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V2l),ap(c_2Elist_2ELIST__TO__SET(ty_2Elist_2Elist(A_27a)),V1L)))))))))))) # label(conj_thm_2Elist_2EMEM__FLAT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3636 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (V0l = c_2Elist_2ENIL(A_27a) <-> p(ap(c_2Elist_2ENULL(A_27a),V0l))))))) # label(conj_thm_2Elist_2ENULL__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3637 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l) <-> p(ap(c_2Elist_2ENULL(A_27a),V0l))))))) # label(conj_thm_2Elist_2ENULL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3638 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1x (mem(V1x,A_27a) -> (all V2ls (mem(V2ls,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2ls))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V1x)),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V2ls))))))))))))) # label(conj_thm_2Elist_2ESUM__MAP__MEM__bound) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3639 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = V1n)))))) # label(conj_thm_2Elist_2ELENGTH__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3640 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2ESNOC(ty_2Enum_2Enum),V0x),V1l)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V1l)),V0x))))) # label(conj_thm_2Elist_2ESUM__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3641 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27a,A_27b))) -> (all V1e (mem(V1e,A_27b) -> (all V2x (mem(V2x,A_27a) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V3l)) = ap(ap(V0f,ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),V3l)),V2x))))))))))))) # label(conj_thm_2Elist_2EFOLDL__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3642 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),bool),c_2Ecombin_2EK(bool,A_27a)),ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n))),ap(c_2Ecombin_2EK(arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))),V1l) = ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l))))))) # label(conj_thm_2Elist_2EDROP__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3643 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool))) -> (all V1k (mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V0P),V1k),c_2Elist_2ENIL(A_27b)) = ap(ap(V1k,c_2Elist_2ENIL(A_27b)),c_2Elist_2ENIL(A_27b)))))) & (all V2P (mem(V2P,arr(ty_2Enum_2Enum,arr(A_27b,bool))) -> (all V3k (mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V4h (mem(V4h,A_27b) -> (all V5t (mem(V5t,ty_2Elist_2Elist(A_27b)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(V2P,c_2Enum_2E0),V4h)),ap(ap(V3k,c_2Elist_2ENIL(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V4h),V5t))),ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27b,bool),ty_2Enum_2Enum),V2P),c_2Enum_2ESUC)),f439(A_27a,A_27b,V3k,V4h)),V5t)) = ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V2P),V3k),ap(ap(c_2Elist_2ECONS(A_27b),V4h),V5t)))))))))))))) # label(ax_thm_2Elist_2EsplitAtPki__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3644 (all A_27a (ne(A_27a) -> (all V1P (mem(V1P,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERYi(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) <-> p(ap(ap(c_2Elist_2EEVERYi(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),ty_2Enum_2Enum),V1P),c_2Enum_2ESUC)),V3t)) & p(ap(ap(V1P,c_2Enum_2E0),V2h))))))))) & (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> ($T <-> p(ap(ap(c_2Elist_2EEVERYi(A_27a),V0P),c_2Elist_2ENIL(A_27a)))))))) # label(ax_thm_2Elist_2EEVERYi__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3645 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2P (mem(V2P,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3k (mem(V3k,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27b))) -> (p(ap(ap(c_2Elist_2EEVERYi(A_27a),f440(A_27a,V2P)),V0l1)) & (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V1l2))) -> p(ap(ap(V2P,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(c_2Elist_2EHD(A_27a),V1l2)))) -> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27b,A_27a),V2P),V3k),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(V3k,V0l1),V1l2)))))))))))))) # label(conj_thm_2Elist_2EsplitAtPki__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3646 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1t)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),c_2Elist_2ENIL(A_27a))) = ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))) & c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EREVERSE(A_27a),c_2Elist_2ENIL(A_27a)))) # label(ax_thm_2Elist_2EREVERSE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3647 (all A_27b all A_27a all V0l f465(A_27a,A_27b,V0l) = ap(f466(A_27b,A_27a),V0l)) # label(lameq_f466) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3648 (all A_27b all A_27a all V0x (mem(V0x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))) -> (all V2fn1 ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),ap(V2fn1,c_2Elist_2ENIL(A_27a))),V0x)),ap(c_2Ebool_2E_21(A_27a),f388(A_27b,A_27a,V2fn1,V1f))) = ap(f389(A_27b,A_27a,V0x,V1f),V2fn1)))))) # label(lameq_f389) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3649 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0),V0l) = ap(c_2Elist_2EHD(A_27a),V0l))) & (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EEL(A_27a),V2n),ap(c_2Elist_2ETL(A_27a),V1l)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Enum_2ESUC,V2n)),V1l))))))) # label(ax_thm_2Elist_2EEL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3650 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (all V2f (mem(V2f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c)))) -> (all V3a (mem(V3a,A_27c) -> ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f415(A_27a,A_27b,A_27c,V2f)),V3a),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V2f),V3a),V0l1),V1l2)))))))))))))))) # label(conj_thm_2Elist_2EFOLDL2__FOLDL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3651 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V0l)) = V1x)))))) # label(conj_thm_2Elist_2EEL__LENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3652 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((all V3i (mem(V3i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n)) -> ap(V1f,V3i) = ap(ap(c_2Elist_2EEL(A_27a),V3i),V0ls)))) & V2n = ap(c_2Elist_2ELENGTH(A_27a),V0ls) -> ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n) = V0ls))))))))) # label(conj_thm_2Elist_2EGENLIST__EL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3653 (all A_27a (ne(A_27a) -> ap(ap(c_2Erelation_2EWFREC(arr(A_27a,bool),ty_2Elist_2Elist(A_27a)),ap(c_2Emin_2E_40(arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))),f420(A_27a))),f422(A_27a)) = c_2Elist_2ESET__TO__LIST(A_27a))) # label(ax_thm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3654 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2ETAKE(A_27a),c_2Enum_2E0),V0l))))) # label(conj_thm_2Elist_2ETAKE__0) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3655 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V2l1),V3l2)) & (all V4x (mem(V4x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V4x),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V2l1),V3l2))))) & p(ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0P),V4x)) -> p(ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V1Q),V4x))))) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1Q),V2l1),V3l2))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3656 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),ap(c_2Elist_2EFRONT(A_27a),V1t))))))))) # label(ax_thm_2Elist_2EFRONT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3657 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)))),V2l2)) = V1x)))))))) # label(conj_thm_2Elist_2Eel__append3) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3658 (all A_27a (ne(A_27a) -> mem(c_2Elist_2Enub(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) # label(mem_c_2Elist_2Enub) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3659 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b))) -> (all V2e (mem(V2e,A_27b) -> ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f),V2e),ap(c_2Elist_2EZIP(A_27a,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V0ls),V0ls))) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),f436(A_27a,A_27b,V1f)),V2e),V0ls))))))))))) # label(conj_thm_2Elist_2EFOLDL__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3660 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0s),c_2Epred__set_2EEMPTY(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Elist_2ESET__TO__LIST(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s))))))))) # label(conj_thm_2Elist_2ESET__TO__LIST__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3661 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Enum_2Enum),V0c)),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2s)))),V2s) = ap(ap(ap(c_2Elist_2EPAD__LEFT(A_27a),V0c),V1n),V2s))))))))) # label(ax_thm_2Elist_2EPAD__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3662 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELRC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Elist_2ELRC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3663 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1f),V0s) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1f),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)))))))))) # label(conj_thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3664 (all A_27c all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27c,A_27b)) -> (all V6a ap(f410(A_27c,A_27b,A_27a,V0R,V2f),V6a) = f409(A_27b,A_27a,A_27c,V6a,V0R,V2f)))))) # label(lameq_f410) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3665 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2e (mem(V2e,A_27a) -> (p(ap(c_2Ecombin_2ECOMM(A_27a,A_27a),V0f)) & p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) -> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27a),V0f),V2e),V1l) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27a),V0f),V2e),V1l)))))))))) # label(conj_thm_2Elist_2EFOLDL__EQ__FOLDR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3666 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0ls)))))) # label(conj_thm_2Elist_2ELIST__TO__SET__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3667 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1l_27 (mem(V1l_27,ty_2Elist_2Elist(A_27a)) -> (all V2b (mem(V2b,A_27b) -> (all V3b_27 (mem(V3b_27,A_27b) -> (all V4f (mem(V4f,arr(A_27b,arr(A_27a,A_27b))) -> (all V5f_27 (mem(V5f_27,arr(A_27b,arr(A_27a,A_27b))) -> (V1l_27 = V0l & (all V6x (mem(V6x,A_27a) -> (all V7a (mem(V7a,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l_27))) -> ap(ap(V5f_27,V7a),V6x) = ap(ap(V4f,V7a),V6x)))))) & V3b_27 = V2b -> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V5f_27),V3b_27),V1l_27) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V4f),V2b),V0l)))))))))))))))))) # label(conj_thm_2Elist_2EFOLDL__CONG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3668 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EPAD__LEFT(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) # label(mem_c_2Elist_2EPAD__LEFT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3669 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0l),c_2Eoption_2ENONE(A_27a)),f463(A_27a)) = ap(c_2Elist_2EoHD(A_27a),V0l))))) # label(ax_thm_2Elist_2EoHD__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3670 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> V0l = c_2Elist_2ENIL(A_27a) | (exists V1h (mem(V1h,A_27a) & (exists V2t (V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t) & mem(V2t,ty_2Elist_2Elist(A_27a)))))))))) # label(conj_thm_2Elist_2Elist__CASES) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3671 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,ty_2Elist_2Elist(A_27a)) -> (all V1t (mem(V1t,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27a)),V0h),V1t)) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0h),ap(c_2Elist_2EFLAT(A_27a),V1t)))))) & c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EFLAT(A_27a),c_2Elist_2ENIL(ty_2Elist_2Elist(A_27a))))) # label(ax_thm_2Elist_2EFLAT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3672 (all A_27a all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V3h1 (mem(V3h1,A_27a) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V6h2 ap(f446(A_27a,V2R,V3h1,V4t1),V6h2) = f445(A_27a,V6h2,V2R,V3h1,V4t1)))))))) # label(lameq_f446) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3673 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l1_27 (mem(V1l1_27,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (all V3l2_27 (mem(V3l2_27,ty_2Elist_2Elist(A_27b)) -> (all V4P (mem(V4P,arr(A_27a,arr(A_27b,bool))) -> (all V5P_27 (mem(V5P_27,arr(A_27a,arr(A_27b,bool))) -> (V0l1 = V1l1_27 & V3l2_27 = V2l2 & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V7y),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27))) -> (p(ap(ap(V5P_27,V6x),V7y)) <-> p(ap(ap(V4P,V6x),V7y)))))))) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V5P_27),V1l1_27),V3l2_27)) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V4P),V0l1),V2l2)))))))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__cong) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3674 (all A_27b all A_27a all A_27c all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27c,A_27a)) -> (all V6x f455(A_27a,A_27c,A_27b,V0P,V1f,V6x) = ap(f456(A_27b,A_27a,A_27c,V0P,V1f),V6x)))))) # label(lameq_f456) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3675 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> c_2Elist_2ENIL(A_27c) = ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)))) & (all V1f (mem(V1f,arr(A_27d,arr(A_27e,A_27f))) -> (all V2h1 (mem(V2h1,A_27d) -> (all V3t1 (mem(V3t1,ty_2Elist_2Elist(A_27d)) -> (all V4h2 (mem(V4h2,A_27e) -> (all V5t2 (mem(V5t2,ty_2Elist_2Elist(A_27e)) -> ap(ap(ap(c_2Elist_2EMAP2(A_27f,A_27d,A_27e),V1f),ap(ap(c_2Elist_2ECONS(A_27d),V2h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27e),V4h2),V5t2)) = ap(ap(c_2Elist_2ECONS(A_27f),ap(ap(V1f,V2h1),V4h2)),ap(ap(ap(c_2Elist_2EMAP2(A_27f,A_27d,A_27e),V1f),V3t1),V5t2)))))))))))))))))))))))) # label(conj_thm_2Elist_2EMAP2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3676 (all A_27a all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V2x ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) = ap(f450(A_27a,V0l1),V2x)))) # label(lameq_f450) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3677 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1ls))))))))) # label(conj_thm_2Elist_2EdropWhile__eq__nil) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3678 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)))))))))))) # label(conj_thm_2Elist_2EMEM__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3679 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (ap(c_2Elist_2EREVERSE(A_27a),V0l1) = ap(c_2Elist_2EREVERSE(A_27a),V1l2) <-> V1l2 = V0l1))))))) # label(conj_thm_2Elist_2EREVERSE__11) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3680 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ELLEX(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))))) # label(mem_c_2Elist_2ELLEX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3681 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1ls)) -> -p(ap(V0P,ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls))))))))))) # label(conj_thm_2Elist_2EHD__dropWhile) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3682 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Enum_2Enum)) -> (all V2ls (mem(V2ls,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V2ls))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1g),V2ls))) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),f453(A_27a,V0f,V1g)),V2ls)))))))))) # label(conj_thm_2Elist_2ESUM__MAP__PLUS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3683 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l)) <-> -p(ap(ap(c_2Elist_2EEVERY(A_27a),f392(A_27a,V0P)),V1l))))))))) # label(conj_thm_2Elist_2EEXISTS__NOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3684 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f449(A_27a,V1l2)),V0l1))),ap(c_2Elist_2Enub(A_27a),V1l2)))))))) # label(conj_thm_2Elist_2Enub__append) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3685 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> (p(ap(ap(c_2Elist_2EEVERY(ty_2Elist_2Elist(A_27a)),ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),c_2Elist_2ENIL(A_27a))),V0ls)) <-> c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EFLAT(A_27a),V0ls)))))) # label(conj_thm_2Elist_2EFLAT__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3686 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27c,A_27a)) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27c)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> (all V4Q (mem(V4Q,arr(A_27c,arr(A_27d,bool))) -> (all V5g (mem(V5g,arr(A_27b,A_27d)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),f456(A_27b,A_27a,A_27c,V0P,V1f)),V2l1),V3l2)) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27c,A_27a),V1f),V2l1)),V3l2))) & (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V4Q),V2l1),ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V5g),V3l2))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),f458(A_27b,A_27d,A_27c,V4Q,V5g)),V2l1),V3l2))))))))))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3687 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l)) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3688 (all A_27a (ne(A_27a) -> (all V0a0 (mem(V0a0,A_27a) -> (all V1a1 (mem(V1a1,ty_2Elist_2Elist(A_27a)) -> (all V2a0_27 (mem(V2a0_27,A_27a) -> (all V3a1_27 (mem(V3a1_27,ty_2Elist_2Elist(A_27a)) -> (V3a1_27 = V1a1 & V0a0 = V2a0_27 <-> ap(ap(c_2Elist_2ECONS(A_27a),V2a0_27),V3a1_27) = ap(ap(c_2Elist_2ECONS(A_27a),V0a0),V1a1)))))))))))) # label(conj_thm_2Elist_2ECONS__11) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3689 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)) = V0s))))) # label(conj_thm_2Elist_2ESET__TO__LIST__INV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3690 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (-p(ap(c_2Elist_2ENULL(A_27a),V0l)) -> V0l = ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Elist_2EHD(A_27a),V0l)),ap(c_2Elist_2ETL(A_27a),V0l))))))) # label(conj_thm_2Elist_2ECONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3691 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> ((all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(V0P,V1l)) -> (all V2a (mem(V2a,A_27a) -> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2a),V1l)))))))) & p(ap(V0P,c_2Elist_2ENIL(A_27a))) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> p(ap(V0P,V3l))))))))) # label(conj_thm_2Elist_2Elist__INDUCT0) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3692 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),V1l) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))),ap(c_2Elist_2ETL(A_27a),V1l)) & ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Elist_2ETL(A_27a),V1l)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),V1l))))))) # label(conj_thm_2Elist_2EEL__simp) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3693 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f0 (mem(V0f0,A_27b) -> (all V1f1 (mem(V1f1,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),arr(A_27b,A_27b)))) -> (exists V2fn (mem(V2fn,arr(ty_2Elist_2Elist(A_27a),A_27b)) & (all V3a0 (mem(V3a0,A_27a) -> (all V4a1 (mem(V4a1,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(V1f1,V3a0),V4a1),ap(V2fn,V4a1)) = ap(V2fn,ap(ap(c_2Elist_2ECONS(A_27a),V3a0),V4a1)))))) & ap(V2fn,c_2Elist_2ENIL(A_27a)) = V0f0)))))))))) # label(conj_thm_2Elist_2Elist__Axiom) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3694 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EEVERYi(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))))) # label(mem_c_2Elist_2EEVERYi) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3695 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(V0f,c_2Enum_2E0) = ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n))))))))) # label(conj_thm_2Elist_2EHD__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3696 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,ty_2Elist_2Elist(A_27a)) -> (all V1b (mem(V1b,ty_2Elist_2Elist(A_27a)) -> (all V2c (mem(V2c,ty_2Elist_2Elist(A_27a)) -> (all V3d (mem(V3d,ty_2Elist_2Elist(A_27a)) -> (all V4x (mem(V4x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1b))) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0a))) & ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0a),ap(ap(c_2Elist_2ECONS(A_27a),V4x),c_2Elist_2ENIL(A_27a)))),V1b) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2c),ap(ap(c_2Elist_2ECONS(A_27a),V4x),c_2Elist_2ENIL(A_27a)))),V3d) -> V2c = V0a & V1b = V3d))))))))))))) # label(conj_thm_2Elist_2EMEM__APPEND__lemma) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3697 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V1cs (mem(V1cs,ty_2Elist_2Elist(A_27c)) -> (all V2c (mem(V2c,A_27c) -> (all V3bs (mem(V3bs,ty_2Elist_2Elist(A_27b)) -> (all V4b (mem(V4b,A_27b) -> (all V5a (mem(V5a,A_27a) -> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V0f),ap(ap(ap(V0f,V5a),V4b),V2c)),V3bs),V1cs) = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V0f),V5a),ap(ap(c_2Elist_2ECONS(A_27b),V4b),V3bs)),ap(ap(c_2Elist_2ECONS(A_27c),V2c),V1cs)))))))))))))) & (all V6f (mem(V6f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V7cs (mem(V7cs,ty_2Elist_2Elist(A_27c)) -> (all V8a (mem(V8a,A_27a) -> V8a = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V6f),V8a),c_2Elist_2ENIL(A_27b)),V7cs))))))) & (all V9v7 (mem(V9v7,ty_2Elist_2Elist(A_27b)) -> (all V10v6 (mem(V10v6,A_27b) -> (all V11f (mem(V11f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V12a (mem(V12a,A_27a) -> V12a = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V11f),V12a),ap(ap(c_2Elist_2ECONS(A_27b),V10v6),V9v7)),c_2Elist_2ENIL(A_27c)))))))))))))))) # label(conj_thm_2Elist_2EFOLDL2__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3698 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EEXISTS(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),bool))))) # label(mem_c_2Elist_2EEXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3699 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),V0h),ap(c_2Elist_2ELAST(A_27a),V1t)))))))) # label(conj_thm_2Elist_2ELAST__CONS__cond) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3700 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V1m = ap(c_2Elist_2ELENGTH(A_27a),V0l) -> V0l = ap(ap(c_2Elist_2ETAKE(A_27a),V1m),V0l)))))))) # label(conj_thm_2Elist_2ETAKE__LENGTH__ID__rwt) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3701 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ETAKE(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l)),V0l) = V0l)))) # label(conj_thm_2Elist_2ETAKE__LENGTH__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3702 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1h1 (mem(V1h1,A_27b) -> (all V2h2 (mem(V2h2,A_27b) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V1h1),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V3t))) = ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V3t)))))))) & (all V0x (mem(V0x,A_27a) -> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) = V0x)))))) # label(conj_thm_2Elist_2ELAST__compute) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3703 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V2l))) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),f391(A_27b,A_27a,V1f,V0P)),V2l))))))))))))) # label(conj_thm_2Elist_2EEXISTS__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3704 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1n),V0xs) = c_2Elist_2ENIL(A_27a) <-> V0xs = c_2Elist_2ENIL(A_27a)))))))))) # label(conj_thm_2Elist_2ELUPDATE__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.38 3705 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1xs2 (mem(V1xs2,ty_2Elist_2Elist(A_27a)) -> (all V2xs1 (mem(V2xs1,ty_2Elist_2Elist(A_27a)) -> (all V3zs (mem(V3zs,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V2xs1),V1xs2)),V3zs)) <-> (exists V4ys1 ((exists V5ys2 (mem(V5ys2,ty_2Elist_2Elist(A_27b)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1xs2),V5ys2)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V2xs1),V4ys1)) & V3zs = ap(ap(c_2Elist_2EAPPEND(A_27b),V4ys1),V5ys2))) & mem(V4ys1,ty_2Elist_2Elist(A_27b))))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__SPLIT1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3706 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2ELIST__REL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool)))))))) # label(mem_c_2Elist_2ELIST__REL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3707 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(f418(A_27a,V0P),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(V0P,V2x))))) # label(lameq_f418) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3708 (all A_27a (ne(A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) <-> p(ap(V1P,V2h)) | p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1P),V3t))))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> ($F <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),c_2Elist_2ENIL(A_27a)))))))) # label(ax_thm_2Elist_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3709 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (V1l2 != V0l1 -> (all V2h1 (mem(V2h1,A_27a) -> (all V3h2 (mem(V3h2,A_27a) -> ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V1l2) != ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V0l1)))))))))))) # label(conj_thm_2Elist_2ELIST__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3710 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))),ap(c_2Elist_2Enub(A_27a),V1l)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(c_2Elist_2Enub(A_27a),V1l))))))) & c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2Enub(A_27a),c_2Elist_2ENIL(A_27a)))) # label(ax_thm_2Elist_2Enub__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3711 (all A_27a all V0R (mem(V0R,arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) -> (all V1s ap(f419(A_27a,V0R),V1s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Epred__set_2EFINITE(A_27a),V1s)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V1s),c_2Epred__set_2EEMPTY(A_27a))))),ap(ap(V0R,ap(c_2Epred__set_2EREST(A_27a),V1s)),V1s))))) # label(lameq_f419) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3712 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V6a ap(f404(A_27b,A_27a,V0P),V6a) = f403(A_27a,A_27b,V6a,V0P)))) # label(lameq_f404) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3713 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Elist_2ESET__TO__LIST(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) = ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)))))) # label(conj_thm_2Elist_2ESET__TO__LIST__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3714 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0ls) = c_2Elist_2ENIL(A_27a) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0ls)))))))))) # label(conj_thm_2Elist_2EDROP__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3715 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3f_27 (mem(V3f_27,arr(A_27a,A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) -> ap(V2f,V4x) = ap(V3f_27,V4x)))) & V0l1 = V1l2 -> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V2f),V0l1) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f_27),V1l2)))))))))))))) # label(conj_thm_2Elist_2EMAP__CONG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3716 (all A_27a (ne(A_27a) -> -p(ap(c_2Epred__set_2EFINITE(ty_2Elist_2Elist(A_27a)),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(A_27a)))))) # label(conj_thm_2Elist_2EINFINITE__LIST__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3717 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> ($T <-> p(ap(ap(c_2Elist_2EisPREFIX(A_27a),c_2Elist_2ENIL(A_27a)),V0l))))) & (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V3l),c_2Ebool_2EF),f424(A_27a,V1h,V2t))) <-> p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3l))))))))))) # label(ax_thm_2Elist_2EisPREFIX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3718 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,ty_2Elist_2Elist(A_27b))) -> V0f = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE(A_27b)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE(A_27b)),V0f)))))))) # label(conj_thm_2Elist_2EREVERSE__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3719 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l1),V2l2)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(c_2Elist_2ELENGTH(A_27a),V2l2)))))))))))) # label(conj_thm_2Elist_2ESHORTLEX__LENGTH__LE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3720 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls)))) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)))))))))))) # label(conj_thm_2Elist_2EMEM__dropWhile__IMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3721 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(V1f,c_2Enum_2E0) = ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n))))))))) # label(conj_thm_2Elist_2EHD__GENLIST__COR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3722 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) = ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),c_2Elist_2ENIL(A_27b))))) & (all V2x1 (mem(V2x1,A_27a) -> (all V3l1 (mem(V3l1,ty_2Elist_2Elist(A_27a)) -> (all V4x2 (mem(V4x2,A_27b) -> (all V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V2x1),V3l1)),ap(ap(c_2Elist_2ECONS(A_27b),V4x2),V5l2))) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x1),V4x2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V3l1),V5l2))))))))))) & (all V0l2 (mem(V0l2,ty_2Elist_2Elist(A_27b)) -> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),V0l2)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))))))) # label(ax_thm_2Elist_2EZIP__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3723 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (-p(ap(c_2Elist_2ENULL(A_27a),V0l)) <-> (exists V1e (mem(V1e,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V1e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))))))))) # label(conj_thm_2Elist_2ENOT__NULL__MEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3724 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27b,arr(A_27a,bool))) -> (all V1xs2 (mem(V1xs2,ty_2Elist_2Elist(A_27a)) -> (all V2xs1 (mem(V2xs1,ty_2Elist_2Elist(A_27a)) -> (all V3zs (mem(V3zs,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V3zs),ap(ap(c_2Elist_2EAPPEND(A_27a),V2xs1),V1xs2))) <-> (exists V4ys1 ((exists V5ys2 (mem(V5ys2,ty_2Elist_2Elist(A_27b)) & V3zs = ap(ap(c_2Elist_2EAPPEND(A_27b),V4ys1),V5ys2) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V5ys2),V1xs2)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V4ys1),V2xs1)))) & mem(V4ys1,ty_2Elist_2Elist(A_27b))))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__SPLIT2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3725 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l)) <-> V1l = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))))))) # label(conj_thm_2Elist_2EFILTER__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3726 (all A_27a (ne(A_27a) -> (all V0a1 (mem(V0a1,ty_2Elist_2Elist(A_27a)) -> (all V1a0 (mem(V1a0,A_27a) -> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1))))))) # label(conj_thm_2Elist_2Elist__distinct) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3727 (all A_27a all A_27b all V0x (mem(V0x,A_27a) -> (all V3L1 (mem(V3L1,ty_2Elist_2Elist(A_27a)) -> (all V1y (mem(V1y,A_27b) -> (all V4L2 ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3L1)),ap(ap(c_2Elist_2ECONS(A_27b),V1y),V4L2)) = ap(f411(A_27a,A_27b,V0x,V3L1,V1y),V4L2)))))))) # label(lameq_f411) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3728 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1y (mem(V1y,ty_2Elist_2Elist(A_27b)) -> (all V2x (mem(V2x,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),V1y)) <-> c_2Elist_2ENIL(A_27b) = V1y) & (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2x),c_2Elist_2ENIL(A_27b))) <-> c_2Elist_2ENIL(A_27a) = V2x))))))))))) # label(conj_thm_2Elist_2ELIST__REL__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3729 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (all V3s (mem(V3s,arr(A_27b,bool)) -> (all V4x ap(f430(A_27b,A_27a,V0f,V3s),V4x) = ap(ap(c_2Epred__set_2EUNION(A_27b),V3s),ap(V0f,V4x))))))) # label(lameq_f430) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3730 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2m1 (mem(V2m1,ty_2Elist_2Elist(A_27a)) -> (all V3m2 (mem(V3m2,ty_2Elist_2Elist(A_27a)) -> ((exists V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) & V0l1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V2m1),V4l) & ap(ap(c_2Elist_2EAPPEND(A_27a),V4l),V1l2) = V3m2)) | (exists V5l (mem(V5l,ty_2Elist_2Elist(A_27a)) & V2m1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V5l) & ap(ap(c_2Elist_2EAPPEND(A_27a),V5l),V3m2) = V1l2)) <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2m1),V3m2)))))))))))) # label(conj_thm_2Elist_2EAPPEND__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3731 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> ap(c_2Elist_2EMAP(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EMAP(A_27b,A_27c),V0f)),ap(c_2Elist_2EMAP(A_27a,A_27b),V1g)))))))))))) # label(conj_thm_2Elist_2EMAP__o) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3732 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (V0l1 = ap(c_2Elist_2EREVERSE(A_27a),V1l2) <-> V1l2 = ap(c_2Elist_2EREVERSE(A_27a),V0l1)))))))) # label(conj_thm_2Elist_2ESWAP__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3733 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) -> (all V2f (mem(V2f,arr(A_27a,arr(A_27b,A_27c))) -> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V2f),V0l1),V1l2) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))))))) # label(conj_thm_2Elist_2EMAP2__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3734 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2ys (mem(V2ys,ty_2Elist_2Elist(A_27a)) -> ap(c_2Elist_2ELENGTH(A_27a),V2ys) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2ys)))))))))) # label(conj_thm_2Elist_2ELENGTH__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3735 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Elist_2ELIST__LIFT2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27a))))))))))) # label(mem_c_2Elist_2ELIST__LIFT2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3736 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EdropWhile(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EdropWhile) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3737 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l))) -> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V1l)),V0n))),V1l) = ap(ap(c_2Elist_2EEL(A_27a),V0n),ap(c_2Elist_2EREVERSE(A_27a),V1l))))))))) # label(conj_thm_2Elist_2EEL__REVERSE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3738 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2as (mem(V2as,ty_2Elist_2Elist(A_27a)) -> (all V3b (mem(V3b,A_27b) -> (all V4bs (mem(V4bs,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2as),V4bs)) & p(ap(ap(V0R,V1a),V3b)) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1a),V2as)),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)))) & ($F <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)))) & ($F <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1a),V2as)),c_2Elist_2ENIL(A_27b)))) & (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))) <-> $T))))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3739 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EDROP(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EDROP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3740 (all A_27a (ne(A_27a) -> (all V0xs (mem(V0xs,ty_2Elist_2Elist(A_27a)) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> ap(ap(c_2Elist_2EoEL(A_27a),V2n),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3x),V1i),V0xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1i),V2n))),ap(ap(c_2Elist_2EoEL(A_27a),V2n),V0xs)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Elist_2ELENGTH(A_27a),V0xs))),ap(c_2Eoption_2ESOME(A_27a),V3x)),c_2Eoption_2ENONE(A_27a))))))))))))) # label(conj_thm_2Elist_2EoEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3741 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) <-> (exists V2l1 ((exists V3l2 (V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3l2)) & mem(V3l2,ty_2Elist_2Elist(A_27a)))) & mem(V2l1,ty_2Elist_2Elist(A_27a))))))))))) # label(conj_thm_2Elist_2EMEM__SPLIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3742 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(c_2Elist_2ELENGTH(A_27a),V1l2)) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)))))))) # label(conj_thm_2Elist_2ELENGTH__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3743 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1))) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2))))))))))))) # label(conj_thm_2Elist_2EMEM__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3744 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (all V3R_27 (mem(V3R_27,arr(A_27a,arr(A_27a,bool))) -> (all V4l1_27 (mem(V4l1_27,ty_2Elist_2Elist(A_27a)) -> (all V5l2_27 (mem(V5l2_27,ty_2Elist_2Elist(A_27a)) -> (V4l1_27 = V1l1 & (all V6a (mem(V6a,A_27a) -> (all V7b (mem(V7b,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V7b),ap(c_2Elist_2ELIST__TO__SET(A_27a),V5l2_27))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V6a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V4l1_27))) -> (p(ap(ap(V0R,V6a),V7b)) <-> p(ap(ap(V3R_27,V6a),V7b)))))))) & V5l2_27 = V2l2 -> (p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l1),V2l2)) <-> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V3R_27),V4l1_27),V5l2_27)))))))))))))))))) # label(conj_thm_2Elist_2ELLEX__CONG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3745 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2a (mem(V2a,ty_2Elist_2Elist(A_27b)) -> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,ty_2Elist_2Elist(A_27b)),f396(A_27b,A_27a,V0f)),V2a),V1ls) = ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls)),V2a))))))))))) # label(conj_thm_2Elist_2EFOLDR__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3746 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($F <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a))))))) & (all V1x (mem(V1x,A_27a) -> (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))) <-> V1x = V2h | p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3t)))))))))))) # label(conj_thm_2Elist_2EMEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3747 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((exists V4ls (mem(V4ls,ty_2Elist_2Elist(A_27a)) & ap(c_2Elist_2ELENGTH(A_27a),V4ls) = V1n & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V4ls),V2x),V3y)))) <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V3y))))))))))))) # label(conj_thm_2Elist_2ENRC__LRC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3748 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) & ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> ap(ap(c_2Elist_2EEL(ty_2Epair_2Eprod(A_27a,A_27b)),V2n),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l1)),ap(ap(c_2Elist_2EEL(A_27b),V2n),V1l2))))))))))))) # label(conj_thm_2Elist_2EEL__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3749 (all A_27a all V4h (mem(V4h,A_27a) -> (all V5t ap(f461(A_27a,V4h),V5t) = ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t))))) # label(lameq_f461) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3750 (all A_27a (ne(A_27a) -> mem(c_2Elist_2ESHORTLEX(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))))) # label(mem_c_2Elist_2ESHORTLEX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3751 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) & ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))) # label(conj_thm_2Elist_2ELENGTH__ZIP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3752 (all A_27a (ne(A_27a) -> (all V0L (mem(V0L,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EREV(A_27a),V0L),c_2Elist_2ENIL(A_27a)) = ap(c_2Elist_2EREVERSE(A_27a),V0L))))) # label(conj_thm_2Elist_2EREVERSE__REV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3753 (all A_27b all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool))) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27b)) -> (all V3i ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V3i),ap(c_2Elist_2ELENGTH(A_27b),V2l))),ap(ap(V0P,V3i),ap(ap(c_2Elist_2EEL(A_27b),V3i),V2l))) = ap(f441(A_27b,V0P,V2l),V3i)))))) # label(lameq_f441) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3754 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V3l)) -> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V3l)))))))))))) # label(conj_thm_2Elist_2EEVERY__MONOTONIC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3755 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27c)) -> (all V2g (mem(V2g,arr(A_27c,ty_2Elist_2Elist(A_27b))) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V1l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EMAP(A_27b,A_27a),V0f)),V2g)) = ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),ap(ap(c_2Elist_2ELIST__BIND(A_27b,A_27c),V1l),V2g)))))))))))))) # label(conj_thm_2Elist_2EMAP__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3756 (all A_27a all V2P (mem(V2P,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V4i ap(f440(A_27a,V2P),V4i) = ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),ap(V2P,V4i))))) # label(lameq_f440) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3757 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (-p(ap(c_2Elist_2ENULL(A_27a),V0l)) -> ap(c_2Elist_2ETL(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),ap(c_2Elist_2ETL(A_27a),V0l))))))))))) # label(conj_thm_2Elist_2EMAP__TL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3758 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27b)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27b)) -> (ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27b),V2l1),V3l2) <-> (exists V4l10 ((exists V5l20 (mem(V5l20,ty_2Elist_2Elist(A_27a)) & V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l10),V5l20) & V3l2 = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V5l20) & V2l1 = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V4l10))) & mem(V4l10,ty_2Elist_2Elist(A_27a))))))))))))))))) # label(conj_thm_2Elist_2EMAP__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3759 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(A_27b),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27b,A_27a),V0f),V1g)),V2n) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2EGENLIST(A_27a),V1g),V2n)))))))))))) # label(conj_thm_2Elist_2EMAP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3760 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EEL(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l1)),ap(ap(c_2Elist_2EEL(A_27a),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),V1l2)))))))))) # label(conj_thm_2Elist_2EEL__APPEND__EQN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3761 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V1l)),V0n) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l)))))))) # label(conj_thm_2Elist_2ELENGTH__DROP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3762 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27a)) -> (all V3x (mem(V3x,A_27a) -> (ap(ap(c_2Elist_2EoEL(A_27a),V0n),ap(ap(c_2Elist_2ETAKE(A_27a),V1m),V2xs)) = ap(c_2Eoption_2ESOME(A_27a),V3x) -> ap(c_2Eoption_2ESOME(A_27a),V3x) = ap(ap(c_2Elist_2EoEL(A_27a),V0n),V2xs)))))))))))) # label(conj_thm_2Elist_2EoEL__TAKE__E) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3763 (all A_27b all A_27a all V1k (mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27b)) -> (all V4i ap(f442(A_27b,A_27a,V1k,V2l),V4i) = ap(ap(V1k,ap(ap(c_2Elist_2ETAKE(A_27b),V4i),V2l)),ap(ap(c_2Elist_2EDROP(A_27b),V4i),V2l))))))) # label(lameq_f442) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3764 (all V0ls (mem(V0ls,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> (c_2Enum_2E0 = ap(c_2Elist_2ESUM,V0ls) <-> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),V0ls))) -> c_2Enum_2E0 = V1x)))))) # label(conj_thm_2Elist_2ESUM__eq__0) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3765 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1t (mem(V1t,ty_2Elist_2Elist(ty_2Enum_2Enum)) -> ap(ap(c_2Earithmetic_2E_2B,V0h),ap(c_2Elist_2ESUM,V1t)) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0h),V1t)))))) # label(ax_thm_2Elist_2ESUM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3766 (all A_27b all A_27a all A_27c all V6a (mem(V6a,A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27c,A_27b)) -> (all V7b ap(ap(V0R,V6a),ap(V2f,V7b)) = ap(f409(A_27b,A_27a,A_27c,V6a,V0R,V2f),V7b)))))))) # label(lameq_f409) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3767 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V2f ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Elist_2ENULL(A_27a),V0l)),V1b),ap(ap(V2f,ap(c_2Elist_2EHD(A_27a),V0l)),ap(c_2Elist_2ETL(A_27a),V0l))) = ap(f464(A_27b,A_27a,V1b,V0l),V2f)))))) # label(lameq_f464) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3768 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27b)) -> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(arr(A_27b,A_27a)),V0f),c_2Elist_2ENIL(arr(A_27b,A_27a)))),V1l) = ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),V1l))))))))) # label(conj_thm_2Elist_2ESINGL__APPLY__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3769 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EisPREFIX(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))))) # label(mem_c_2Elist_2EisPREFIX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3770 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2t (mem(V2t,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))),f412(A_27b,A_27a,V0x,V1y))),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V2t)) = ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),V2t)) & ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)) = ap(c_2Elist_2EUNZIP(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))))))))))) # label(conj_thm_2Elist_2EUNZIP__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3771 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (V0l = c_2Elist_2ENIL(A_27a) <-> c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l)))))) # label(conj_thm_2Elist_2ELENGTH__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3772 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) -> p(ap(c_2Erelation_2Etotal(ty_2Elist_2Elist(A_27a)),ap(c_2Erelation_2ERC(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R))))))))) # label(conj_thm_2Elist_2ELLEX__total) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3773 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ((exists V2x (mem(V2x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))) & -p(ap(V0P,V2x)))) <-> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) != V1l))))))) # label(conj_thm_2Elist_2EFILTER__NEQ__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3774 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ((all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2x),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) -> ap(ap(c_2Elist_2EEL(A_27a),V2x),V0l1) = ap(ap(c_2Elist_2EEL(A_27a),V2x),V1l2)))) & ap(c_2Elist_2ELENGTH(A_27a),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> V1l2 = V0l1))))))) # label(conj_thm_2Elist_2ELIST__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3775 (all A_27a (ne(A_27a) -> (all V0acc (mem(V0acc,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EREV(A_27a),c_2Elist_2ENIL(A_27a)),V0acc) = V0acc)) & (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3acc (mem(V3acc,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EREV(A_27a),V2t),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3acc)) = ap(ap(c_2Elist_2EREV(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3acc))))))))) # label(ax_thm_2Elist_2EREV__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3776 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l)) <-> -p(ap(ap(c_2Elist_2EEXISTS(A_27a),f392(A_27a,V0P)),V1l))))))))) # label(conj_thm_2Elist_2EEVERY__NOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3777 (all A_27b all A_27a all V1f (mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))) -> (all V2fn1 (mem(V2fn1,arr(ty_2Elist_2Elist(A_27a),A_27b)) -> (all V3h (mem(V3h,A_27a) -> (all V4t ap(f387(A_27b,A_27a,V1f,V2fn1,V3h),V4t) = ap(ap(c_2Emin_2E_3D(A_27b),ap(V2fn1,ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4t))),ap(ap(ap(V1f,ap(V2fn1,V4t)),V3h),V4t))))))))) # label(lameq_f387) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3778 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l1_27 (mem(V1l1_27,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (all V3l2_27 (mem(V3l2_27,ty_2Elist_2Elist(A_27b)) -> (all V4f (mem(V4f,arr(A_27a,arr(A_27b,A_27c))) -> (all V5f_27 (mem(V5f_27,arr(A_27a,arr(A_27b,A_27c))) -> (V0l1 = V1l1_27 & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27b),V7y),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27))) -> ap(ap(V5f_27,V6x),V7y) = ap(ap(V4f,V6x),V7y)))))) & V3l2_27 = V2l2 -> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V4f),V0l1),V2l2) = ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V5f_27),V1l1_27),V3l2_27)))))))))))))))))))) # label(conj_thm_2Elist_2EMAP2__CONG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3779 (all A_27a (ne(A_27a) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls))) -> p(ap(ap(V1R,V2x),V2x))))) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V1R),V0ls),V0ls))))))))) # label(conj_thm_2Elist_2EEVERY2__refl) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3780 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2EsplitAtPki(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,arr(A_27b,bool)),arr(arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)),arr(ty_2Elist_2Elist(A_27b),A_27a)))))))) # label(mem_c_2Elist_2EsplitAtPki) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3781 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27b)) -> (all V3v1 (mem(V3v1,A_27a) -> (all V4v2 (mem(V4v2,A_27b) -> (all V5n (mem(V5n,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1l1),V2l2)) & p(ap(ap(V0P,V3v1),V4v2)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3v1),V5n),V1l1)),ap(ap(ap(c_2Elist_2ELUPDATE(A_27b),V4v2),V5n),V2l2)))))))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__LUPDATE__same) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3782 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f450(A_27a,V0l1)),V1l2)))))))) # label(conj_thm_2Elist_2Elist__to__set__diff) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3783 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(f395(A_27a,A_27b,V0f,V3x),V4y) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V0f,V3x)),V4y)))))) # label(lameq_f395) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3784 (all A_27a (ne(A_27a) -> (all V1x (mem(V1x,A_27a) -> (all V2x_27 (mem(V2x_27,A_27a) -> (all V3l (mem(V3l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2ESNOC(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2x_27),V3l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2x_27),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V3l)))))))) & (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Elist_2ESNOC(A_27a),V0x),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)))))) # label(ax_thm_2Elist_2ESNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3785 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27c)) -> (all V1g (mem(V1g,arr(A_27c,ty_2Elist_2Elist(A_27b))) -> (all V2f (mem(V2f,arr(A_27b,ty_2Elist_2Elist(A_27a))) -> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V0l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Ecombin_2EC(ty_2Elist_2Elist(A_27b),arr(A_27b,ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND(A_27a,A_27b)),V2f)),V1g)) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ELIST__BIND(A_27b,A_27c),V0l),V1g)),V2f))))))))))))) # label(conj_thm_2Elist_2ELIST__BIND__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3786 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V4a f407(A_27a,A_27b,V4a,V0R) = ap(f408(A_27b,A_27a,V0R),V4a)))) # label(lameq_f408) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3787 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l)),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l)) = V1l)))))) # label(conj_thm_2Elist_2ETAKE__DROP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3788 (all A_27a (ne(A_27a) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> (all V3h1 (mem(V3h1,A_27a) -> (all V4t1 (mem(V4t1,ty_2Elist_2Elist(A_27a)) -> (all V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V5l2),c_2Ebool_2EF),f446(A_27a,V2R,V3h1,V4t1))) <-> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),V5l2))))))))))) & (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1l2)) <-> c_2Elist_2ENIL(A_27a) != V1l2))))))) # label(ax_thm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3789 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EREVERSE(A_27a),V0l) <-> V0l = c_2Elist_2ENIL(A_27a)))))) # label(conj_thm_2Elist_2EREVERSE__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3790 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (all V2n1 (mem(V2n1,ty_2Enum_2Enum) -> (all V3n2 (mem(V3n2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n1),ap(c_2Elist_2ELENGTH(A_27a),V1l))) & p(ap(V0P,ap(ap(c_2Elist_2EEL(A_27a),V2n1),V1l))) & ap(ap(c_2Elist_2EEL(A_27a),V3n2),V1l) = ap(ap(c_2Elist_2EEL(A_27a),V2n1),V1l) & p(ap(ap(c_2Eprim__rec_2E_3C,V3n2),ap(c_2Elist_2ELENGTH(A_27a),V1l))) & p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l))) -> V2n1 = V3n2))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3791 (all A_27a all A_27b all A_27c all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool)))) -> (all V3s ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27c,bool)),f433(A_27b,A_27c,A_27a,V0f,V3s)) = ap(f434(A_27a,A_27b,A_27c,V0f),V3s)))) # label(lameq_f434) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3792 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (ap(c_2Elist_2ELENGTH(A_27b),V1l2) = ap(c_2Elist_2ELENGTH(A_27a),V0l1) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V2P),V0l1)) <-> p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),f460(A_27b,A_27a,V2P)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))))))))))))) # label(conj_thm_2Elist_2Eevery__zip__fst) # label(axiom) # label(non_clause). [assumption]. 6.43/6.39 3793 (all A_27a (ne(A_27a) -> (all V0h (mem(V0h,A_27a) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1t))) <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))))))) & ($T <-> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),c_2Elist_2ENIL(A_27a)))))) # label(ax_thm_2Elist_2EALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3794 (all A_27a all A_27b all V8a (mem(V8a,A_27a) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V9b ap(f405(A_27a,A_27b,V8a,V1Q),V9b) = ap(ap(V1Q,V8a),V9b)))))) # label(lameq_f405) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3795 (all A_27a all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2m ap(f429(A_27a,V1n,V0f),V2m) = ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eprim__rec_2EPRE,V1n)),V2m))))))) # label(lameq_f429) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3796 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(V0R1,V2x),V3y)) -> p(ap(ap(V1R2,V3y),V2x))))))) -> (all V4x (mem(V4x,ty_2Elist_2Elist(A_27a)) -> (all V5y (mem(V5y,ty_2Elist_2Elist(A_27b)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V4x),V5y)) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V1R2),V5y),V4x)))))))))))))))) # label(conj_thm_2Elist_2EEVERY2__sym) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3797 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)) = ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27b),f454(A_27a,A_27b,V1ls,V0f)),ap(c_2Epred__set_2Ecount,ap(c_2Elist_2ELENGTH(A_27a),V1ls))))))))))) # label(conj_thm_2Elist_2EIMAGE__EL__count__LENGTH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3798 (all A_27a all V1a0_27 (mem(V1a0_27,ty_2Eind__type_2Erecspace(A_27a)) -> (all V2_27list_27 ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f384(A_27a,V2_27list_27))),ap(V2_27list_27,V1a0_27)) = ap(f385(A_27a,V1a0_27),V2_27list_27)))) # label(lameq_f385) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3799 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1h (mem(V1h,A_27a) -> (all V2t (mem(V2t,ty_2Elist_2Elist(A_27a)) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5e (mem(V5e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V5e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2t))) & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3x),V4y)) -> (exists V6z ((exists V7p (mem(V7p,ty_2Elist_2Elist(A_27a)) & p(ap(ap(V0R,V6z),V5e)) & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V7p),V3x),V6z)))) & mem(V6z,A_27a)))))))))))))))))) # label(conj_thm_2Elist_2ELRC__MEM__right) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3800 (all A_27a (ne(A_27a) -> (all V4l1 (mem(V4l1,ty_2Elist_2Elist(A_27a)) -> (all V5l2 (mem(V5l2,ty_2Elist_2Elist(A_27a)) -> (ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V5l2) = V4l1 <-> c_2Elist_2ENIL(A_27a) = V5l2))))) & (all V6l1 (mem(V6l1,ty_2Elist_2Elist(A_27a)) -> (all V7l2 (mem(V7l2,ty_2Elist_2Elist(A_27a)) -> (ap(ap(c_2Elist_2EAPPEND(A_27a),V6l1),V7l2) = V7l2 <-> c_2Elist_2ENIL(A_27a) = V6l1))))) & (all V2l1 (mem(V2l1,ty_2Elist_2Elist(A_27a)) -> (all V3l2 (mem(V3l2,ty_2Elist_2Elist(A_27a)) -> (V2l1 = c_2Elist_2ENIL(A_27a) <-> V3l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2)))))) & (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (V1l2 = c_2Elist_2ENIL(A_27a) <-> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = V0l1))))))) # label(conj_thm_2Elist_2EAPPEND__EQ__SELF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3801 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(arr(A_27a,arr(A_27b,arr(A_27c,A_27a))),arr(A_27a,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),bool))))) -> ((all V1f (mem(V1f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (all V4bs (mem(V4bs,ty_2Elist_2Elist(A_27b)) -> (all V5c (mem(V5c,A_27c) -> (all V6cs (mem(V6cs,ty_2Elist_2Elist(A_27c)) -> (p(ap(ap(ap(ap(V0P,V1f),ap(ap(ap(V1f,V2a),V3b),V5c)),V4bs),V6cs)) -> p(ap(ap(ap(ap(V0P,V1f),V2a),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)),ap(ap(c_2Elist_2ECONS(A_27c),V5c),V6cs)))))))))))))))) & (all V10f (mem(V10f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V11a (mem(V11a,A_27a) -> (all V12v6 (mem(V12v6,A_27b) -> (all V13v7 (mem(V13v7,ty_2Elist_2Elist(A_27b)) -> p(ap(ap(ap(ap(V0P,V10f),V11a),ap(ap(c_2Elist_2ECONS(A_27b),V12v6),V13v7)),c_2Elist_2ENIL(A_27c))))))))))) & (all V7f (mem(V7f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V8a (mem(V8a,A_27a) -> (all V9cs (mem(V9cs,ty_2Elist_2Elist(A_27c)) -> p(ap(ap(ap(ap(V0P,V7f),V8a),c_2Elist_2ENIL(A_27b)),V9cs)))))))) -> (all V14v (mem(V14v,arr(A_27a,arr(A_27b,arr(A_27c,A_27a)))) -> (all V15v1 (mem(V15v1,A_27a) -> (all V16v2 (mem(V16v2,ty_2Elist_2Elist(A_27b)) -> (all V17v3 (mem(V17v3,ty_2Elist_2Elist(A_27c)) -> p(ap(ap(ap(ap(V0P,V14v),V15v1),V16v2),V17v3))))))))))))))))))) # label(conj_thm_2Elist_2EFOLDL2__ind) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3802 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1ls (mem(V1ls,ty_2Elist_2Elist(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4e (mem(V4e,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))) & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V1ls),V2x),V3y)) -> (exists V5z (mem(V5z,A_27a) & (exists V6t (p(ap(ap(V0R,V4e),V5z)) & p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V6t),V5z),V3y)) & mem(V6t,ty_2Elist_2Elist(A_27a))))))))))))))))))) # label(conj_thm_2Elist_2ELRC__MEM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3803 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) -> (p(ap(V0P,c_2Elist_2ENIL(A_27a))) <-> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V1l) -> p(ap(V0P,V1l)))))))))) # label(conj_thm_2Elist_2ELENGTH__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3804 (all A_27a (ne(A_27a) -> mem(c_2Elist_2EREV(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))))) # label(mem_c_2Elist_2EREV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3805 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ((exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))))) <-> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))))))) # label(conj_thm_2Elist_2EFILTER__NEQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3806 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V3x ap(f396(A_27b,A_27a,V0f),V3x) = f395(A_27a,A_27b,V0f,V3x)))) # label(lameq_f396) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3807 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(c_2Epred__set_2EFINITE(A_27a),V0s)) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3808 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1l1 (mem(V1l1,ty_2Elist_2Elist(A_27a)) -> (all V2l2 (mem(V2l2,ty_2Elist_2Elist(A_27a)) -> (all V3l3 (mem(V3l3,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V2l2),V3l3)) & p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V1l1),V2l2)) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4n),ap(c_2Elist_2ELENGTH(A_27a),V1l1))) & p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V2l2)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V3l3))) & p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V2l2))) -> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V3l3)))))) -> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V1l1),V3l3))))))))))))) # label(conj_thm_2Elist_2ELIST__REL__trans) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3809 (all A_27a (ne(A_27a) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4l (mem(V4l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),V3n),ap(ap(c_2Elist_2ECONS(A_27a),ap(V2f,V3n)),V4l)) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(c_2Enum_2ESUC,V3n)),V4l))))))) & (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),c_2Enum_2E0),V1l) = V1l)))))) # label(ax_thm_2Elist_2EGENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3810 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Elist_2ECONS(A_27a),ap(V0f,c_2Enum_2E0)),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27a,ty_2Enum_2Enum),V0f),c_2Enum_2ESUC)),V1n)))))))) # label(conj_thm_2Elist_2EGENLIST__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3811 (all A_27a (ne(A_27a) -> (all V0ys (mem(V0ys,ty_2Elist_2Elist(A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3k (mem(V3k,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EEL(A_27a),V2i),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V1x),V3k),V0ys)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2i),V3k)),ap(ap(c_2Eprim__rec_2E_3C,V3k),ap(c_2Elist_2ELENGTH(A_27a),V0ys)))),V1x),ap(ap(c_2Elist_2EEL(A_27a),V2i),V0ys)))))))))))) # label(conj_thm_2Elist_2EEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3812 (all A_27a (ne(A_27a) -> (all V0P1 (mem(V0P1,arr(A_27a,bool)) -> (all V1P2 (mem(V1P2,arr(A_27a,bool)) -> (all V2l (mem(V2l,ty_2Elist_2Elist(A_27a)) -> (p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),ap(ap(c_2Elist_2EFILTER(A_27a),V1P2),V2l))) <-> p(ap(ap(c_2Elist_2EEVERY(A_27a),f397(A_27a,V1P2,V0P1)),V2l))))))))))) # label(conj_thm_2Elist_2EEVERY__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3813 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27b)) -> (all V2f (mem(V2f,arr(A_27a,arr(A_27b,bool))) -> (ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) & p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))) <-> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V2f),V0l1),V1l2))))))))))))) # label(conj_thm_2Elist_2EEVERY2__EVERY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3814 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(A_27a)) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) -> ap(ap(c_2Elist_2ETAKE(A_27a),V2n),V0l1) = ap(ap(c_2Elist_2ETAKE(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2))))))))))) # label(conj_thm_2Elist_2ETAKE__APPEND1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3815 (all A_27a all V7a0 ap(f381(A_27a),V7a0) = f380(A_27a,V7a0)) # label(lameq_f381) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3816 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Elist_2ELIST__BIND(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27b),arr(arr(A_27b,ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)))))))) # label(mem_c_2Elist_2ELIST__BIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3817 (all A_27a (ne(A_27a) -> (all V0l (mem(V0l,ty_2Elist_2Elist(A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EEL(A_27a),V1n),V0l) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(c_2Elist_2EHD(A_27a),V0l)),ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,V1n)),ap(c_2Elist_2ETL(A_27a),V0l))))))))) # label(conj_thm_2Elist_2EEL__compute) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3818 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1xs (mem(V1xs,ty_2Elist_2Elist(A_27a)) -> (V1xs = c_2Elist_2ENIL(A_27a) <-> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1xs)) = c_2Elist_2ENIL(A_27a)))))) & (all V4x (mem(V4x,A_27a) -> (all V5xs (mem(V5xs,ty_2Elist_2Elist(A_27a)) -> (p(ap(c_2Elist_2ENULL(A_27a),V5xs)) <-> p(ap(c_2Elist_2ENULL(A_27a),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5xs))))))))) & (all V2x (mem(V2x,A_27a) -> (all V3xs (mem(V3xs,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) = V3xs <-> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)) = c_2Elist_2ENIL(A_27a)))))))) # label(conj_thm_2Elist_2EFRONT__CONS__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3819 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> V0x = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)))))))) # label(conj_thm_2Elist_2ELAST__SNOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3820 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1L (mem(V1L,ty_2Elist_2Elist(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L))) & p(ap(V0P,V2x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1L))))))))))))) # label(conj_thm_2Elist_2EMEM__FILTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3821 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,bool) -> (all V1l (mem(V1l,ty_2Elist_2Elist(A_27a)) -> (c_2Elist_2ENIL(A_27a) != V1l & p(V0c) <-> p(ap(ap(c_2Elist_2EEXISTS(A_27a),k(A_27a,V0c)),V1l))))))))) # label(conj_thm_2Elist_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3822 (all A_27a (ne(A_27a) -> (all V0l1 (mem(V0l1,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> (all V1l2 (mem(V1l2,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a))) -> ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EAPPEND(ty_2Elist_2Elist(A_27a)),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0l1)),ap(c_2Elist_2EFLAT(A_27a),V1l2)))))))) # label(conj_thm_2Elist_2EFLAT__APPEND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3823 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ls (mem(V0ls,ty_2Elist_2Elist(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls))) & ap(V1f,V2x) = ap(V1f,V3y) -> V2x = V3y))))) & p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) -> p(ap(c_2Elist_2EALL__DISTINCT(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0ls)))))))))))) # label(conj_thm_2Elist_2EALL__DISTINCT__MAP__INJ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3824 (all A_27d all A_27c all A_27b all V8x (mem(V8x,A_27c) -> (all V4Q (mem(V4Q,arr(A_27c,arr(A_27d,bool))) -> (all V5g (mem(V5g,arr(A_27b,A_27d)) -> (all V9y ap(f457(A_27d,A_27c,A_27b,V8x,V4Q,V5g),V9y) = ap(ap(V4Q,V8x),ap(V5g,V9y))))))))) # label(lameq_f457) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3825 (all A_27b all A_27a all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V3i ap(f478(A_27b,A_27a,V2R,V1Q),V3i) = ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1Q),f477(A_27a,A_27b,V3i,V2R))))))) # label(lameq_f478) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3826 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f481(A_27a,V0P),V3x) = ap(c_2Ebool_2E_7E,ap(V0P,V3x))))) # label(lameq_f481) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3827 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1j (mem(V1j,A_27a) -> (p(ap(V0P,V1j)) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Emin_2E_3D(A_27a),V1j)),f473(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3828 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m1 (mem(V1m1,arr(A_27a,A_27b)) -> (all V2m2 (mem(V2m2,arr(A_27a,A_27b)) -> (ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V2m2) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m1) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0p)) -> ap(V1m1,V3x) = ap(V2m2,V3x))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__ABSTRACT__EQUAL__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3829 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> (c_2Epred__set_2EEMPTY(A_27b) != V1s <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1s),k(A_27b,c_2Ebool_2ET)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__T) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3830 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f491(A_27a,V2t,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V2t)),f482(A_27a,V0P)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3831 (all A_27b all A_27a all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V3x (mem(V3x,A_27b) -> (all V4i ap(ap(V1R,V4i),V3x) = ap(f474(A_27b,A_27a,V1R,V3x),V4i)))))) # label(lameq_f474) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3832 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P)) -> V1s != c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3833 (all A_27b all A_27a all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V3i ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1Q),f477(A_27a,A_27b,V3i,V2R)) = ap(f489(A_27b,A_27a,V2R,V1Q),V3i)))))) # label(lameq_f489) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3834 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p)) <-> p(ap(c_2Ebool_2E_21(A_27a),V0p))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3835 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f493(A_27a,V1s,V0P),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)),ap(V0P,V3x))))))) # label(lameq_f493) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3836 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (all V3i ap(f487(A_27a,V1Q,V2R),V3i) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1Q,V3i)),ap(V2R,V3i))))))) # label(lameq_f487) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3837 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0p),V1m)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f496(A_27a,V0p,V1m)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3838 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P)) | p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2t),V0P)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),V0P))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNION) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3839 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2ET))) <-> p(ap(c_2Ebool_2E_3F_21(A_27b),f494(A_27b,V1s)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3840 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F(A_27a),V0p)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3841 (all A_27a all V3x (mem(V3x,A_27a) -> (all V4s ap(ap(c_2Ebool_2EIN(A_27a),V3x),V4s) = ap(f486(A_27a,V3x),V4s)))) # label(lameq_f486) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3842 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),V0P)) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P)) & p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2t),V0P))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__UNION) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3843 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f108(A_27a,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f481(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ENOT__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3844 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1f)) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f63(A_27a,V1f,V0P))) & p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f61(A_27a,V1f)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3845 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f468(A_27a,V1Q))) | p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f469(A_27a,V2R))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f487(A_27a,V1Q,V2R)))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3846 (all A_27a all V2t (mem(V2t,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V5x ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t))),ap(V0P,V5x)) = ap(f491(A_27a,V2t,V0P),V5x)))))) # label(lameq_f491) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3847 (all A_27b all A_27a all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V5j (mem(V5j,A_27b) -> (all V6i ap(f479(A_27b,A_27a,V2R,V5j),V6i) = ap(ap(V2R,V6i),V5j)))))) # label(lameq_f479) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3848 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27b) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f476(A_27b,A_27a,V1R))) <-> (all V3x (mem(V3x,A_27b) -> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f474(A_27b,A_27a,V1R,V3x)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3849 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(arr(A_27a,bool)),V1sos),f484(A_27a,V0x)))))))))) # label(conj_thm_2Eres__quan_2EIN__BIGUNION__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3850 (all A_27a all A_27b all V3i (mem(V3i,A_27a) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V4j ap(f477(A_27a,A_27b,V3i,V2R),V4j) = ap(ap(V2R,V3i),V4j)))))) # label(lameq_f477) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3851 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> ((exists V4y (mem(V4y,A_27b) & V1s = ap(ap(c_2Epred__set_2EINSERT(A_27b),V4y),c_2Epred__set_2EEMPTY(A_27b)))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2ET)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3852 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p)) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),V0p))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3853 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,bool) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0p),k(A_27a,V1m))) <-> (exists V3x (ap(ap(c_2Epred__set_2EINSERT(A_27a),V3x),c_2Epred__set_2EEMPTY(A_27a)) = V0p & mem(V3x,A_27a))) & p(V1m)))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NULL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3854 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f467(A_27a,V1Q,V2R))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f468(A_27a,V1Q))) & p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f469(A_27a,V2R)))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3855 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),f470(A_27a,V0P,V1Q)),f471(A_27a,V2R))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1Q),f472(A_27a,V2R))) & p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f469(A_27a,V2R)))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3856 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1j (mem(V1j,A_27a) -> (p(ap(V0P,V1j)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Emin_2E_3D(A_27a),V1j)),f473(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3857 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> ap(c_2Emin_2E_40(A_27a),V0p) = ap(ap(c_2Ebool_2ERES__SELECT(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0p))))) # label(conj_thm_2Eres__quan_2ERES__SELECT__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3858 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,A_27b)) -> ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m)) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m))))))))) # label(conj_thm_2Eres__quan_2ERES__ABSTRACT__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3859 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),f481(A_27a,V0P))) <-> -p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f108(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ENOT__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3860 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V3i ap(f488(A_27a,V0P,V1Q),V3i) = ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V3i)),ap(V1Q,V3i))))))) # label(lameq_f488) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3861 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V4x ap(f482(A_27a,V0P),V4x) = ap(V0P,V4x)))) # label(lameq_f482) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3862 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)) -> ap(V1m,V2x) = ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m),V2x)))))))))))) # label(conj_thm_2Eres__quan_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3863 (all A_27a all V2R (mem(V2R,arr(A_27a,bool)) -> (all V4i ap(V2R,V4i) = ap(f471(A_27a,V2R),V4i)))) # label(lameq_f471) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3864 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V4i ap(f468(A_27a,V1Q),V4i) = ap(V1Q,V4i)))) # label(lameq_f468) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3865 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> -p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27b),V1s),k(A_27b,c_2Ebool_2EF))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3866 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,bool) -> (p(V1m) | V0p = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),k(A_27a,V1m)))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__NULL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3867 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f486(A_27a,V3x))) -> p(ap(V0P,V3x))))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos)),f108(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3868 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)),f108(A_27a,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f485(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3869 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2i ap(V0P,V2i) = ap(f473(A_27a,V0P),V2i)))) # label(lameq_f473) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3870 (all A_27a all A_27b all V5i (mem(V5i,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V6x ap(ap(V1R,V5i),V6x) = ap(f475(A_27a,A_27b,V5i,V1R),V6x)))))) # label(lameq_f475) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3871 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V1s),V0P)) -> c_2Epred__set_2EEMPTY(A_27a) != V1s))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3872 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),V1sos)),f108(A_27a,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(arr(A_27a,bool)),V1sos),f492(A_27a,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3873 (all A_27a all V0x (mem(V0x,A_27a) -> (all V2s ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s) = ap(f484(A_27a,V0x),V2s)))) # label(lameq_f484) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3874 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1s),V0P)) -> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V2t),V0P)))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3875 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3876 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos)),f108(A_27a,V0P))) <-> (exists V3x (mem(V3x,A_27a) & p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f486(A_27a,V3x))) & p(ap(V0P,V3x))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3877 (all A_27a all A_27b all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V5j ap(f480(A_27a,A_27b,V2R,V0P),V5j) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f479(A_27b,A_27a,V2R,V5j))))))) # label(lameq_f480) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3878 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> (c_2Epred__set_2EEMPTY(A_27b) = V1s <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1s),k(A_27b,c_2Ebool_2EF)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__F) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3879 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1sos (mem(V1sos,arr(arr(A_27a,bool),bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EBIGINTER(A_27a),V1sos))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(arr(A_27a,bool)),V1sos),f484(A_27a,V0x)))))))))) # label(conj_thm_2Eres__quan_2EIN__BIGINTER__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3880 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V1s),f108(A_27a,V0P))) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),f493(A_27a,V1s,V0P)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3881 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f469(A_27a,V2R))) | p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1Q),f472(A_27a,V2R))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),f488(A_27a,V0P,V1Q)),f471(A_27a,V2R)))))))))))) # label(conj_thm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3882 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27c) -> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1s),k(A_27b,c_2Ebool_2ET))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__T) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3883 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V2t),V0P)) -> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P)))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__SUBSET) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3884 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1s)) -> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1s))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3885 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3886 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,A_27a) -> (all V1s (mem(V1s,A_27b) -> (all V2x (mem(V2x,arr(A_27c,bool)) -> -p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27c),V2x),k(A_27c,c_2Ebool_2EF))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__F) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3887 (all A_27a all V2R (mem(V2R,arr(A_27a,bool)) -> (all V6i ap(f472(A_27a,V2R),V6i) = ap(V2R,V6i)))) # label(lameq_f472) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3888 (all A_27b all V1s (mem(V1s,arr(A_27b,bool)) -> (all V4x ap(f494(A_27b,V1s),V4x) = ap(ap(c_2Ebool_2EIN(A_27b),V4x),V1s)))) # label(lameq_f494) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3889 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m1 (mem(V1m1,arr(A_27a,A_27b)) -> (all V2m2 (mem(V2m2,arr(A_27a,A_27b)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0p)) -> ap(V2m2,V3x) = ap(V1m1,V3x)))) -> ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V2m2) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m1)))))))))))) # label(conj_thm_2Eres__quan_2ERES__ABSTRACT__EQUAL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3890 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1f)) <-> (exists V2x (mem(V2x,A_27a) & p(ap(V1f,V2x)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3891 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),V0P)) -> V1s != c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3892 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3s ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V3s),f482(A_27a,V0P)) = ap(f492(A_27a,V0P),V3s)))) # label(lameq_f492) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3893 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f496(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V2x)),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f495(A_27a,V1m,V2x)))))))) # label(lameq_f496) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3894 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V3j ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V3j)),ap(V1Q,V3j)) = ap(f470(A_27a,V0P,V1Q),V3j)))))) # label(lameq_f470) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3895 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3s ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V3s),f482(A_27a,V0P)) = ap(f485(A_27a,V0P),V3s)))) # label(lameq_f485) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3896 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m (mem(V0m,arr(A_27a,A_27b)) -> V0m = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),c_2Epred__set_2EUNIV(A_27a)),V0m))))))) # label(conj_thm_2Eres__quan_2ERES__ABSTRACT__UNIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3897 (all A_27b all A_27a all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V5i ap(f476(A_27b,A_27a,V1R),V5i) = ap(c_2Ebool_2E_21(A_27b),f475(A_27a,A_27b,V5i,V1R))))) # label(lameq_f476) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3898 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27b),V1Q),f490(A_27a,A_27b,V2R,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f489(A_27b,A_27a,V2R,V1Q)))))))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3899 (all A_27a all V2R (mem(V2R,arr(A_27a,bool)) -> (all V5i ap(V2R,V5i) = ap(f469(A_27a,V2R),V5i)))) # label(lameq_f469) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3900 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p)))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3901 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2EF)) = ap(ap(c_2Ebool_2ERES__SELECT(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0p))))) # label(conj_thm_2Eres__quan_2ERES__SELECT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3902 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f478(A_27b,A_27a,V2R,V1Q))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27b),V1Q),f480(A_27a,A_27b,V2R,V0P)))))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3903 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) -> p(ap(V1f,V2x))))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V1f))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3904 (all A_27a all A_27b all V2R (mem(V2R,arr(A_27a,arr(A_27b,bool))) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V5j ap(f490(A_27a,A_27b,V2R,V0P),V5j) = ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f479(A_27b,A_27a,V2R,V5j))))))) # label(lameq_f490) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3905 (all A_27a all V2t (mem(V2t,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V5x ap(f483(A_27a,V2t,V0P),V5x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t))),ap(V0P,V5x))))))) # label(lameq_f483) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3906 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,bool) -> (c_2Epred__set_2EEMPTY(A_27a) != V0p & p(V1m) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),k(A_27a,V1m)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__NULL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3907 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),V1m)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0p),V1m)),V0p)) & p(ap(V1m,ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0p),V1m)))))))))) # label(conj_thm_2Eres__quan_2ERES__EXISTS__ALT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3908 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2R (mem(V2R,arr(A_27a,bool)) -> (all V3i ap(f467(A_27a,V1Q,V2R),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1Q,V3i)),ap(V2R,V3i))))))) # label(lameq_f467) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3909 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27b) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1s),f483(A_27a,V2t,V0P))) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1s),V2t)),f482(A_27a,V0P)))))))))))))))) # label(conj_thm_2Eres__quan_2ERES__FORALL__DIFF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3910 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1m,V3y)),ap(ap(c_2Emin_2E_3D(A_27a),V3y),V2x)) = ap(f495(A_27a,V1m,V2x),V3y)))))) # label(lameq_f495) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3911 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> ap(c_2Emin_2E_40(A_27a),f64(A_27a,V0P,V1f)) = ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0P),V1f))))))) # label(conj_thm_2Eres__quan_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3912 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,A_27a)) -> f518(A_27a,A_27state,V0f) = ap(c_2Estate__transformer_2EREAD(A_27a,A_27state),V0f))))))) # label(ax_thm_2Estate__transformer_2EREAD__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3913 (all A_27state all A_27b all A_27a all V3r ap(f521(A_27state,A_27b,A_27a),V3r) = f520(A_27a,A_27b,A_27state,V3r)) # label(lameq_f521) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3914 (all A_27a all A_27b all A_27state all V3r (mem(V3r,A_27a) -> (all V4s1 ap(f520(A_27a,A_27b,A_27state,V3r),V4s1) = ap(ap(c_2Epair_2E_2C(A_27a,A_27state),V3r),ap(c_2Epair_2ESND(A_27b,A_27state),V4s1))))) # label(lameq_f520) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3915 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Estate__transformer_2Esequence(A_27a,A_27b) = ap(ap(c_2Elist_2EFOLDR(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a))),f530(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b))))))) # label(ax_thm_2Estate__transformer_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3916 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0k (mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> (all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(c_2Estate__transformer_2EJOIN(A_27a,A_27c),ap(ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27b),V1m),V0k)) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0k),V1m))))))))))) # label(conj_thm_2Estate__transformer_2EJOIN__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3917 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27s (ne(A_27s) -> mem(c_2Estate__transformer_2EMCOMP(A_27a,A_27b,A_27c,A_27s),arr(arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))),arr(arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))),arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)))))))))))))) # label(mem_c_2Estate__transformer_2EMCOMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3918 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),c_2Estate__transformer_2EUNIT(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))))) # label(conj_thm_2Estate__transformer_2EJOIN__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3919 (all A_27a all A_27b all A_27state all V0f (mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state))) -> (all V1s1 (mem(V1s1,A_27b) -> (all V2s2 ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),ap(c_2Epair_2EUNCURRY(A_27a,A_27state,ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),f524(A_27state,A_27b,A_27a,V1s1))),ap(V0f,V2s2)) = ap(f525(A_27a,A_27b,A_27state,V0f,V1s1),V2s2)))))) # label(lameq_f525) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3920 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27c)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EJOIN(A_27a,A_27b)))))))))) # label(conj_thm_2Estate__transformer_2EMMAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3921 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27c)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27b),V0f)) = ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f))))))))) # label(conj_thm_2Estate__transformer_2EEXT__JM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3922 (all A_27a all A_27b all V0g (mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a))) -> (all V1b (mem(V1b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> (all V2gv ap(f531(A_27a,A_27b,V0g,V1b),V2gv) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))),V2gv),ap(ap(c_2Estate__transformer_2EIGNORE__BIND(A_27a,ty_2Eone_2Eone,A_27b),V1b),ap(ap(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),V0g),V1b))),ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Eone_2Eone),c_2Eone_2Eone))))))) # label(lameq_f531) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3923 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(bool,A_27a)),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))))))))) # label(mem_c_2Estate__transformer_2EMWHILE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3924 (all A_27state all A_27a all V7a (mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V8h (mem(V8h,A_27a) -> (all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V9t ap(f512(A_27state,A_27a,V7a,V8h,V4FOREACH),V9t) = ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V7a,V8h)),k(ty_2Eone_2Eone,ap(V4FOREACH,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V9t),V7a)))))))))))) # label(lameq_f512) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3925 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V5a_27 ap(f516(A_27state,A_27a,V4FOREACH),V5a_27) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5a_27),f515(A_27state,A_27a,V4FOREACH))))) # label(lameq_f516) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3926 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EUNIT(A_27a,A_27b)) = ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27c),c_2Estate__transformer_2EUNIT(A_27a,A_27c)),V0f))))))))) # label(conj_thm_2Estate__transformer_2EMMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3927 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b)),ty_2Elist_2Elist(arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2Esequence(A_27b,A_27c)),ap(c_2Elist_2EMAP(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))),V0f)) = ap(c_2Estate__transformer_2EmapM(A_27a,A_27b,A_27c),V0f))))))))) # label(ax_thm_2Estate__transformer_2EmapM__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3928 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> ap(c_2Estate__transformer_2EUNIT(A_27a,A_27b),V0x) = f497(A_27b,A_27a,V0x))))))) # label(ax_thm_2Estate__transformer_2EUNIT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3929 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0k (mem(V0k,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> (all V1x (mem(V1x,A_27a) -> ap(V0k,V1x) = ap(ap(c_2Estate__transformer_2EBIND(A_27b,A_27a,A_27c),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V1x)),V0k))))))))))) # label(conj_thm_2Estate__transformer_2EBIND__LEFT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3930 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V5a_27 ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V5a_27),f505(A_27state,V4FOR)) = ap(f506(A_27state,V4FOR),V5a_27)))) # label(lameq_f506) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3931 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> ap(ap(c_2Ecombin_2Eo(A_27b,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2ESND(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V0x)) = c_2Ecombin_2EI(A_27b))))))) # label(conj_thm_2Estate__transformer_2ESND__o__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3932 (all A_27a all A_27b all V3y (mem(V3y,A_27b) -> (all V4ys ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V3y),V4ys)) = ap(f533(A_27a,A_27b,V3y),V4ys)))) # label(lameq_f533) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3933 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> c_2Estate__transformer_2EFOREACH(A_27a,A_27state) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))),f511(A_27state,A_27a))),f517(A_27state,A_27a)))))) # label(ax_thm_2Estate__transformer_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3934 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V7v1 ap(f504(A_27state,V4FOR,V6i),V7v1) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V7v1),f503(A_27state,V6i,V4FOR))))))) # label(lameq_f504) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3935 (all A_27state all V0f (mem(V0f,arr(A_27state,A_27state)) -> (all V1s ap(f519(A_27state,V0f),V1s) = ap(ap(c_2Epair_2E_2C(ty_2Eone_2Eone,A_27state),c_2Eone_2Eone),ap(V0f,V1s))))) # label(lameq_f519) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3936 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Estate__transformer_2Esequence(A_27a,A_27b),arr(ty_2Elist_2Elist(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))))))) # label(mem_c_2Estate__transformer_2Esequence) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3937 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V6v ap(f515(A_27state,A_27a,V4FOREACH),V6v) = f514(A_27state,A_27a,V4FOREACH,V6v)))) # label(lameq_f515) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3938 (all A_27a all A_27b all V0m (mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> (all V1ms ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),V0m),f528(A_27a,A_27b,V1ms)) = ap(f529(A_27a,A_27b,V0m),V1ms)))) # label(lameq_f529) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3939 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)) = ap(c_2Estate__transformer_2Esequence(A_27a,A_27b),c_2Elist_2ENIL(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(conj_thm_2Estate__transformer_2Esequence__nil) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3940 (all A_27state all A_27a all V1h (mem(V1h,A_27a) -> (all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))) -> (all V2a ap(f509(A_27state,A_27a,V1h,V0R),V2a) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27a)),f508(A_27state,A_27a,V0R,V1h,V2a))))))) # label(lameq_f509) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3941 (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,A_27state)) -> f519(A_27state,V0f) = ap(c_2Estate__transformer_2EWRITE(A_27state),V0f))))) # label(ax_thm_2Estate__transformer_2EWRITE__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3942 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Estate__transformer_2EIGNORE__BIND(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))))))))) # label(mem_c_2Estate__transformer_2EIGNORE__BIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3943 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all V0f (mem(V0f,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> (all V1g (mem(V1g,arr(A_27e,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b)))) -> (all V2h (mem(V2h,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27e,A_27b)))) -> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27e,A_27c,A_27b),ap(ap(c_2Estate__transformer_2EMCOMP(A_27e,A_27d,A_27c,A_27b),V0f),V1g)),V2h) = ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),V0f),ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27e,A_27d,A_27b),V1g),V2h)))))))))))))))))) # label(conj_thm_2Estate__transformer_2EMCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3944 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> V0f = ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),ap(c_2Estate__transformer_2EEXT(A_27a,A_27c,A_27b),V0f)),c_2Estate__transformer_2EUNIT(A_27b,A_27a)))))))))) # label(conj_thm_2Estate__transformer_2EEXT__o__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3945 (all A_27b all A_27a all V0x (mem(V0x,A_27b) -> (all V1s ap(f497(A_27b,A_27a,V0x),V1s) = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V0x),V1s)))) # label(lameq_f497) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3946 (all A_27state all A_27a all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))) -> (all V1h (mem(V1h,A_27a) -> (all V2a (mem(V2a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V3t ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V3t),V2a)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3t)),V2a)) = ap(f508(A_27state,A_27a,V0R,V1h,V2a),V3t)))))))) # label(lameq_f508) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3947 (all A_27state all A_27a all V7a (mem(V7a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V8h f512(A_27state,A_27a,V7a,V8h,V4FOREACH) = ap(f513(A_27state,A_27a,V7a,V4FOREACH),V8h)))))) # label(lameq_f513) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3948 (all A_27state all A_27a all V0R ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V0R)),ap(c_2Ebool_2E_21(A_27a),f510(A_27state,A_27a,V0R))) = ap(f511(A_27state,A_27a),V0R)) # label(lameq_f511) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3949 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))))))))) # label(mem_c_2Estate__transformer_2EMMAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3950 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V6i f504(A_27state,V4FOR,V6i) = ap(f505(A_27state,V4FOR),V6i)))) # label(lameq_f505) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3951 (all A_27state all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V1a ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f499(A_27state,V0R,V1a)) = ap(f500(A_27state,V0R),V1a)))) # label(lameq_f500) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3952 (all A_27state (ne(A_27state) -> (all V0j (mem(V0j,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1i),V0j)),ap(V2a,V1i)),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V2a,V1i)),k(ty_2Eone_2Eone,ap(c_2Estate__transformer_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V0j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V0j),V2a)))))) = ap(c_2Estate__transformer_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V0j),V2a))))))))))) # label(conj_thm_2Estate__transformer_2EFOR__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3953 (all A_27a all A_27b all V0m f529(A_27a,A_27b,V0m) = ap(f530(A_27a,A_27b),V0m)) # label(lameq_f530) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3954 (all A_27state all A_27b all A_27a all V1s1 (mem(V1s1,A_27b) -> (all V3r f523(A_27b,A_27a,A_27state,V1s1,V3r) = ap(f524(A_27state,A_27b,A_27a,V1s1),V3r)))) # label(lameq_f524) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3955 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27c,A_27d)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27d,A_27b),ap(ap(c_2Ecombin_2Eo(A_27b,A_27d,A_27c),V0f),V1g)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27d,A_27c),V0f)),ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V1g)))))))))))))) # label(conj_thm_2Estate__transformer_2EMMAP__COMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.40 3956 (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27s (ne(A_27s) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)))) -> (all V1m (mem(V1m,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))) -> ap(ap(c_2Ecombin_2Eo(A_27s,ty_2Epair_2Eprod(A_27c,A_27s),ty_2Epair_2Eprod(A_27b,A_27s)),ap(c_2Epair_2EUNCURRY(A_27b,A_27s,ty_2Epair_2Eprod(A_27c,A_27s)),V0f)),V1m) = ap(ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),V0f),V1m))))))))))) # label(ax_thm_2Estate__transformer_2EEXT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3957 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Estate__transformer_2EmapM(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b))),arr(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b))))))))))) # label(mem_c_2Estate__transformer_2EmapM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3958 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b)))) -> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),V0g),V1f) = ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27b),ty_2Epair_2Eprod(A_27d,A_27b)),ap(c_2Epair_2EUNCURRY(A_27d,A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),V0g)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27d,A_27b)),V1f))))))))))))))) # label(conj_thm_2Estate__transformer_2EMCOMP__ALT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3959 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27d,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a)))) -> ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),ap(ap(c_2Estate__transformer_2EMCOMP(A_27b,A_27d,A_27c,A_27a),V0g),V1f)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a))),ap(c_2Estate__transformer_2EEXT(A_27d,A_27c,A_27a),V0g)),ap(c_2Estate__transformer_2EEXT(A_27b,A_27d,A_27a),V1f)))))))))))))) # label(conj_thm_2Estate__transformer_2EEXT__MCOMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3960 (all A_27b all A_27a all A_27state all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))) -> (all V0v (mem(V0v,A_27b) -> (all V2s ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),ty_2Epair_2Eprod(A_27a,A_27state)),ap(c_2Epair_2EUNCURRY(A_27a,ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,A_27state)),f521(A_27state,A_27b,A_27a))),ap(V1f,ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V0v),V2s))) = ap(f522(A_27b,A_27a,A_27state,V1f,V0v),V2s)))))) # label(lameq_f522) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3961 (all A_27c all A_27d all A_27a all A_27b all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> (all V2n (mem(V2n,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a)))) -> (all V3a ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27d),ap(V1m,V3a)),V2n) = ap(f532(A_27c,A_27d,A_27a,A_27b,V1m,V2n),V3a)))))) # label(lameq_f532) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3962 (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27s (ne(A_27s) -> mem(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),arr(arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))),arr(arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s)),arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s))))))))))) # label(mem_c_2Estate__transformer_2EEXT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3963 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2EWIDEN(A_27a,A_27b,A_27state),arr(arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)),arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))))))))) # label(mem_c_2Estate__transformer_2EWIDEN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3964 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0z (mem(V0z,arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))) -> ap(c_2Estate__transformer_2EJOIN(A_27a,A_27b),V0z) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),V0z),c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))))) # label(ax_thm_2Estate__transformer_2EJOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3965 (all A_27state (ne(A_27state) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool)) -> ((all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2j (mem(V2j,ty_2Enum_2Enum) -> (all V3a (mem(V3a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> ((V1i != V2j -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V3a))))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V3a))))))))))) -> (all V4v (mem(V4v,ty_2Enum_2Enum) -> (all V5v1 (mem(V5v1,ty_2Enum_2Enum) -> (all V6v2 (mem(V6v2,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V4v),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5v1),V6v2))))))))))))))) # label(conj_thm_2Estate__transformer_2EFOR__ind) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3966 (all A_27a all A_27c all A_27b all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27c)) -> (all V3y ap(f534(A_27a,A_27c,A_27b,V0f,V2xs),V3y) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),V2xs)),f533(A_27a,A_27b,V3y))))))) # label(lameq_f534) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3967 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) -> ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27c)) = ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)))))))))) # label(conj_thm_2Estate__transformer_2EmapM__nil) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3968 (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2EFOR(A_27state),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))) # label(mem_c_2Estate__transformer_2EFOR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3969 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V0a (mem(V0a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),c_2Elist_2ENIL(A_27a)),V0a)) = ap(c_2Estate__transformer_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone))) & (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27a) -> (all V3a (mem(V3a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t)),V3a)) = ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V3a,V2h)),k(ty_2Eone_2Eone,ap(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V1t),V3a)))))))))))))) # label(conj_thm_2Estate__transformer_2EFOREACH__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3970 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0g (mem(V0g,arr(A_27a,ty_2Epair_2Eprod(bool,A_27a))) -> (all V1b (mem(V1b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> ap(ap(c_2Estate__transformer_2EBIND(A_27a,bool,ty_2Eone_2Eone),V0g),f531(A_27a,A_27b,V0g,V1b)) = ap(ap(c_2Estate__transformer_2EMWHILE(A_27a,A_27b),V0g),V1b))))))))) # label(ax_thm_2Estate__transformer_2EMWHILE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3971 (all A_27a all A_27b all V1ms (mem(V1ms,arr(A_27a,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a))) -> (all V2x ap(f528(A_27a,A_27b,V1ms),V2x) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),V1ms),f527(A_27a,A_27b,V2x))))) # label(lameq_f528) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3972 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0k (mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> V0k = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27b),V0k),c_2Estate__transformer_2EUNIT(A_27a,A_27b)))))))) # label(conj_thm_2Estate__transformer_2EBIND__RIGHT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3973 (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2EWRITE(A_27state),arr(arr(A_27state,A_27state),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))) # label(mem_c_2Estate__transformer_2EWRITE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3974 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(c_2Estate__transformer_2EEXT(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27c,A_27a),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f)) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),V0f)),c_2Estate__transformer_2EJOIN(A_27a,A_27b)))))))))) # label(conj_thm_2Estate__transformer_2EEXT__o__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3975 (all A_27state all A_27a all A_27b all V0f (mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state))) -> (all V1s1 ap(f526(A_27state,A_27a,A_27b,V0f),V1s1) = f525(A_27a,A_27b,A_27state,V0f,V1s1)))) # label(lameq_f526) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3976 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Ecombin_2EK(A_27a,A_27b),V0x) = ap(ap(c_2Ecombin_2Eo(A_27b,A_27a,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2EFST(A_27a,A_27b)),ap(c_2Estate__transformer_2EUNIT(A_27b,A_27a),V0x)))))))) # label(conj_thm_2Estate__transformer_2EFST__o__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3977 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0g (mem(V0g,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Epair_2Eprod(A_27c,A_27a),ty_2Epair_2Eprod(A_27b,A_27a)),ap(c_2Epair_2EUNCURRY(A_27b,A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),V1f)),V0g) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0g),V1f))))))))))) # label(ax_thm_2Estate__transformer_2EBIND__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3978 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2EREAD(A_27a,A_27state),arr(arr(A_27state,A_27a),arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state)))))))) # label(mem_c_2Estate__transformer_2EREAD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3979 (all A_27state all V0R ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V0R)),ap(c_2Ebool_2E_21(arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),f500(A_27state,V0R))) = ap(f501(A_27state),V0R)) # label(lameq_f501) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3980 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all V0g (mem(V0g,arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)))) -> (all V1f (mem(V1f,arr(A_27d,arr(A_27e,ty_2Epair_2Eprod(A_27f,A_27e)))) -> V1f = ap(ap(c_2Estate__transformer_2EMCOMP(A_27d,A_27f,A_27f,A_27e),c_2Estate__transformer_2EUNIT(A_27e,A_27f)),V1f) & ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27a,A_27c,A_27b),V0g),c_2Estate__transformer_2EUNIT(A_27b,A_27a)) = V0g)))))))))))))))) # label(conj_thm_2Estate__transformer_2EMCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3981 (all A_27state all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V8j f502(A_27state,V6i,V8j,V4FOR) = ap(f503(A_27state,V6i,V4FOR),V8j)))))) # label(lameq_f503) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3982 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0k (mem(V0k,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> (all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)))) -> (all V2n (mem(V2n,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27d,A_27a)))) -> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27d),ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),V0k),V1m)),V2n) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27d),V0k),f532(A_27c,A_27d,A_27a,A_27b,V1m,V2n)))))))))))))))) # label(conj_thm_2Estate__transformer_2EBIND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3983 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state))) -> ap(c_2Epair_2EUNCURRY(A_27b,A_27state,ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),f526(A_27state,A_27a,A_27b,V0f)) = ap(c_2Estate__transformer_2EWIDEN(A_27a,A_27b,A_27state),V0f))))))))) # label(ax_thm_2Estate__transformer_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3984 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Estate__transformer_2EJOIN(A_27a,A_27b),arr(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(mem_c_2Estate__transformer_2EJOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3985 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0m (mem(V0m,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))) -> (all V1f (mem(V1f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) -> ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V0m),V1f) = ap(ap(c_2Estate__transformer_2EEXT(A_27c,A_27b,A_27a),V1f),V0m))))))))))) # label(conj_thm_2Estate__transformer_2EBIND__EXT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3986 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))))) # label(conj_thm_2Estate__transformer_2EMMAP__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3987 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Estate__transformer_2EJOIN(A_27a,A_27b) = ap(c_2Estate__transformer_2EEXT(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b,A_27a),c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(conj_thm_2Estate__transformer_2EJOIN__EXT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3988 (all A_27state all V1a (mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V2j (mem(V2j,ty_2Enum_2Enum) -> (all V3i ap(f498(A_27state,V1a,V0R,V2j),V3i) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3i),V2j))),ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V3i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V1a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V3i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V2j),V1a))))))))))) # label(lameq_f498) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3989 (all A_27state all A_27a all V4FOREACH f516(A_27state,A_27a,V4FOREACH) = ap(f517(A_27state,A_27a),V4FOREACH)) # label(lameq_f517) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3990 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,ty_2Epair_2Eprod(A_27a,A_27c))) -> ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,ty_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2EFST(A_27a,A_27c)),V1g)) = ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,ty_2Epair_2Eprod(A_27b,A_27c)),c_2Epair_2EFST(A_27b,A_27c)),ap(ap(c_2Estate__transformer_2EMMAP(A_27c,A_27b,A_27a),V0f),V1g)))))))))))) # label(conj_thm_2Estate__transformer_2EFST__o__MMAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3991 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,ty_2Epair_2Eprod(A_27a,A_27b)) -> V0s = ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT(A_27b,A_27a)),V0s))))))) # label(conj_thm_2Estate__transformer_2EUNIT__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3992 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27s (ne(A_27s) -> (all V0g (mem(V0g,arr(A_27b,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s)))) -> ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27b,A_27c,A_27s),V0g),V1f) = ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27s,ty_2Epair_2Eprod(A_27c,A_27s)),arr(A_27s,ty_2Epair_2Eprod(A_27b,A_27s))),ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27s),V0g)),V1f))))))))))))) # label(ax_thm_2Estate__transformer_2EMCOMP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3993 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) = ap(c_2Estate__transformer_2EEXT(A_27b,A_27b,A_27a),c_2Estate__transformer_2EUNIT(A_27a,A_27b)))))) # label(conj_thm_2Estate__transformer_2EEXT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3994 (all A_27state all A_27a all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool))) -> (all V1h ap(f510(A_27state,A_27a,V0R),V1h) = ap(c_2Ebool_2E_21(arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),f509(A_27state,A_27a,V1h,V0R))))) # label(lameq_f510) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3995 (all A_27state all V4FOR f506(A_27state,V4FOR) = ap(f507(A_27state),V4FOR)) # label(lameq_f507) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3996 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),c_2Estate__transformer_2EUNIT(A_27a,A_27b))) = c_2Ecombin_2EI(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))))))) # label(conj_thm_2Estate__transformer_2EJOIN__MMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3997 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),ap(c_2Estate__transformer_2EMMAP(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(A_27a,ty_2Epair_2Eprod(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN(A_27a,A_27b)),c_2Estate__transformer_2EJOIN(A_27a,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(conj_thm_2Estate__transformer_2EJOIN__MAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3998 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1m (mem(V1m,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))) -> ap(ap(c_2Estate__transformer_2EMMAP(A_27a,A_27b,A_27c),V0f),V1m) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V1m),ap(ap(c_2Ecombin_2Eo(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),A_27b),c_2Estate__transformer_2EUNIT(A_27a,A_27b)),V0f)))))))))))) # label(ax_thm_2Estate__transformer_2EMMAP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 3999 (all A_27state all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V8j (mem(V8j,ty_2Enum_2Enum) -> (all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V9a ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6i),V8j)),ap(V9a,V6i)),ap(ap(c_2Estate__transformer_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V9a,V6i)),k(ty_2Eone_2Eone,ap(V4FOR,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V6i),V8j)),ap(ap(c_2Earithmetic_2E_2B,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V8j),V9a))))))) = ap(f502(A_27state,V6i,V8j,V4FOR),V9a)))))))) # label(lameq_f502) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4000 (all A_27a all A_27b all V2x (mem(V2x,A_27b) -> (all V3xs ap(c_2Estate__transformer_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V2x),V3xs)) = ap(f527(A_27a,A_27b,V2x),V3xs)))) # label(lameq_f527) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4001 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Estate__transformer_2EUNIT(A_27b,A_27a) = ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI(ty_2Epair_2Eprod(A_27a,A_27b))))))) # label(conj_thm_2Estate__transformer_2EUNIT__CURRY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4002 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V1x (mem(V1x,A_27c) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2Estate__transformer_2EmapM(A_27c,A_27a,A_27b),V0f),ap(ap(c_2Elist_2ECONS(A_27c),V1x),V2xs)) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),ap(V0f,V1x)),f534(A_27a,A_27c,A_27b,V0f,V2xs)))))))))))))) # label(conj_thm_2Estate__transformer_2EmapM__cons) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4003 (all A_27a all A_27state all V0f (mem(V0f,arr(A_27state,A_27a)) -> (all V1s ap(ap(c_2Epair_2E_2C(A_27a,A_27state),ap(V0f,V1s)),V1s) = ap(f518(A_27a,A_27state,V0f),V1s)))) # label(lameq_f518) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4004 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2EFOREACH(A_27a,A_27state),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))))) # label(mem_c_2Estate__transformer_2EFOREACH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4005 (all A_27b all A_27a all A_27state all V1s1 (mem(V1s1,A_27b) -> (all V3r (mem(V3r,A_27a) -> (all V4s3 ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),V3r),ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V1s1),V4s3)) = ap(f523(A_27b,A_27a,A_27state,V1s1,V3r),V4s3)))))) # label(lameq_f523) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4006 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27d,A_27c)) -> (all V1f (mem(V1f,arr(A_27a,A_27d)) -> ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),A_27c),c_2Estate__transformer_2EUNIT(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27d),V0g),V1f)) = ap(ap(c_2Estate__transformer_2EMCOMP(A_27a,A_27d,A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27d,arr(A_27b,ty_2Epair_2Eprod(A_27c,A_27b)),A_27c),c_2Estate__transformer_2EUNIT(A_27b,A_27c)),V0g)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27d,A_27b)),A_27d),c_2Estate__transformer_2EUNIT(A_27b,A_27d)),V1f)))))))))))))) # label(conj_thm_2Estate__transformer_2EUNIT__o__MCOMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4007 (all A_27state all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V1a (mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V2j ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f498(A_27state,V1a,V0R,V2j)) = ap(f499(A_27state,V0R,V1a),V2j)))))) # label(lameq_f499) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4008 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))) -> f522(A_27b,A_27a,A_27state,V1f,V0v) = ap(ap(c_2Estate__transformer_2ENARROW(A_27a,A_27b,A_27state),V0v),V1f))))))))))) # label(ax_thm_2Estate__transformer_2ENARROW__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4009 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> mem(c_2Estate__transformer_2ENARROW(A_27a,A_27b,A_27state),arr(A_27b,arr(arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),arr(A_27state,ty_2Epair_2Eprod(A_27a,A_27state))))))))))) # label(mem_c_2Estate__transformer_2ENARROW) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4010 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))) -> (all V1g (mem(V1g,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a))) -> ap(ap(c_2Estate__transformer_2EIGNORE__BIND(A_27a,A_27b,A_27c),V0f),V1g) = ap(ap(c_2Estate__transformer_2EBIND(A_27a,A_27c,A_27b),V0f),k(A_27c,V1g)))))))))))) # label(ax_thm_2Estate__transformer_2EIGNORE__BIND__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4011 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Estate__transformer_2EBIND(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)),arr(arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))),arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a))))))))))) # label(mem_c_2Estate__transformer_2EBIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4012 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,A_27c)) -> ap(c_2Estate__transformer_2EMMAP(A_27a,A_27c,A_27b),V0f) = ap(c_2Estate__transformer_2EEXT(A_27b,A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27c,A_27a)),A_27c),c_2Estate__transformer_2EUNIT(A_27a,A_27c)),V0f)))))))))) # label(conj_thm_2Estate__transformer_2EMMAP__EXT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4013 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (all V6v (mem(V6v,ty_2Elist_2Elist(A_27a)) -> (all V7a ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),V6v),ap(c_2Ecombin_2EI(arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Estate__transformer_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone))),f513(A_27state,A_27a,V7a,V4FOREACH)) = ap(f514(A_27state,A_27a,V4FOREACH,V6v),V7a)))))) # label(lameq_f514) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4014 (all A_27state (ne(A_27state) -> ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))),f501(A_27state))),f507(A_27state)) = c_2Estate__transformer_2EFOR(A_27state))) # label(ax_thm_2Estate__transformer_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4015 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Estate__transformer_2EUNIT(A_27a,A_27b),arr(A_27b,arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(mem_c_2Estate__transformer_2EUNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4016 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),bool)) -> ((all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (all V4a (mem(V4a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> (p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V3t),V4a))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)),V4a)))))))))) & (all V1a (mem(V1a,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),c_2Elist_2ENIL(A_27a)),V1a))))) -> (all V5v (mem(V5v,ty_2Elist_2Elist(A_27a)) -> (all V6v1 (mem(V6v1,arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V5v),V6v1)))))))))))))) # label(conj_thm_2Estate__transformer_2EFOREACH__ind) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4017 (all V0lo (mem(V0lo,ty_2Enum_2Enum) -> (all V1hi (mem(V1hi,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0lo),V1hi)) -> ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi) = ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0lo),ap(ap(c_2ElistRange_2ElistRangeLHI,ap(ap(c_2Earithmetic_2E_2B,V0lo),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1hi))))))) # label(conj_thm_2ElistRange_2ElistRangeLHI__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4018 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeINC,V1m),V2n)))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V2n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0x))))))))) # label(conj_thm_2ElistRange_2EMEM__listRangeINC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4019 (all V0lo (mem(V0lo,ty_2Enum_2Enum) -> (all V1hi (mem(V1hi,ty_2Enum_2Enum) -> ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi)) = ap(ap(c_2Earithmetic_2E_2D,V1hi),V0lo))))) # label(conj_thm_2ElistRange_2ELENGTH__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4020 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0x)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V2n)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V1m),V2n))))))))))) # label(conj_thm_2ElistRange_2EMEM__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4021 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) -> c_2Elist_2ENIL(ty_2Enum_2Enum) = ap(ap(c_2ElistRange_2ElistRangeINC,V1m),V0n)))))) # label(conj_thm_2ElistRange_2ElistRangeINC__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4022 (all V0m (mem(V0m,ty_2Enum_2Enum) -> c_2Elist_2ENIL(ty_2Enum_2Enum) = ap(ap(c_2ElistRange_2ElistRangeLHI,V0m),V0m))) # label(conj_thm_2ElistRange_2ElistRangeLHI__EQ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4023 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V2i ap(ap(c_2Earithmetic_2E_2B,V0m),V2i) = ap(f535(V0m),V2i)))) # label(lameq_f535) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4024 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),f535(V0m)),ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)) = ap(ap(c_2ElistRange_2ElistRangeLHI,V0m),V1n))))) # label(ax_thm_2ElistRange_2ElistRangeLHI__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4025 (all V0hi (mem(V0hi,ty_2Enum_2Enum) -> (all V1lo (mem(V1lo,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0hi),V1lo)) -> c_2Elist_2ENIL(ty_2Enum_2Enum) = ap(ap(c_2ElistRange_2ElistRangeLHI,V1lo),V0hi)))))) # label(conj_thm_2ElistRange_2ElistRangeLHI__EMPTY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4026 (all V0lo (mem(V0lo,ty_2Enum_2Enum) -> (all V1hi (mem(V1hi,ty_2Enum_2Enum) -> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Enum_2Enum),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V1hi))))))) # label(conj_thm_2ElistRange_2ElistRangeLHI__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4027 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0m),c_2Elist_2ENIL(ty_2Enum_2Enum)) = ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V0m))) # label(conj_thm_2ElistRange_2ElistRangeINC__SING) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4028 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V1n) = ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0m),ap(ap(c_2ElistRange_2ElistRangeINC,ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1n))))))) # label(conj_thm_2ElistRange_2ElistRangeINC__CONS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4029 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),f535(V0m)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0m)) = ap(ap(c_2ElistRange_2ElistRangeINC,V0m),V1n))))) # label(ax_thm_2ElistRange_2ElistRangeINC__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4030 (all V0lo (mem(V0lo,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2hi (mem(V2hi,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0lo),V1i)),V2hi)) -> ap(ap(c_2Earithmetic_2E_2B,V0lo),V1i) = ap(ap(c_2Elist_2EEL(ty_2Enum_2Enum),V1i),ap(ap(c_2ElistRange_2ElistRangeLHI,V0lo),V2hi))))))))) # label(conj_thm_2ElistRange_2EEL__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4031 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xM (mem(V0xM,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> V0xM = ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),V0xM),c_2EerrorStateMonad_2EES__FAIL(A_27b,A_27a)))))))) # label(conj_thm_2EerrorStateMonad_2EES__CHOICE__FAIL__RID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4032 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EEXT(A_27a,A_27b,A_27c),arr(arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))))))))))) # label(mem_c_2EerrorStateMonad_2EEXT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4033 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(c_2EerrorStateMonad_2EMMAP(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))))))) # label(conj_thm_2EerrorStateMonad_2EMMAP__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4034 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2ENARROW(A_27a,A_27b,A_27state),arr(A_27b,arr(arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state)))))))))))) # label(mem_c_2EerrorStateMonad_2ENARROW) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4035 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)) = ap(ap(c_2EerrorStateMonad_2EmapM(A_27c,A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27c)))))))))) # label(conj_thm_2EerrorStateMonad_2EmapM__nil) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4036 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EES__APPLY(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27c,A_27b),A_27a))),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))))))))))) # label(mem_c_2EerrorStateMonad_2EES__APPLY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4037 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V1t (mem(V1t,ty_2Elist_2Elist(A_27a)) -> (all V2h (mem(V2h,A_27a) -> (all V3a (mem(V3a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V3a,V2h)),k(ty_2Eone_2Eone,ap(c_2EerrorStateMonad_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V1t),V3a)))) = ap(c_2EerrorStateMonad_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t)),V3a)))))))) & (all V0a (mem(V0a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> ap(c_2EerrorStateMonad_2EFOREACH(A_27a,A_27state),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),c_2Elist_2ENIL(A_27a)),V0a)) = ap(c_2EerrorStateMonad_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone))))))) # label(conj_thm_2EerrorStateMonad_2EFOREACH__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4038 (all A_27state all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V8j f544(A_27state,V6i,V8j,V4FOR) = ap(f545(A_27state,V6i,V4FOR),V8j)))))) # label(lameq_f545) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4039 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))))) -> ap(c_2EerrorStateMonad_2EmapM(A_27a,A_27b,A_27c),V0f) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b))),ty_2Elist_2Elist(arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))))),c_2EerrorStateMonad_2Esequence(A_27b,A_27c)),ap(c_2Elist_2EMAP(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b)))),V0f)))))))))) # label(ax_thm_2EerrorStateMonad_2EmapM__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4040 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> ap(ap(c_2Ecombin_2Eo(arr(A_27d,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27d))),arr(A_27d,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27d))),arr(A_27d,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27d)))),ap(c_2EerrorStateMonad_2EMMAP(A_27d,A_27b,A_27a),V0f)),ap(c_2EerrorStateMonad_2EMMAP(A_27d,A_27a,A_27c),V1g)) = ap(c_2EerrorStateMonad_2EMMAP(A_27d,A_27b,A_27c),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)))))))))))))) # label(conj_thm_2EerrorStateMonad_2EMMAP__COMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4041 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1xM (mem(V1xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2EerrorStateMonad_2EMMAP(A_27a,A_27b,A_27c),V0f),V1xM) = ap(ap(c_2EerrorStateMonad_2EES__APPLY(A_27a,A_27b,A_27c),ap(c_2EerrorStateMonad_2EUNIT(A_27a,arr(A_27c,A_27b)),V0f)),V1xM))))))))))) # label(conj_thm_2EerrorStateMonad_2EAPPLY__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4042 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2EREAD(A_27a,A_27state),arr(arr(A_27state,A_27a),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state))))))))) # label(mem_c_2EerrorStateMonad_2EREAD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4043 (all A_27a all A_27b all V3y (mem(V3y,A_27b) -> (all V4ys ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V3y),V4ys)) = ap(f576(A_27a,A_27b,V3y),V4ys)))) # label(lameq_f576) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4044 (all A_27state all A_27a all V4FOREACH ap(f559(A_27state,A_27a),V4FOREACH) = f558(A_27state,A_27a,V4FOREACH)) # label(lameq_f559) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4045 (all A_27state all A_27a all V7a (mem(V7a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V8h ap(f555(A_27state,A_27a,V7a,V4FOREACH),V8h) = f554(A_27state,A_27a,V7a,V8h,V4FOREACH)))))) # label(lameq_f555) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4046 (all A_27state all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),bool))) -> (all V1a ap(f542(A_27state,V0R),V1a) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f541(A_27state,V0R,V1a))))) # label(lameq_f542) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4047 (all A_27state all V4FOR ap(f549(A_27state),V4FOR) = f548(A_27state,V4FOR)) # label(lameq_f549) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4048 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,A_27a)) -> f560(A_27a,A_27state,V0f) = ap(c_2EerrorStateMonad_2EREAD(A_27a,A_27state),V0f))))))) # label(ax_thm_2EerrorStateMonad_2EREAD__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4049 (all A_27state all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V8j (mem(V8j,ty_2Enum_2Enum) -> (all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V9a ap(c_2Ecombin_2EI(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6i),V8j)),ap(V9a,V6i)),ap(ap(c_2EerrorStateMonad_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V9a,V6i)),k(ty_2Eone_2Eone,ap(V4FOR,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V6i),V8j)),ap(ap(c_2Earithmetic_2E_2B,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V6i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V8j),V9a))))))) = ap(f544(A_27state,V6i,V8j,V4FOR),V9a)))))))) # label(lameq_f544) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4050 (all A_27state all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),bool))) -> (all V1a (mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V2j ap(f541(A_27state,V0R,V1a),V2j) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f540(A_27state,V1a,V0R,V2j))))))) # label(lameq_f541) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4051 (all A_27b all A_27a all V0x (mem(V0x,A_27b) -> (all V1s ap(f536(A_27b,A_27a,V0x),V1s) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(A_27b,A_27a)),ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V0x),V1s))))) # label(lameq_f536) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4052 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EerrorStateMonad_2Esequence(A_27a,A_27b),arr(ty_2Elist_2Elist(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a))))))))) # label(mem_c_2EerrorStateMonad_2Esequence) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4053 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EerrorStateMonad_2EES__FAIL(A_27a,A_27b),arr(A_27b,ty_2Eoption_2Eoption(A_27a))))))) # label(mem_c_2EerrorStateMonad_2EES__FAIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4054 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27d,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27b))))) -> ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))),arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27b)))),ap(c_2EerrorStateMonad_2EEXT(A_27b,A_27c,A_27d),V0g)),V1f) = ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,ty_2Epair_2Eprod(A_27c,A_27b),A_27d,A_27b),V0g),V1f))))))))))))) # label(conj_thm_2EerrorStateMonad_2EMCOMP__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4055 (all A_27state (ne(A_27state) -> (all V0j (mem(V0j,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> ap(c_2EerrorStateMonad_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V0j),V2a))) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1i),V0j)),ap(V2a,V1i)),ap(ap(c_2EerrorStateMonad_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V2a,V1i)),k(ty_2Eone_2Eone,ap(c_2EerrorStateMonad_2EFOR(A_27state),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V0j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V0j),V2a)))))))))))))) # label(conj_thm_2EerrorStateMonad_2EFOR__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4056 (all A_27state all A_27b all A_27a all V1s1 (mem(V1s1,A_27b) -> (all V4r f566(A_27b,A_27a,A_27state,V4r,V1s1) = ap(f567(A_27state,A_27b,A_27a,V1s1),V4r)))) # label(lameq_f567) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4057 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xM (mem(V0xM,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V1yM (mem(V1yM,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V2zM (mem(V2zM,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),V0xM),V1yM)),V2zM) = ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),V0xM),ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),V1yM),V2zM)))))))))))) # label(conj_thm_2EerrorStateMonad_2EES__CHOICE__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4058 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ecombin_2EI(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN(A_27a,A_27b)),c_2EerrorStateMonad_2EUNIT(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))) # label(conj_thm_2EerrorStateMonad_2EJOIN__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4059 (all A_27state all A_27a all V1h (mem(V1h,A_27a) -> (all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V2a ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27a)),f550(A_27state,A_27a,V0R,V1h,V2a)) = ap(f551(A_27state,A_27a,V1h,V0R),V2a)))))) # label(lameq_f551) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4060 (all A_27a all A_27b all V1ms (mem(V1ms,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))) -> (all V2x ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),V1ms),f571(A_27a,A_27b,V2x)) = ap(f572(A_27a,A_27b,V1ms),V2x)))) # label(lameq_f572) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4061 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a)))),V0b),ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Eone_2Eone),c_2Eone_2Eone)),c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a),A_27a)) = ap(c_2EerrorStateMonad_2EES__GUARD(A_27a),V0b))))) # label(ax_thm_2EerrorStateMonad_2EES__GUARD__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4062 (all A_27a all V3v1 ap(f578(A_27a),V3v1) = ap(c_2Eoption_2ESOME(A_27a),V3v1)) # label(lameq_f578) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4063 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27b)))) -> (all V1g (mem(V1g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b)))) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27b,A_27a,A_27c),V0f),k(A_27a,V1g)) = ap(ap(c_2EerrorStateMonad_2EIGNORE__BIND(A_27a,A_27b,A_27c),V0f),V1g))))))))))) # label(ax_thm_2EerrorStateMonad_2EIGNORE__BIND__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4064 (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,A_27state)) -> f561(A_27state,V0f) = ap(c_2EerrorStateMonad_2EWRITE(A_27state),V0f))))) # label(ax_thm_2EerrorStateMonad_2EWRITE__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4065 (all A_27a all A_27b all V0m ap(f574(A_27a,A_27b),V0m) = f573(A_27a,A_27b,V0m)) # label(lameq_f574) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4066 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0xM (mem(V0xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27b,A_27a),A_27a) = ap(ap(c_2EerrorStateMonad_2EIGNORE__BIND(A_27c,A_27a,A_27b),c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27c,A_27a),A_27a)),V0xM) & ap(ap(c_2EerrorStateMonad_2EIGNORE__BIND(A_27b,A_27a,A_27d),V0xM),c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27d,A_27a),A_27a)) = c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27d,A_27a),A_27a))))))))))) # label(conj_thm_2EerrorStateMonad_2EIGNORE__BIND__FAIL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4067 (all A_27state all A_27a all V7a (mem(V7a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V8h (mem(V8h,A_27a) -> (all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V9t ap(c_2Ecombin_2EI(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(ap(c_2EerrorStateMonad_2EBIND(A_27state,ty_2Eone_2Eone,ty_2Eone_2Eone),ap(V7a,V8h)),k(ty_2Eone_2Eone,ap(V4FOREACH,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V9t),V7a))))) = ap(f554(A_27state,A_27a,V7a,V8h,V4FOREACH),V9t)))))))) # label(lameq_f554) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4068 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN(A_27a,A_27b)),ap(c_2EerrorStateMonad_2EMMAP(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN(A_27a,A_27b))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN(A_27a,A_27b)),c_2EerrorStateMonad_2EJOIN(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))) # label(conj_thm_2EerrorStateMonad_2EJOIN__MAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4069 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xM (mem(V0xM,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> V0xM = ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27b,A_27a),c_2EerrorStateMonad_2EES__FAIL(A_27b,A_27a)),V0xM))))))) # label(conj_thm_2EerrorStateMonad_2EES__CHOICE__FAIL__LID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4070 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> mem(c_2EerrorStateMonad_2EES__LIFT2(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27c,arr(A_27d,A_27b)),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))))))))) # label(mem_c_2EerrorStateMonad_2EES__LIFT2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4071 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1m (mem(V1m,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27b),V1m),ap(ap(c_2Ecombin_2Eo(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27b),c_2EerrorStateMonad_2EUNIT(A_27a,A_27b)),V0f)) = ap(ap(c_2EerrorStateMonad_2EMMAP(A_27a,A_27b,A_27c),V0f),V1m))))))))))) # label(ax_thm_2EerrorStateMonad_2EMMAP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4072 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2EerrorStateMonad_2Esequence(A_27a,A_27b) = ap(ap(c_2Elist_2EFOLDR(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27b),A_27a)))),f574(A_27a,A_27b)),ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b))))))) # label(ax_thm_2EerrorStateMonad_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4073 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EerrorStateMonad_2EUNIT(A_27a,A_27b),arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))) # label(mem_c_2EerrorStateMonad_2EUNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4074 (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2EWRITE(A_27state),arr(arr(A_27state,A_27state),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))))) # label(mem_c_2EerrorStateMonad_2EWRITE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4075 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xM (mem(V0xM,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V1yM (mem(V1yM,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V2s (mem(V2s,A_27b) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),ap(V0xM,V2s)),ap(V1yM,V2s)),f578(A_27a)) = ap(ap(ap(c_2EerrorStateMonad_2EES__CHOICE(A_27a,A_27b),V0xM),V1yM),V2s))))))))))) # label(ax_thm_2EerrorStateMonad_2EES__CHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4076 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V6i (mem(V6i,ty_2Enum_2Enum) -> (all V7v1 ap(f546(A_27state,V4FOR,V6i),V7v1) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V7v1),f545(A_27state,V6i,V4FOR))))))) # label(lameq_f546) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4077 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0fM (mem(V0fM,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27b,A_27a),A_27a) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27b),c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27c,A_27a),A_27a)),V0fM))))))))) # label(conj_thm_2EerrorStateMonad_2EBIND__FAIL__L) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4078 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27c,arr(A_27d,A_27b))) -> (all V1xM (mem(V1xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> (all V2yM (mem(V2yM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27a)))) -> ap(ap(ap(c_2EerrorStateMonad_2EES__LIFT2(A_27a,A_27b,A_27c,A_27d),V0f),V1xM),V2yM) = ap(ap(c_2EerrorStateMonad_2EES__APPLY(A_27a,A_27b,A_27d),ap(ap(c_2EerrorStateMonad_2EMMAP(A_27a,arr(A_27d,A_27b),A_27c),V0f),V1xM)),V2yM))))))))))))))) # label(ax_thm_2EerrorStateMonad_2EES__LIFT2__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4079 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all A_27g (ne(A_27g) -> (all V0g (mem(V0g,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(A_27c)))) -> (all V1f (mem(V1f,arr(A_27d,arr(A_27e,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27f,A_27g))))) -> V0g = ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,A_27c,A_27a,A_27b),V0g),c_2EerrorStateMonad_2EUNIT(A_27b,A_27a)) & V1f = ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27d,A_27e,ty_2Epair_2Eprod(A_27f,A_27g),A_27f,A_27g),c_2EerrorStateMonad_2EUNIT(A_27g,A_27f)),V1f))))))))))))))))))) # label(conj_thm_2EerrorStateMonad_2EMCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4080 (all A_27a all A_27c all A_27b all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V4b f537(A_27c,A_27b,A_27a,V4b,V1f) = ap(f538(A_27a,A_27c,A_27b,V1f),V4b)))) # label(lameq_f538) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4081 (all A_27state all A_27a all V0R ap(f553(A_27state,A_27a),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V0R)),ap(c_2Ebool_2E_21(A_27a),f552(A_27state,A_27a,V0R)))) # label(lameq_f553) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4082 (all A_27b all A_27a all A_27c all V2f (mem(V2f,arr(A_27c,A_27b)) -> (all V3x ap(c_2EerrorStateMonad_2EUNIT(A_27a,A_27b),ap(V2f,V3x)) = ap(f579(A_27b,A_27a,A_27c,V2f),V3x)))) # label(lameq_f579) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4083 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0fM (mem(V0fM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27c,A_27b),A_27a)))) -> (all V1xM (mem(V1xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2EerrorStateMonad_2EES__APPLY(A_27a,A_27b,A_27c),V0fM),V1xM) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,arr(A_27c,A_27b),A_27b),V0fM),f580(A_27a,A_27c,A_27b,V1xM)))))))))))) # label(ax_thm_2EerrorStateMonad_2EES__APPLY__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4084 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0g (mem(V0g,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> (all V1m (mem(V1m,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> ap(ap(c_2EerrorStateMonad_2EEXT(A_27a,A_27b,A_27c),V0g),V1m) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27b),V1m),V0g))))))))))) # label(ax_thm_2EerrorStateMonad_2EEXT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4085 (all A_27state all A_27a all A_27b all V0f (mem(V0f,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state)))) -> (all V1s1 f569(A_27a,A_27b,A_27state,V0f,V1s1) = ap(f570(A_27state,A_27a,A_27b,V0f),V1s1)))) # label(lameq_f570) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4086 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V5a_27 ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V5a_27),f547(A_27state,V4FOR)) = ap(f548(A_27state,V4FOR),V5a_27)))) # label(lameq_f548) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4087 (all A_27a all A_27c all A_27b all V1xM (mem(V1xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))) -> (all V2f ap(f580(A_27a,A_27c,A_27b,V1xM),V2f) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27b),V1xM),f579(A_27b,A_27a,A_27c,V2f))))) # label(lameq_f580) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4088 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EIGNORE__BIND(A_27a,A_27b,A_27c),arr(arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27b))),arr(arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))),arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b)))))))))))) # label(mem_c_2EerrorStateMonad_2EIGNORE__BIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4089 (all A_27state all V1a (mem(V1a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),bool))) -> (all V2j (mem(V2j,ty_2Enum_2Enum) -> (all V3i ap(f540(A_27state,V1a,V0R,V2j),V3i) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3i),V2j))),ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V3i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V3i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V2j),V1a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V3i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V2j),V1a))))))))))) # label(lameq_f540) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4090 (all A_27state (ne(A_27state) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),bool)) -> ((all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2j (mem(V2j,ty_2Enum_2Enum) -> (all V3a (mem(V3a,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> ((V1i != V2j -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1i),V2j)),ap(ap(c_2Earithmetic_2E_2B,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V2j),V3a))))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V1i),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V2j),V3a))))))))))) -> (all V4v (mem(V4v,ty_2Enum_2Enum) -> (all V5v1 (mem(V5v1,ty_2Enum_2Enum) -> (all V6v2 (mem(V6v2,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),V4v),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V5v1),V6v2))))))))))))))) # label(conj_thm_2EerrorStateMonad_2EFOR__ind) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4091 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EerrorStateMonad_2EJOIN(A_27a,A_27b),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))) # label(mem_c_2EerrorStateMonad_2EJOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4092 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1x (mem(V1x,A_27c) -> ap(c_2EerrorStateMonad_2EUNIT(A_27a,A_27b),ap(V0f,V1x)) = ap(ap(c_2EerrorStateMonad_2EES__APPLY(A_27a,A_27b,A_27c),ap(c_2EerrorStateMonad_2EUNIT(A_27a,arr(A_27c,A_27b)),V0f)),ap(c_2EerrorStateMonad_2EUNIT(A_27a,A_27c),V1x)))))))))))) # label(conj_thm_2EerrorStateMonad_2EAPPLY__UNIT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4093 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EmapM(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b)))),arr(ty_2Elist_2Elist(A_27a),arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27c),A_27b)))))))))))) # label(mem_c_2EerrorStateMonad_2EmapM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4094 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> (all V0f (mem(V0f,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state)))) -> ap(c_2EerrorStateMonad_2EWIDEN(A_27a,A_27b,A_27state),V0f) = ap(c_2Epair_2EUNCURRY(A_27b,A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))),f570(A_27state,A_27a,A_27b,V0f)))))))))) # label(ax_thm_2EerrorStateMonad_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4095 (all A_27state all A_27b all A_27a all V4r ap(f563(A_27state,A_27b,A_27a),V4r) = f562(A_27a,A_27b,A_27state,V4r)) # label(lameq_f563) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4096 (all A_27state all V4FOR (mem(V4FOR,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V6i ap(f547(A_27state,V4FOR),V6i) = f546(A_27state,V4FOR,V6i)))) # label(lameq_f547) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4097 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))) -> f565(A_27a,A_27b,A_27state,V1f,V0v) = ap(ap(c_2EerrorStateMonad_2ENARROW(A_27a,A_27b,A_27state),V0v),V1f))))))))))) # label(ax_thm_2EerrorStateMonad_2ENARROW__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4098 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool)) -> ((all V1a (mem(V1a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),c_2Elist_2ENIL(A_27a)),V1a))))) & (all V2h (mem(V2h,A_27a) -> (all V3t (mem(V3t,ty_2Elist_2Elist(A_27a)) -> (all V4a (mem(V4a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V3t),V4a))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)),V4a)))))))))) -> (all V5v (mem(V5v,ty_2Elist_2Elist(A_27a)) -> (all V6v1 (mem(V6v1,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V5v),V6v1)))))))))))))) # label(conj_thm_2EerrorStateMonad_2EFOREACH__ind) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4099 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2EFOREACH(A_27a,A_27state),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))))))) # label(mem_c_2EerrorStateMonad_2EFOREACH) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4100 (all A_27state (ne(A_27state) -> c_2EerrorStateMonad_2EFOR(A_27state) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),bool))),f543(A_27state))),f549(A_27state)))) # label(ax_thm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4101 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V6v f556(A_27state,A_27a,V4FOREACH,V6v) = ap(f557(A_27state,A_27a,V4FOREACH),V6v)))) # label(lameq_f557) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4102 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all V0g (mem(V0g,arr(A_27d,arr(A_27e,ty_2Eoption_2Eoption(A_27c)))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27e))))) -> ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Eoption_2Eoption(A_27c)),ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,ty_2Epair_2Eprod(A_27d,A_27e),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27d,A_27e,ty_2Eoption_2Eoption(A_27c)),V0g)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27e))),V1f))) = ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,A_27c,A_27d,A_27e),V0g),V1f))))))))))))))) # label(ax_thm_2EerrorStateMonad_2EMCOMP__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4103 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Ecombin_2Eo(arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27c))),A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),c_2EerrorStateMonad_2EJOIN(A_27c,A_27b)),ap(c_2EerrorStateMonad_2EMMAP(A_27c,arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27c)))),ap(c_2EerrorStateMonad_2EMMAP(A_27c,A_27b,A_27a),V0f))) = ap(ap(c_2Ecombin_2Eo(arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27c))),A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27c)))),ap(c_2EerrorStateMonad_2EMMAP(A_27c,A_27b,A_27a),V0f)),c_2EerrorStateMonad_2EJOIN(A_27c,A_27a)))))))))) # label(conj_thm_2EerrorStateMonad_2EMMAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4104 (all A_27a all A_27b all V2x (mem(V2x,A_27b) -> (all V3xs ap(f571(A_27a,A_27b,V2x),V3xs) = ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V2x),V3xs))))) # label(lameq_f571) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4105 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27c),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)))))))))))) # label(mem_c_2EerrorStateMonad_2EBIND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4106 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),A_27b),c_2EerrorStateMonad_2EUNIT(A_27c,A_27b)),V0f) = ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27c))),arr(A_27c,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27c)))),ap(c_2EerrorStateMonad_2EMMAP(A_27c,A_27b,A_27a),V0f)),c_2EerrorStateMonad_2EUNIT(A_27c,A_27a)))))))))) # label(conj_thm_2EerrorStateMonad_2EMMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.41 4107 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(c_2Epair_2ECURRY(A_27a,A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2EerrorStateMonad_2EUNIT(A_27b,A_27a))))) # label(conj_thm_2EerrorStateMonad_2EUNIT__CURRY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4108 (all A_27state all A_27a all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V1h ap(c_2Ebool_2E_21(arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),f551(A_27state,A_27a,V1h,V0R)) = ap(f552(A_27state,A_27a,V0R),V1h)))) # label(lameq_f552) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4109 (all A_27a all A_27c all A_27b all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27c)) -> (all V3y ap(f577(A_27a,A_27c,A_27b,V0f,V2xs),V3y) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),ap(ap(c_2EerrorStateMonad_2EmapM(A_27c,A_27a,A_27b),V0f),V2xs)),f576(A_27a,A_27b,V3y))))))) # label(lameq_f577) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4110 (all A_27a all A_27b all A_27state all V0f (mem(V0f,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state)))) -> (all V1s1 (mem(V1s1,A_27b) -> (all V2s2 ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(A_27a,A_27state),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))),ap(V0f,V2s2)),c_2Eoption_2ENONE(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))),f568(A_27b,A_27a,A_27state,V1s1)) = ap(f569(A_27a,A_27b,A_27state,V0f,V1s1),V2s2)))))) # label(lameq_f569) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4111 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0fM (mem(V0fM,arr(ty_2Eone_2Eone,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> ap(V0fM,c_2Eone_2Eone) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,ty_2Eone_2Eone,A_27b),ap(c_2EerrorStateMonad_2EES__GUARD(A_27a),c_2Ebool_2ET)),V0fM) & c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27b,A_27a),A_27a) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,ty_2Eone_2Eone,A_27b),ap(c_2EerrorStateMonad_2EES__GUARD(A_27a),c_2Ebool_2EF)),V0fM))))))) # label(conj_thm_2EerrorStateMonad_2EBIND__ESGUARD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4112 (all A_27a all A_27b all A_27state all V1f (mem(V1f,arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))))) -> (all V0v (mem(V0v,A_27b) -> (all V2s ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state))),ap(V1f,ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V0v),V2s))),c_2Eoption_2ENONE(ty_2Epair_2Eprod(A_27a,A_27state))),f564(A_27state,A_27b,A_27a)) = ap(f565(A_27a,A_27b,A_27state,V1f,V0v),V2s)))))) # label(lameq_f565) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4113 (all A_27a all A_27b all A_27state all V4r (mem(V4r,A_27a) -> (all V5s1 ap(f562(A_27a,A_27b,A_27state,V4r),V5s1) = ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(A_27a,A_27state)),ap(ap(c_2Epair_2E_2C(A_27a,A_27state),V4r),ap(c_2Epair_2ESND(A_27b,A_27state),V5s1)))))) # label(lameq_f562) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4114 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all A_27g (ne(A_27g) -> (all V0f (mem(V0f,arr(A_27d,arr(A_27e,ty_2Eoption_2Eoption(A_27c)))) -> (all V1g (mem(V1g,arr(A_27f,arr(A_27g,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27e))))) -> (all V2h (mem(V2h,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27f,A_27g))))) -> ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,A_27c,A_27d,A_27e),V0f),ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,ty_2Epair_2Eprod(A_27d,A_27e),A_27f,A_27g),V1g),V2h)) = ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,A_27c,A_27f,A_27g),ap(ap(c_2EerrorStateMonad_2EMCOMP(A_27f,A_27g,A_27c,A_27d,A_27e),V0f),V1g)),V2h))))))))))))))))))))) # label(conj_thm_2EerrorStateMonad_2EMCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4115 (all A_27a (ne(A_27a) -> mem(c_2EerrorStateMonad_2EES__GUARD(A_27a),arr(bool,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27a))))))) # label(mem_c_2EerrorStateMonad_2EES__GUARD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4116 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0xM (mem(V0xM,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> c_2EerrorStateMonad_2EES__FAIL(ty_2Epair_2Eprod(A_27b,A_27a),A_27a) = ap(ap(c_2EerrorStateMonad_2EIGNORE__BIND(ty_2Eone_2Eone,A_27a,A_27b),ap(c_2EerrorStateMonad_2EES__GUARD(A_27a),c_2Ebool_2EF)),V0xM) & ap(ap(c_2EerrorStateMonad_2EIGNORE__BIND(ty_2Eone_2Eone,A_27a,A_27b),ap(c_2EerrorStateMonad_2EES__GUARD(A_27a),c_2Ebool_2ET)),V0xM) = V0xM)))))) # label(conj_thm_2EerrorStateMonad_2EIGNORE__BIND__ESGUARD) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4117 (all A_27a all A_27state all V0f (mem(V0f,arr(A_27state,A_27a)) -> (all V1s ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(A_27a,A_27state)),ap(ap(c_2Epair_2E_2C(A_27a,A_27state),ap(V0f,V1s)),V1s)) = ap(f560(A_27a,A_27state,V0f),V1s)))) # label(lameq_f560) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4118 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2EWIDEN(A_27a,A_27b,A_27state),arr(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state))),arr(ty_2Epair_2Eprod(A_27b,A_27state),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)))))))))))) # label(mem_c_2EerrorStateMonad_2EWIDEN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4119 (all A_27state all V0R ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))))),V0R)),ap(c_2Ebool_2E_21(arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),f542(A_27state,V0R))) = ap(f543(A_27state),V0R)) # label(lameq_f543) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4120 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> f536(A_27b,A_27a,V0x) = ap(c_2EerrorStateMonad_2EUNIT(A_27a,A_27b),V0x))))))) # label(ax_thm_2EerrorStateMonad_2EUNIT__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4121 (all A_27c all A_27b all A_27a all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V3v ap(f539(A_27c,A_27b,A_27a,V1f),V3v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a)),A_27b,A_27a),V3v),f538(A_27a,A_27c,A_27b,V1f))))) # label(lameq_f539) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4122 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))) -> (all V1x (mem(V1x,A_27c) -> (all V2xs (mem(V2xs,ty_2Elist_2Elist(A_27c)) -> ap(ap(c_2EerrorStateMonad_2EmapM(A_27c,A_27a,A_27b),V0f),ap(ap(c_2Elist_2ECONS(A_27c),V1x),V2xs)) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),ap(V0f,V1x)),f577(A_27a,A_27c,A_27b,V0f,V2xs)))))))))))))) # label(conj_thm_2EerrorStateMonad_2EmapM__cons) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4123 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(c_2EerrorStateMonad_2EUNIT(A_27a,ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)) = ap(c_2EerrorStateMonad_2Esequence(A_27a,A_27b),c_2Elist_2ENIL(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))) # label(conj_thm_2EerrorStateMonad_2Esequence__nil) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4124 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0z (mem(V0z,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))) -> ap(c_2EerrorStateMonad_2EJOIN(A_27a,A_27b),V0z) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27b),V0z),c_2Ecombin_2EI(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))))))))))) # label(ax_thm_2EerrorStateMonad_2EJOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4125 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0k (mem(V0k,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V2n (mem(V2n,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27a))))) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27d),ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27c),V0k),V1m)),V2n) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27d),V0k),f575(A_27c,A_27d,A_27a,A_27b,V1m,V2n)))))))))))))))) # label(conj_thm_2EerrorStateMonad_2EBIND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4126 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V5a_27 ap(f558(A_27state,A_27a,V4FOREACH),V5a_27) = ap(ap(c_2Epair_2Epair__CASE(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))),ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V5a_27),f557(A_27state,A_27a,V4FOREACH))))) # label(lameq_f558) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4127 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EerrorStateMonad_2EMMAP(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))))))))))) # label(mem_c_2EerrorStateMonad_2EMMAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4128 (all A_27state all A_27a all V4FOREACH (mem(V4FOREACH,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V6v (mem(V6v,ty_2Elist_2Elist(A_27a)) -> (all V7a ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),V6v),ap(c_2Ecombin_2EI(arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(c_2EerrorStateMonad_2EUNIT(A_27state,ty_2Eone_2Eone),c_2Eone_2Eone))),f555(A_27state,A_27a,V7a,V4FOREACH)) = ap(f556(A_27state,A_27a,V4FOREACH,V6v),V7a)))))) # label(lameq_f556) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4129 (all A_27a (ne(A_27a) -> (all A_27state (ne(A_27state) -> c_2EerrorStateMonad_2EFOREACH(A_27a,A_27state) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))),f553(A_27state,A_27a))),f559(A_27state,A_27a)))))) # label(ax_thm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4130 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0k (mem(V0k,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27c),V0k),V1m) = ap(c_2EerrorStateMonad_2EJOIN(A_27a,A_27c),ap(ap(c_2EerrorStateMonad_2EMMAP(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),A_27b),V1m),V0k)))))))))))) # label(conj_thm_2EerrorStateMonad_2EJOIN__MAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4131 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ecombin_2EI(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) = ap(ap(c_2Ecombin_2Eo(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN(A_27a,A_27b)),ap(c_2EerrorStateMonad_2EMMAP(A_27a,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a))),A_27b),c_2EerrorStateMonad_2EUNIT(A_27a,A_27b))))))) # label(conj_thm_2EerrorStateMonad_2EJOIN__MMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4132 (all A_27state all A_27a all V0R (mem(V0R,arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),bool))) -> (all V1h (mem(V1h,A_27a) -> (all V2a (mem(V2a,arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))) -> (all V3t ap(ap(V0R,ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),V3t),V2a)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3t)),V2a)) = ap(f550(A_27state,A_27a,V0R,V1h,V2a),V3t)))))))) # label(lameq_f550) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4133 (all A_27c all A_27b all A_27a all V4b (mem(V4b,A_27b) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V5s ap(f537(A_27c,A_27b,A_27a,V4b,V1f),V5s) = ap(ap(V1f,V4b),V5s)))))) # label(lameq_f537) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4134 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0k (mem(V0k,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> V0k = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27b),V0k),c_2EerrorStateMonad_2EUNIT(A_27a,A_27b)))))))) # label(conj_thm_2EerrorStateMonad_2EBIND__RIGHT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4135 (all A_27state all A_27b all A_27a all V3v ap(f564(A_27state,A_27b,A_27a),V3v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,A_27state)),A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),V3v),f563(A_27state,A_27b,A_27a))) # label(lameq_f564) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4136 (all A_27c all A_27d all A_27a all A_27b all V1m (mem(V1m,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V2n (mem(V2n,arr(A_27c,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27a))))) -> (all V3a ap(f575(A_27c,A_27d,A_27a,A_27b,V1m,V2n),V3a) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27c,A_27d),ap(V1m,V3a)),V2n)))))) # label(lameq_f575) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4137 (all A_27a all A_27b all V0m (mem(V0m,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V1ms ap(f573(A_27a,A_27b,V0m),V1ms) = ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,ty_2Elist_2Elist(A_27b)),V0m),f572(A_27a,A_27b,V1ms))))) # label(lameq_f573) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4138 (all A_27b all A_27a all A_27state all V4r (mem(V4r,A_27a) -> (all V1s1 (mem(V1s1,A_27b) -> (all V5s3 ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(A_27b,A_27state)),V4r),ap(ap(c_2Epair_2E_2C(A_27b,A_27state),V1s1),V5s3))) = ap(f566(A_27b,A_27a,A_27state,V4r,V1s1),V5s3)))))) # label(lameq_f566) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4139 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,A_27b) -> ap(c_2EerrorStateMonad_2EES__FAIL(A_27a,A_27b),V0s) = c_2Eoption_2ENONE(A_27a))))))) # label(ax_thm_2EerrorStateMonad_2EES__FAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4140 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0k (mem(V0k,arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27b))))) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2EerrorStateMonad_2EBIND(A_27b,A_27a,A_27c),ap(c_2EerrorStateMonad_2EUNIT(A_27b,A_27a),V1x)),V0k) = ap(V0k,V1x))))))))))) # label(conj_thm_2EerrorStateMonad_2EBIND__LEFT__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4141 (all A_27state (ne(A_27state) -> mem(c_2EerrorStateMonad_2EFOR(A_27state),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)))))),arr(A_27state,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state))))))) # label(mem_c_2EerrorStateMonad_2EFOR) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4142 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EerrorStateMonad_2EES__CHOICE(A_27a,A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(A_27b,ty_2Eoption_2Eoption(A_27a))))))))) # label(mem_c_2EerrorStateMonad_2EES__CHOICE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4143 (all A_27state all V0f (mem(V0f,arr(A_27state,A_27state)) -> (all V1s ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Eone_2Eone,A_27state)),ap(ap(c_2Epair_2E_2C(ty_2Eone_2Eone,A_27state),c_2Eone_2Eone),ap(V0f,V1s))) = ap(f561(A_27state,V0f),V1s)))) # label(lameq_f561) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4144 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0g (mem(V0g,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,A_27a)))) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))))) -> (all V2s0 (mem(V2s0,A_27a) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(A_27b,A_27a),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27c,A_27a))),ap(V0g,V2s0)),c_2Eoption_2ENONE(ty_2Epair_2Eprod(A_27c,A_27a))),f539(A_27c,A_27b,A_27a,V1f)) = ap(ap(ap(c_2EerrorStateMonad_2EBIND(A_27a,A_27b,A_27c),V0g),V1f),V2s0))))))))))))) # label(ax_thm_2EerrorStateMonad_2EBIND__DEF) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4145 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> mem(c_2EerrorStateMonad_2EMCOMP(A_27a,A_27b,A_27c,A_27d,A_27e),arr(arr(A_27d,arr(A_27e,ty_2Eoption_2Eoption(A_27c))),arr(arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27d,A_27e)))),arr(A_27a,arr(A_27b,ty_2Eoption_2Eoption(A_27c)))))))))))))))) # label(mem_c_2EerrorStateMonad_2EMCOMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4146 (all A_27b all A_27a all A_27state all V1s1 (mem(V1s1,A_27b) -> (all V3v ap(f568(A_27b,A_27a,A_27state,V1s1),V3v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27state))),A_27a,A_27state),V3v),f567(A_27state,A_27b,A_27a,V1s1))))) # label(lameq_f568) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4147 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V20x ap(f677(A_27b,V1P),V20x) = ap(V1P,V20x)))) # label(lameq_f677) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4148 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V28x ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V28x)),ap(V2Q,V28x)) = ap(f647(A_27b,V1P,V2Q),V28x)))))) # label(lameq_f647) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4149 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V9x ap(V2Q,V9x) = ap(f652(A_27b,V2Q),V9x)))) # label(lameq_f652) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4150 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__EXISTS__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4151 (all A_27c all A_27a all V8x (mem(V8x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V9y ap(f749(A_27c,A_27a,V8x,V1P),V9y) = ap(ap(V1P,V8x),V9y)))))) # label(lameq_f749) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4152 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V7x ap(c_2Ebool_2E_7E,ap(V1P,V7x)) = ap(f602(A_27b,V1P),V7x)))) # label(lameq_f602) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4153 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V20x ap(V3P1,V20x) = ap(f662(A_27b,V3P1),V20x)))) # label(lameq_f662) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4154 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V5x ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V5x),c_2Eone_2Eone)) = ap(f754(A_27b,A_27a,V0i),V5x)))) # label(lameq_f754) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4155 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V10x ap(c_2Ebool_2E_7E,ap(V1P,V10x)) = ap(f589(A_27b,V1P),V10x)))) # label(lameq_f589) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4156 (all A_27c all A_27a all A_27b all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V14fv ap(f711(A_27c,A_27a,A_27b,V0iy),V14fv) = ap(ap(V0iy,ap(c_2Epair_2EFST(A_27a,A_27b),V14fv)),ap(c_2Epair_2ESND(A_27a,A_27b),V14fv))))) # label(lameq_f711) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4157 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> ((all V2fv (mem(V2fv,A_27a) -> -p(ap(V1P,ap(V0i,V2fv))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__FORALL__POINT__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4158 (all A_27b all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V18x ap(V4P2,V18x) = ap(f660(A_27b,V4P2),V18x)))) # label(lameq_f660) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4159 (all A_27b all V4bc (mem(V4bc,bool) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V16x ap(ap(ap(c_2Ebool_2ECOND(bool),V4bc),ap(V1P,V16x)),ap(V2Q,V16x)) = ap(f674(A_27b,V4bc,V1P,V2Q),V16x)))))))) # label(lameq_f674) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4160 (all A_27b all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V27x ap(f669(A_27b,V4P2),V27x) = ap(V4P2,V27x)))) # label(lameq_f669) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4161 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V15x ap(f633(A_27b,V1P,V2Q),V15x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V15x)),ap(V2Q,V15x))))))) # label(lameq_f633) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4162 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V30x ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V30x)),ap(V2Q,V30x)) = ap(f648(A_27b,V1P,V2Q),V30x)))))) # label(lameq_f648) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4163 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27b,A_27c)) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> ((all V6y (mem(V6y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f748(A_27a,A_27c,V1P,V6y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f750(A_27a,A_27c,V1P)))) & ((all V2y (mem(V2y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f702(A_27a,A_27c,V1P,V2y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f747(A_27a,A_27c,V1P)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4164 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1p (mem(V1p,bool) -> ($T <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),k(A_27b,V1p)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONSTANT__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4165 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V21x ap(f618(A_27b,V1P,V2Q),V21x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V21x)),ap(V2Q,V21x))))))) # label(lameq_f618) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4166 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V8x ap(f750(A_27a,A_27c,V1P),V8x) = ap(c_2Ebool_2E_3F_21(A_27a),f749(A_27c,A_27a,V8x,V1P))))) # label(lameq_f750) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4167 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V4x ap(V1P,V4x) = ap(f599(A_27b,V1P),V4x)))) # label(lameq_f599) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4168 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V35x ap(V3b,V35x) = ap(f690(A_27b,V3b),V35x)))) # label(lameq_f690) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4169 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> ((all V4v (mem(V4v,A_27b) -> (-p(ap(V1P,V4v)) -> (exists V5fv (mem(V5fv,A_27a) & -p(ap(V1P,ap(V0i,V5fv)))))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) <-> (all V2v (mem(V2v,A_27b) -> (p(ap(V1P,V2v)) -> (exists V3fv (mem(V3fv,A_27a) & p(ap(V1P,ap(V0i,V3fv))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__FORALL__REWRITES) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4170 (all A_27a (ne(A_27a) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (-p(ap(V1P,V0i)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),V1P))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__TRIVIAL__FORALL__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4171 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V43x ap(f698(A_27b,V1P,V3b,V2Q),V43x) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V43x)),ap(V1P,V43x)),ap(V2Q,V43x))))))))) # label(lameq_f698) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4172 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V38x ap(V3b,V38x) = ap(f693(A_27b,V3b),V38x)))) # label(lameq_f693) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4173 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27b,A_27a)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V1P,V3x)) -> p(ap(V2Q,V3x))))) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V0i),V2Q)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__STRENGTHEN__FORALL__GAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4174 (all A_27b all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V24x ap(V4P2,V24x) = ap(f666(A_27b,V4P2),V24x)))) # label(lameq_f666) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4175 (all A_27a (ne(A_27a) -> mem(c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL(A_27a),arr(A_27a,arr(A_27a,arr(bool,bool)))))) # label(mem_c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4176 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V4x ap(f747(A_27a,A_27c,V1P),V4x) = ap(c_2Ebool_2E_3F_21(A_27a),f746(A_27c,A_27a,V4x,V1P))))) # label(lameq_f747) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4177 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V31x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V31x)),ap(V1P,V31x)),ap(V2Q,V31x)) = ap(f686(A_27b,V1P,V3b,V2Q),V31x)))))))) # label(lameq_f686) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4178 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,A_27b)) -> (all V2Q (mem(V2Q,arr(A_27a,A_27b)) -> (ap(V1P,V0i) = ap(V2Q,V0i) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),f593(A_27b,A_27a,V1P,V2Q)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__EXISTS__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4179 (all A_27c all A_27a all V9x (mem(V9x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V10y ap(f723(A_27c,A_27a,V9x,V1P),V10y) = ap(ap(V1P,V9x),V10y)))))) # label(lameq_f723) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4180 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4181 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V5x ap(c_2Ebool_2E_21(A_27a),f704(A_27c,A_27a,V5x,V1P)) = ap(f705(A_27a,A_27c,V1P),V5x)))) # label(lameq_f705) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4182 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V13x ap(f608(A_27b,V1P),V13x) = ap(c_2Ebool_2E_7E,ap(V1P,V13x))))) # label(lameq_f608) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4183 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f581(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f582(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f584(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f583(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f585(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f586(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f590(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f589(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f592(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f591(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f587(A_27b,V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f588(A_27b,V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__NEG__REWRITE) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4184 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V7x ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V7x)),ap(V2Q,V7x)) = ap(f630(A_27b,V1P,V2Q),V7x)))))) # label(lameq_f630) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4185 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V9x ap(f631(A_27b,V1P,V2Q),V9x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V9x)),ap(V2Q,V9x))))))) # label(lameq_f631) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4186 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V28x ap(f670(A_27b,V3P1,V4P2),V28x) = ap(ap(c_2Emin_2E_3D(bool),ap(V3P1,V28x)),ap(V4P2,V28x))))))) # label(lameq_f670) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4187 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V30x ap(f685(A_27b,V1P),V30x) = ap(V1P,V30x)))) # label(lameq_f685) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4188 (all A_27c all A_27a all A_27b all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V19fv ap(f715(A_27c,A_27a,A_27b,V0iy),V19fv) = ap(ap(V0iy,ap(c_2Epair_2EFST(A_27a,A_27b),V19fv)),ap(c_2Epair_2ESND(A_27a,A_27b),V19fv))))) # label(lameq_f715) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4189 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V31x ap(f628(A_27b,V2Q),V31x) = ap(V2Q,V31x)))) # label(lameq_f628) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4190 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V5p (mem(V5p,bool) -> (all V25x ap(ap(c_2Emin_2E_3D_3D_3E,V5p),ap(V2Q,V25x)) = ap(f646(A_27b,V2Q,V5p),V25x)))))) # label(lameq_f646) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4191 (all A_27c all A_27a all V10x (mem(V10x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V11y ap(ap(V1P,V10x),V11y) = ap(f708(A_27c,A_27a,V10x,V1P),V11y)))))) # label(lameq_f708) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4192 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V22x ap(f679(A_27b,V1P,V3b,V2Q),V22x) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V22x)),ap(V1P,V22x)),ap(V2Q,V22x))))))))) # label(lameq_f679) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4193 (all A_27c all A_27a all V5x (mem(V5x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V6y ap(f704(A_27c,A_27a,V5x,V1P),V6y) = ap(ap(V1P,V5x),V6y)))))) # label(lameq_f704) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4194 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V32x ap(f639(A_27b,V1P,V2Q),V32x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V32x)),ap(V2Q,V32x))))))) # label(lameq_f639) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4195 (all A_27b all V4bc (mem(V4bc,bool) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V13x ap(ap(ap(c_2Ebool_2ECOND(bool),V4bc),ap(V1P,V13x)),ap(V2Q,V13x)) = ap(f673(A_27b,V4bc,V1P,V2Q),V13x)))))))) # label(lameq_f673) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4196 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V10x ap(V1P,V10x) = ap(f605(A_27b,V1P),V10x)))) # label(lameq_f605) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4197 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V7x ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V7x)),ap(V2Q,V7x)) = ap(f609(A_27b,V1P,V2Q),V7x)))))) # label(lameq_f609) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4198 (all A_27c all A_27a all A_27b all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V4fv ap(f703(A_27c,A_27a,A_27b,V0iy),V4fv) = ap(ap(V0iy,ap(c_2Epair_2EFST(A_27a,A_27b),V4fv)),ap(c_2Epair_2ESND(A_27a,A_27b),V4fv))))) # label(lameq_f703) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4199 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V33x ap(V1P,V33x) = ap(f688(A_27b,V1P),V33x)))) # label(lameq_f688) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4200 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),k(A_27b,V0i)),V1P)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27c,A_27a),k(A_27c,V0i)),V1P)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <-> $T))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM4) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4201 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V7y (mem(V7y,A_27a) -> (all V9x ap(f719(A_27a,A_27c,V1P,V7y),V9x) = ap(ap(V1P,V9x),V7y)))))) # label(lameq_f719) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4202 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V6y (mem(V6y,A_27a) -> (all V7x ap(f748(A_27a,A_27c,V1P,V6y),V7x) = ap(ap(V1P,V7x),V6y)))))) # label(lameq_f748) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4203 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V8x ap(V2Q,V8x) = ap(f610(A_27b,V2Q),V8x)))) # label(lameq_f610) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4204 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V19x ap(V2Q,V19x) = ap(f617(A_27b,V2Q),V19x)))) # label(lameq_f617) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4205 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V8x ap(f587(A_27b,V1P),V8x) = ap(c_2Ebool_2E_7E,ap(V1P,V8x))))) # label(lameq_f587) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4206 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V28x ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V28x)),ap(V2Q,V28x)) = ap(f637(A_27b,V1P,V2Q),V28x)))))) # label(lameq_f637) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4207 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V28x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V28x)),ap(V1P,V28x)),ap(V2Q,V28x)) = ap(f683(A_27b,V1P,V3b,V2Q),V28x)))))))) # label(lameq_f683) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4208 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V10x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V10x)),ap(V1P,V10x)),ap(V2Q,V10x)) = ap(f672(A_27b,V1P,V3b,V2Q),V10x)))))))) # label(lameq_f672) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4209 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V23x ap(V3P1,V23x) = ap(f665(A_27b,V3P1),V23x)))) # label(lameq_f665) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4210 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V41x ap(f696(A_27b,V3b),V41x) = ap(V3b,V41x)))) # label(lameq_f696) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4211 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V21x ap(f678(A_27b,V2Q),V21x) = ap(V2Q,V21x)))) # label(lameq_f678) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4212 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V2y (mem(V2y,A_27a) -> (all V3x ap(f702(A_27a,A_27c,V1P,V2y),V3x) = ap(ap(V1P,V3x),V2y)))))) # label(lameq_f702) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4213 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V12x ap(f642(A_27b,V1P,V2Q),V12x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V12x)),ap(V2Q,V12x))))))) # label(lameq_f642) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4214 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4215 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3x ap(V1P,V3x) = ap(f582(A_27b,V1P),V3x)))) # label(lameq_f582) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4216 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V11x ap(V1P,V11x) = ap(f590(A_27b,V1P),V11x)))) # label(lameq_f590) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4217 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V17x ap(V3P1,V17x) = ap(f659(A_27b,V3P1),V17x)))) # label(lameq_f659) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4218 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V40x ap(f695(A_27b,V1P,V3b,V2Q),V40x) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V40x)),ap(V1P,V40x)),ap(V2Q,V40x))))))))) # label(lameq_f695) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4219 (all A_27a (ne(A_27a) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27a,A_27c)) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V7y))),f719(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27c),V0i),f738(A_27a,A_27c,V1P)))) & ((all V12y (mem(V12y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V12y))),f720(A_27a,A_27c,V1P,V12y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27c),V0i),f739(A_27a,A_27c,V1P)))) & ((all V17y (mem(V17y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V17y))),f721(A_27a,A_27c,V1P,V17y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27c),V0i),f740(A_27a,A_27c,V1P)))) & ((all V2y (mem(V2y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V2y))),f718(A_27a,A_27c,V1P,V2y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27c),V0i),f737(A_27a,A_27c,V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV__1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4220 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V7x ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V7x),c_2Eone_2Eone)) = ap(f756(A_27b,A_27a,V0i),V7x)))) # label(lameq_f756) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4221 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V45x ap(f700(A_27b,V1P),V45x) = ap(V1P,V45x)))) # label(lameq_f700) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4222 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V5p (mem(V5p,bool) -> (all V25x ap(ap(c_2Ebool_2E_2F_5C,V5p),ap(V2Q,V25x)) = ap(f636(A_27b,V2Q,V5p),V25x)))))) # label(lameq_f636) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4223 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V15x ap(f643(A_27b,V1P,V2Q),V15x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V15x)),ap(V2Q,V15x))))))) # label(lameq_f643) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4224 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V25y (mem(V25y,A_27a) -> (all V26x ap(f734(A_27a,A_27c,V1P,V25y),V26x) = ap(ap(V1P,V26x),V25y)))))) # label(lameq_f734) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4225 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V26x ap(f623(A_27b,V1P),V26x) = ap(V1P,V26x)))) # label(lameq_f623) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4226 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) -> ($T <-> p(ap(c_2Ebool_2E_3F(A_27b),V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__POINT__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4227 (all A_27c all A_27a all V13x (mem(V13x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V14y ap(ap(V1P,V13x),V14y) = ap(f726(A_27c,A_27a,V13x,V1P),V14y)))))) # label(lameq_f726) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4228 (all A_27c all A_27a all V17x (mem(V17x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V18y ap(ap(V1P,V17x),V18y) = ap(f729(A_27c,A_27a,V17x,V1P),V18y)))))) # label(lameq_f729) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4229 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V6x ap(V2Q,V6x) = ap(f650(A_27b,V2Q),V6x)))) # label(lameq_f650) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4230 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V17y (mem(V17y,A_27a) -> (all V18x ap(ap(V1P,V18x),V17y) = ap(f714(A_27a,A_27c,V1P,V17y),V18x)))))) # label(lameq_f714) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4231 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V13x ap(c_2Ebool_2E_21(A_27a),f726(A_27c,A_27a,V13x,V1P)) = ap(f727(A_27a,A_27c,V1P),V13x)))) # label(lameq_f727) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4232 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) <-> (all V2fv (mem(V2fv,A_27a) -> p(ap(V1P,ap(V0i,V2fv)))))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__POINT__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4233 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V7x ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V7x)),ap(V2Q,V7x)) = ap(f640(A_27b,V1P,V2Q),V7x)))))) # label(lameq_f640) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4234 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V9x ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V9x)),ap(V2Q,V9x)) = ap(f641(A_27b,V1P,V2Q),V9x)))))) # label(lameq_f641) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4235 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (exists V3fv (V2x = ap(V1Q,V3fv) & mem(V3fv,A_27b))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V1Q),V0P))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__ONE__CASE______FORALL__GAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4236 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V6x ap(c_2Ebool_2E_7E,ap(V1P,V6x)) = ap(f585(A_27b,V1P),V6x)))) # label(lameq_f585) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4237 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V4q (mem(V4q,bool) -> (all V23x ap(f635(A_27b,V1P,V4q),V23x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V23x)),V4q)))))) # label(lameq_f635) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4238 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1p (mem(V1p,bool) -> ($T <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),k(A_27b,V1p)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONSTANT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4239 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V29x ap(f684(A_27b,V3b),V29x) = ap(V3b,V29x)))) # label(lameq_f684) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4240 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),k(A_27b,V0i)),V1P)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <-> (all V3v (mem(V3v,A_27a) -> (p(ap(V1P,V3v)) -> V0i = V3v))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM3) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4241 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V7y (mem(V7y,A_27a) -> (all V8x ap(ap(V1P,V8x),V7y) = ap(f706(A_27a,A_27c,V1P,V7y),V8x)))))) # label(lameq_f706) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4242 (all A_27b all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V21x ap(f663(A_27b,V4P2),V21x) = ap(V4P2,V21x)))) # label(lameq_f663) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4243 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V4bc (mem(V4bc,bool) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f590(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f654(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f673(A_27b,V4bc,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f656(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f657(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f674(A_27b,V4bc,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f678(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f677(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f679(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f680(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f621(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f681(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f682(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f683(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f685(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f684(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f686(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f688(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f687(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f689(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f696(A_27b,V3b))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f697(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f698(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f700(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f699(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f701(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f694(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f693(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f695(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f691(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f690(A_27b,V3b))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f692(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f675(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f676(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f652(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f603(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f672(A_27b,V1P,V3b,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f584(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f650(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f671(A_27b,V1P,V3b,V2Q)))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__COND) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4244 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V9x ap(c_2Ebool_2E_3F(A_27a),f723(A_27c,A_27a,V9x,V1P)) = ap(f741(A_27a,A_27c,V1P),V9x)))) # label(lameq_f741) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4245 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V13x ap(c_2Ebool_2E_3F(A_27a),f726(A_27c,A_27a,V13x,V1P)) = ap(f742(A_27a,A_27c,V1P),V13x)))) # label(lameq_f742) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4246 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V37x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V37x)),ap(V1P,V37x)),ap(V2Q,V37x)) = ap(f692(A_27b,V1P,V3b,V2Q),V37x)))))))) # label(lameq_f692) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4247 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V15x ap(f739(A_27a,A_27c,V1P),V15x) = ap(c_2Ebool_2E_3F(A_27a),f712(A_27c,A_27a,V15x,V1P))))) # label(lameq_f739) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4248 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2x ap(f581(A_27b,V1P),V2x) = ap(c_2Ebool_2E_7E,ap(V1P,V2x))))) # label(lameq_f581) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4249 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V17x ap(V1P,V17x) = ap(f616(A_27b,V1P),V17x)))) # label(lameq_f616) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4250 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V19y (mem(V19y,A_27a) -> (all V21x ap(f731(A_27a,A_27c,V1P,V19y),V21x) = ap(ap(V1P,V21x),V19y)))))) # label(lameq_f731) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4251 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V14x ap(V1P,V14x) = ap(f656(A_27b,V1P),V14x)))) # label(lameq_f656) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4252 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V19x ap(ap(c_2Emin_2E_3D(bool),ap(V3P1,V19x)),ap(V4P2,V19x)) = ap(f661(A_27b,V3P1,V4P2),V19x)))))) # label(lameq_f661) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4253 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V12y (mem(V12y,A_27a) -> (all V13x ap(ap(V1P,V13x),V12y) = ap(f710(A_27a,A_27c,V1P,V12y),V13x)))))) # label(lameq_f710) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4254 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V4q (mem(V4q,bool) -> (all V23x ap(f645(A_27b,V1P,V4q),V23x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V23x)),V4q)))))) # label(lameq_f645) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4255 (all A_27a all V0y (mem(V0y,A_27a) -> (all V4x ap(ap(c_2Emin_2E_3D(A_27a),V4x),V0y) = ap(f596(A_27a,V0y),V4x)))) # label(lameq_f596) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4256 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V32x ap(V3b,V32x) = ap(f687(A_27b,V3b),V32x)))) # label(lameq_f687) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4257 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V4x ap(c_2Ebool_2E_7E,ap(V1P,V4x)) = ap(f583(A_27b,V1P),V4x)))) # label(lameq_f583) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4258 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V27x ap(f736(A_27a,A_27c,V1P),V27x) = ap(c_2Ebool_2E_21(A_27a),f735(A_27c,A_27a,V27x,V1P))))) # label(lameq_f736) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4259 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3iK (mem(V3iK,A_27b) -> (all V4q (mem(V4q,bool) -> (all V5p (mem(V5p,bool) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f634(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f638(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f639(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f637(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f621(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f636(A_27b,V2Q,V5p)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f619(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f635(A_27b,V1P,V4q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f633(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f605(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f612(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f632(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f631(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f630(A_27b,V1P,V2Q)))))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__CONJ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4260 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> ((all V17y (mem(V17y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),ap(V0iy,V17y)),f714(A_27a,A_27c,V1P,V17y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f715(A_27c,A_27a,A_27b,V0iy)),f740(A_27a,A_27c,V1P)))) & ((all V12y (mem(V12y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),ap(V0iy,V12y)),f710(A_27a,A_27c,V1P,V12y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f711(A_27c,A_27a,A_27b,V0iy)),f739(A_27a,A_27c,V1P)))) & ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),ap(V0iy,V7y)),f706(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f707(A_27c,A_27a,A_27b,V0iy)),f738(A_27a,A_27c,V1P)))) & ((all V2y (mem(V2y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),ap(V0iy,V2y)),f702(A_27a,A_27c,V1P,V2y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f703(A_27c,A_27a,A_27b,V0iy)),f737(A_27a,A_27c,V1P)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4261 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V30x ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V30x)),ap(V2Q,V30x)) = ap(f638(A_27b,V1P,V2Q),V30x)))))) # label(lameq_f638) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4262 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),ap(ap(c_2Ecombin_2Eo(A_27b,bool,bool),c_2Ebool_2E_7E),V1P))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__NEG__DUALITY) # label(axiom) # label(non_clause). [assumption]. 6.43/6.42 4263 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f602(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f607(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f608(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f605(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f606(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f603(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f604(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f599(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f600(A_27b,V1P)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f597(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f598(A_27b,V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__NEG) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4264 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V32x ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V32x)),ap(V2Q,V32x)) = ap(f649(A_27b,V1P,V2Q),V32x)))))) # label(lameq_f649) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4265 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V12x ap(f654(A_27b,V2Q),V12x) = ap(V2Q,V12x)))) # label(lameq_f654) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4266 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V36x ap(V1P,V36x) = ap(f691(A_27b,V1P),V36x)))) # label(lameq_f691) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4267 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V12x ap(f632(A_27b,V1P,V2Q),V12x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V12x)),ap(V2Q,V12x))))))) # label(lameq_f632) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4268 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V10x ap(c_2Ebool_2E_21(A_27a),f708(A_27c,A_27a,V10x,V1P)) = ap(f709(A_27a,A_27c,V1P),V10x)))) # label(lameq_f709) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4269 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V20x ap(c_2Ebool_2E_21(A_27a),f716(A_27c,A_27a,V20x,V1P)) = ap(f717(A_27a,A_27c,V1P),V20x)))) # label(lameq_f717) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4270 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V14x ap(V2Q,V14x) = ap(f614(A_27b,V2Q),V14x)))) # label(lameq_f614) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4271 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V42x ap(f697(A_27b,V2Q),V42x) = ap(V2Q,V42x)))) # label(lameq_f697) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4272 (all A_27a (ne(A_27a) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27a,A_27c)) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> ((all V12y (mem(V12y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V12y))),f720(A_27a,A_27c,V1P,V12y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27c),V0i),f713(A_27a,A_27c,V1P)))) & ((all V17y (mem(V17y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V17y))),f721(A_27a,A_27c,V1P,V17y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27c),V0i),f717(A_27a,A_27c,V1P)))) & ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V7y))),f719(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27c),V0i),f709(A_27a,A_27c,V1P)))) & ((all V2y (mem(V2y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,ap(V0i,V2y))),f718(A_27a,A_27c,V1P,V2y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27c),V0i),f705(A_27a,A_27c,V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV__1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4273 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V15x ap(c_2Ebool_2E_21(A_27a),f712(A_27c,A_27a,V15x,V1P)) = ap(f713(A_27a,A_27c,V1P),V15x)))) # label(lameq_f713) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4274 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V30x ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V30x)),ap(V2Q,V30x)) = ap(f627(A_27b,V1P,V2Q),V30x)))))) # label(lameq_f627) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4275 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V25x ap(ap(c_2Emin_2E_3D(bool),ap(V3P1,V25x)),ap(V4P2,V25x)) = ap(f667(A_27b,V3P1,V4P2),V25x)))))) # label(lameq_f667) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4276 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) -> ((all V2fv (mem(V2fv,A_27a) -> p(ap(V1P,ap(V0i,V2fv))))) <-> p(ap(c_2Ebool_2E_21(A_27b),V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4277 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V23x ap(f733(A_27a,A_27c,V1P),V23x) = ap(c_2Ebool_2E_21(A_27a),f732(A_27c,A_27a,V23x,V1P))))) # label(lameq_f733) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4278 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V4x ap(f753(A_27b,A_27a,V0i),V4x) = ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V4x),c_2Eone_2Eone))))) # label(lameq_f753) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4279 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3x ap(c_2Ebool_2E_7E,ap(V1P,V3x)) = ap(f598(A_27b,V1P),V3x)))) # label(lameq_f598) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4280 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V3x ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V3x),c_2Eone_2Eone)) = ap(f752(A_27b,A_27a,V0i),V3x)))) # label(lameq_f752) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4281 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4282 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V46x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V46x)),ap(V1P,V46x)),ap(V2Q,V46x)) = ap(f701(A_27b,V1P,V3b,V2Q),V46x)))))))) # label(lameq_f701) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4283 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V27x ap(c_2Ebool_2E_3F(A_27a),f735(A_27c,A_27a,V27x,V1P)) = ap(f745(A_27a,A_27c,V1P),V27x)))) # label(lameq_f745) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4284 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V11y (mem(V11y,A_27a) -> (all V12x ap(ap(V1P,V12x),V11y) = ap(f725(A_27a,A_27c,V1P,V11y),V12x)))))) # label(lameq_f725) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4285 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V44x ap(V3b,V44x) = ap(f699(A_27b,V3b),V44x)))) # label(lameq_f699) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4286 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V26x ap(V3b,V26x) = ap(f682(A_27b,V3b),V26x)))) # label(lameq_f682) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4287 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (((all V3fv (mem(V3fv,A_27a) -> p(ap(V1P,ap(V0i,V3fv))))) <-> (all V2v (mem(V2v,A_27b) -> p(ap(V1P,V2v))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__FORALL__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4288 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) -> (p(ap(c_2Ebool_2E_21(A_27b),V1P)) <-> $F)))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__FORALL__POINT__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4289 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27b,A_27c)) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V2iK (mem(V2iK,A_27c) -> ((all V3y (mem(V3y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f722(A_27a,A_27c,V1P,V3y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f737(A_27a,A_27c,V1P)))) & ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),V0i),f706(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27c),V0i),f741(A_27a,A_27c,V1P)))) & ((all V15y (mem(V15y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f728(A_27a,A_27c,V1P,V15y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f743(A_27a,A_27c,V1P)))) & ((all V25y (mem(V25y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f734(A_27a,A_27c,V1P,V25y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f745(A_27a,A_27c,V1P)))) & ((all V19y (mem(V19y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f731(A_27a,A_27c,V1P,V19y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f744(A_27a,A_27c,V1P)))) & ((all V11y (mem(V11y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f725(A_27a,A_27c,V1P,V11y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f742(A_27a,A_27c,V1P)))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4290 (all A_27c all A_27a all V23x (mem(V23x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V24y ap(f732(A_27c,A_27a,V23x,V1P),V24y) = ap(ap(V1P,V23x),V24y)))))) # label(lameq_f732) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4291 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V19x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V19x)),ap(V1P,V19x)),ap(V2Q,V19x)) = ap(f676(A_27b,V1P,V3b,V2Q),V19x)))))))) # label(lameq_f676) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4292 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V12x ap(f591(A_27b,V1P),V12x) = ap(c_2Ebool_2E_7E,ap(V1P,V12x))))) # label(lameq_f591) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4293 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (((exists V3fv (mem(V3fv,A_27a) & p(ap(V1P,ap(V0i,V3fv))))) <-> (exists V2v (mem(V2v,A_27b) & p(ap(V1P,V2v))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4294 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),k(A_27b,V0i)),V1P)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)) <-> p(ap(V1P,V0i)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM2) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4295 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V29x ap(f626(A_27b,V1P),V29x) = ap(V1P,V29x)))) # label(lameq_f626) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4296 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__WEAKEN__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4297 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V10x ap(ap(c_2Emin_2E_3D(bool),ap(V1P,V10x)),ap(V2Q,V10x)) = ap(f653(A_27b,V1P,V2Q),V10x)))))) # label(lameq_f653) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4298 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V24x ap(V2Q,V24x) = ap(f621(A_27b,V2Q),V24x)))) # label(lameq_f621) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4299 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V15x ap(V2Q,V15x) = ap(f657(A_27b,V2Q),V15x)))) # label(lameq_f657) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4300 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V7x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V7x)),ap(V1P,V7x)),ap(V2Q,V7x)) = ap(f671(A_27b,V1P,V3b,V2Q),V7x)))))))) # label(lameq_f671) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4301 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V3y (mem(V3y,A_27a) -> (all V4x ap(f722(A_27a,A_27c,V1P,V3y),V4x) = ap(ap(V1P,V4x),V3y)))))) # label(lameq_f722) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4302 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P)) <-> (all V4v (mem(V4v,A_27b) -> (-p(ap(V1P,V4v)) -> (exists V5fv (mem(V5fv,A_27a) & -p(ap(V1P,ap(V0i,V5fv))))))))) & (all V16i (mem(V16i,arr(A_27a,A_27b)) -> (all V17P (mem(V17P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V16i),V17P)) <-> (all V18v (mem(V18v,A_27b) -> (-p(ap(V17P,V18v)) -> (exists V19fv (mem(V19fv,A_27a) & ap(V16i,V19fv) = V18v)))))))))) & (all V12i (mem(V12i,arr(A_27a,A_27b)) -> (all V13P (mem(V13P,arr(A_27b,bool)) -> ((all V14v (mem(V14v,A_27b) -> (p(ap(V13P,V14v)) -> (exists V15fv (mem(V15fv,A_27a) & V14v = ap(V12i,V15fv)))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V12i),V13P))))))) & (all V9i (mem(V9i,arr(A_27a,A_27b)) -> (all V10P (mem(V10P,arr(A_27b,bool)) -> ((all V11fv (mem(V11fv,A_27a) -> -p(ap(V10P,ap(V9i,V11fv))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V9i),V10P))))))) & (all V6i (mem(V6i,arr(A_27a,A_27b)) -> (all V7P (mem(V7P,arr(A_27b,bool)) -> ((all V8fv (mem(V8fv,A_27a) -> p(ap(V7P,ap(V6i,V8fv))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V6i),V7P))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) <-> (all V2v (mem(V2v,A_27b) -> (p(ap(V1P,V2v)) -> (exists V3fv (p(ap(V1P,ap(V0i,V3fv))) & mem(V3fv,A_27a))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__REWRITES) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4303 (all A_27a (ne(A_27a) -> mem(c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS(A_27a),arr(A_27a,arr(A_27a,arr(bool,bool)))))) # label(mem_c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4304 (all A_27c all A_27a all V27x (mem(V27x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V28y ap(f735(A_27c,A_27a,V27x,V1P),V28y) = ap(ap(V1P,V27x),V28y)))))) # label(lameq_f735) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4305 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V22x ap(f619(A_27b,V1P),V22x) = ap(V1P,V22x)))) # label(lameq_f619) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4306 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V12x ap(f607(A_27b,V1P),V12x) = ap(V1P,V12x)))) # label(lameq_f607) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4307 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V34x ap(f689(A_27b,V1P,V3b,V2Q),V34x) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V34x)),ap(V1P,V34x)),ap(V2Q,V34x))))))))) # label(lameq_f689) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4308 (all A_27c all A_27a all V4x (mem(V4x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V5y ap(ap(V1P,V4x),V5y) = ap(f746(A_27c,A_27a,V4x,V1P),V5y)))))) # label(lameq_f746) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4309 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V6x ap(f601(A_27b,V1P),V6x) = ap(V1P,V6x)))) # label(lameq_f601) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4310 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V17x ap(c_2Ebool_2E_3F(A_27a),f729(A_27c,A_27a,V17x,V1P)) = ap(f743(A_27a,A_27c,V1P),V17x)))) # label(lameq_f743) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4311 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V21x ap(ap(c_2Ebool_2E_2F_5C,ap(V1P,V21x)),ap(V2Q,V21x)) = ap(f634(A_27b,V1P,V2Q),V21x)))))) # label(lameq_f634) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4312 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V13x ap(f655(A_27b,V1P,V2Q),V13x) = ap(ap(c_2Emin_2E_3D(bool),ap(V1P,V13x)),ap(V2Q,V13x))))))) # label(lameq_f655) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4313 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V2y (mem(V2y,A_27a) -> (all V4x ap(f718(A_27a,A_27c,V1P,V2y),V4x) = ap(ap(V1P,V4x),V2y)))))) # label(lameq_f718) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4314 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27b,A_27a)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V1P,V3x)) -> p(ap(V2Q,V3x))))) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27a),V0i),V2Q)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__STRENGTHEN__EXISTS__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4315 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V23x ap(f744(A_27a,A_27c,V1P),V23x) = ap(c_2Ebool_2E_3F(A_27a),f732(A_27c,A_27a,V23x,V1P))))) # label(lameq_f744) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4316 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V12y (mem(V12y,A_27a) -> (all V14x ap(ap(V1P,V14x),V12y) = ap(f720(A_27a,A_27c,V1P,V12y),V14x)))))) # label(lameq_f720) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4317 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f650(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f584(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f651(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f603(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f652(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f653(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f654(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f590(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f655(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f659(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f660(A_27b,V4P2))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f661(A_27b,V3P1,V4P2)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f662(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f663(A_27b,V4P2))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f664(A_27b,V3P1,V4P2)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f665(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f666(A_27b,V4P2))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f667(A_27b,V3P1,V4P2)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f668(A_27b,V3P1))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f669(A_27b,V4P2))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f670(A_27b,V3P1,V4P2)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f657(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f656(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f658(A_27b,V1P,V2Q)))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUIV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4318 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,A_27c)) -> (all V2Q (mem(V2Q,arr(A_27b,A_27c)) -> ((all V3fv (mem(V3fv,A_27a) -> ap(V1P,ap(V0i,V3fv)) != ap(V2Q,ap(V0i,V3fv)))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f594(A_27c,A_27b,V1P,V2Q)))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__FORALL__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4319 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V5x ap(c_2Ebool_2E_7E,ap(V1P,V5x)) = ap(f600(A_27b,V1P),V5x)))) # label(lameq_f600) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4320 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__FORALL__GAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4321 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V39x ap(V2Q,V39x) = ap(f694(A_27b,V2Q),V39x)))) # label(lameq_f694) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4322 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> ((all V2v (mem(V2v,A_27b) -> (-p(ap(V1P,V2v)) -> (exists V3fv (mem(V3fv,A_27a) & V2v = ap(V0i,V3fv)))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),V1P))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__FORALL__GAP__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4323 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (exists V3fv (mem(V3fv,A_27b) & ap(V1Q,V3fv) = V2x)))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27a),V1Q),V0P))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__ONE__CASE______EXISTS__GAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4324 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V15x ap(f615(A_27b,V1P,V2Q),V15x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V15x)),ap(V2Q,V15x))))))) # label(lameq_f615) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4325 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V9x ap(f588(A_27b,V1P),V9x) = ap(V1P,V9x)))) # label(lameq_f588) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4326 (all A_27a (ne(A_27a) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(V1P,V0i)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),V1P))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__TRIVIAL__EXISTS__POINT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4327 (all A_27c all A_27b all V1P (mem(V1P,arr(A_27b,A_27c)) -> (all V2Q (mem(V2Q,arr(A_27b,A_27c)) -> (all V4x ap(ap(c_2Emin_2E_3D(A_27c),ap(V1P,V4x)),ap(V2Q,V4x)) = ap(f594(A_27c,A_27b,V1P,V2Q),V4x)))))) # label(lameq_f594) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4328 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V4P2 (mem(V4P2,arr(A_27b,bool)) -> (all V22x ap(ap(c_2Emin_2E_3D(bool),ap(V3P1,V22x)),ap(V4P2,V22x)) = ap(f664(A_27b,V3P1,V4P2),V22x)))))) # label(lameq_f664) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4329 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V7x ap(V1P,V7x) = ap(f586(A_27b,V1P),V7x)))) # label(lameq_f586) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4330 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> ((all V2v (mem(V2v,A_27b) -> (p(ap(V1P,V2v)) -> (exists V3fv (mem(V3fv,A_27a) & ap(V0i,V3fv) = V2v))))) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),V1P))))))))))) # label(ax_thm_2EquantHeuristics_2EGUESS__EXISTS__GAP__def) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4331 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4332 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V3b (mem(V3b,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V25x ap(ap(ap(c_2Ebool_2ECOND(bool),ap(V3b,V25x)),ap(V1P,V25x)),ap(V2Q,V25x)) = ap(f681(A_27b,V1P,V3b,V2Q),V25x)))))))) # label(lameq_f681) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4333 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V4q (mem(V4q,bool) -> (all V23x ap(f620(A_27b,V1P,V4q),V23x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V23x)),V4q)))))) # label(lameq_f620) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4334 (all A_27a (ne(A_27a) -> (all V0i (mem(V0i,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Eone_2Eone,A_27a),k(ty_2Eone_2Eone,V0i)),f595(A_27a,V0i))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__EQUATION__EXISTS__GAP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4335 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> ((all V17y (mem(V17y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),ap(V0iy,V17y)),f714(A_27a,A_27c,V1P,V17y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f715(A_27c,A_27a,A_27b,V0iy)),f717(A_27a,A_27c,V1P)))) & ((all V12y (mem(V12y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),ap(V0iy,V12y)),f710(A_27a,A_27c,V1P,V12y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f711(A_27c,A_27a,A_27b,V0iy)),f713(A_27a,A_27c,V1P)))) & ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),ap(V0iy,V7y)),f706(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f707(A_27c,A_27a,A_27b,V0iy)),f709(A_27a,A_27c,V1P)))) & ((all V2y (mem(V2y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),ap(V0iy,V2y)),f702(A_27a,A_27c,V1P,V2y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f703(A_27c,A_27a,A_27b,V0iy)),f705(A_27a,A_27c,V1P)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4336 (all A_27b all A_27a all V1P (mem(V1P,arr(A_27a,A_27b)) -> (all V2Q (mem(V2Q,arr(A_27a,A_27b)) -> (all V4x ap(ap(c_2Emin_2E_3D(A_27b),ap(V1P,V4x)),ap(V2Q,V4x)) = ap(f593(A_27b,A_27a,V1P,V2Q),V4x)))))) # label(lameq_f593) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4337 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V9x ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V9x)),ap(V2Q,V9x)) = ap(f611(A_27b,V1P,V2Q),V9x)))))) # label(lameq_f611) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4338 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V15y (mem(V15y,A_27a) -> (all V16x ap(f728(A_27a,A_27c,V1P,V15y),V16x) = ap(ap(V1P,V16x),V15y)))))) # label(lameq_f728) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4339 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V5p (mem(V5p,bool) -> (all V25x ap(ap(c_2Ebool_2E_5C_2F,V5p),ap(V2Q,V25x)) = ap(f622(A_27b,V2Q,V5p),V25x)))))) # label(lameq_f622) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4340 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V16x ap(ap(c_2Emin_2E_3D(bool),ap(V1P,V16x)),ap(V2Q,V16x)) = ap(f658(A_27b,V1P,V2Q),V16x)))))) # label(lameq_f658) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4341 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V9x ap(f604(A_27b,V1P),V9x) = ap(c_2Ebool_2E_7E,ap(V1P,V9x))))) # label(lameq_f604) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4342 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),V1P)) -> ($T <-> (exists V2v (mem(V2v,A_27b) & p(ap(V1P,V2v)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),V1P)) -> ($F <-> (all V3v (mem(V3v,A_27b) -> p(ap(V1P,V3v)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__POINT__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4343 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V1vt (mem(V1vt,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),f752(A_27b,A_27a,V0i)),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),f753(A_27b,A_27a,V0i)),V1vt))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),f756(A_27b,A_27a,V0i)),V1vt))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),f755(A_27b,A_27a,V0i)),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),f754(A_27b,A_27a,V0i)),V1vt))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b),V0i),V1vt)) <-> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),f751(A_27b,A_27a,V0i)),V1vt))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__ELIM__UNIT) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4344 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V28x ap(f625(A_27b,V1P,V2Q),V28x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V28x)),ap(V2Q,V28x))))))) # label(lameq_f625) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4345 (all A_27c all A_27a all V15x (mem(V15x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V16y ap(ap(V1P,V15x),V16y) = ap(f712(A_27c,A_27a,V15x,V1P),V16y)))))) # label(lameq_f712) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4346 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3iK (mem(V3iK,A_27b) -> (all V4q (mem(V4q,bool) -> (all V5p (mem(V5p,bool) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f611(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f615(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f619(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f620(A_27b,V1P,V4q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f621(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f622(A_27b,V2Q,V5p)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f625(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f629(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f627(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f618(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f612(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f605(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f613(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f609(A_27b,V1P,V2Q)))))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__DISJ) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4347 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V9x ap(c_2Ebool_2E_21(A_27a),f723(A_27c,A_27a,V9x,V1P)) = ap(f724(A_27a,A_27c,V1P),V9x)))) # label(lameq_f724) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4348 (all A_27c all A_27a all A_27b all V0iy (mem(V0iy,arr(A_27a,arr(A_27b,A_27c))) -> (all V9fv ap(f707(A_27c,A_27a,A_27b,V0iy),V9fv) = ap(ap(V0iy,ap(c_2Epair_2EFST(A_27a,A_27b),V9fv)),ap(c_2Epair_2ESND(A_27a,A_27b),V9fv))))) # label(lameq_f707) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4349 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V18x ap(f675(A_27b,V2Q),V18x) = ap(V2Q,V18x)))) # label(lameq_f675) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4350 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b,A_27a),k(A_27b,V0i)),V1P)) -> (p(ap(V1P,V0i)) & (all V3v (mem(V3v,A_27a) -> (p(ap(V1P,V3v)) -> V3v = V0i))) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),V1P)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESSES__UEXISTS__THM1) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4351 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V32x ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V32x)),ap(V2Q,V32x)) = ap(f629(A_27b,V1P,V2Q),V32x)))))) # label(lameq_f629) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4352 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V11x ap(c_2Ebool_2E_7E,ap(V1P,V11x)) = ap(f606(A_27b,V1P),V11x)))) # label(lameq_f606) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4353 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V20x ap(c_2Ebool_2E_3F(A_27a),f716(A_27c,A_27a,V20x,V1P)) = ap(f740(A_27a,A_27c,V1P),V20x)))) # label(lameq_f740) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4354 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V21x ap(f644(A_27b,V1P,V2Q),V21x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P,V21x)),ap(V2Q,V21x))))))) # label(lameq_f644) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4355 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V6x ap(f755(A_27b,A_27a,V0i),V6x) = ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V6x),c_2Eone_2Eone))))) # label(lameq_f755) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4356 (all A_27c all A_27a all V20x (mem(V20x,A_27c) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V21y ap(f716(A_27c,A_27a,V20x,V1P),V21y) = ap(ap(V1P,V20x),V21y)))))) # label(lameq_f716) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4357 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2x ap(V1P,V2x) = ap(f597(A_27b,V1P),V2x)))) # label(lameq_f597) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4358 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V13x ap(V1P,V13x) = ap(f592(A_27b,V1P),V13x)))) # label(lameq_f592) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4359 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V11x ap(f612(A_27b,V2Q),V11x) = ap(V2Q,V11x)))) # label(lameq_f612) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4360 (all A_27a all V0i (mem(V0i,A_27a) -> (all V2x ap(ap(c_2Emin_2E_3D(A_27a),V2x),V0i) = ap(f595(A_27a,V0i),V2x)))) # label(lameq_f595) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4361 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P)) -> (p(ap(c_2Ebool_2E_3F(A_27b),V1P)) <-> (exists V2fv (p(ap(V1P,ap(V0i,V2fv))) & mem(V2fv,A_27a))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4362 (all A_27b all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V27x ap(f624(A_27b,V2Q),V27x) = ap(V2Q,V27x)))) # label(lameq_f624) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4363 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V10x ap(c_2Ebool_2E_3F(A_27a),f708(A_27c,A_27a,V10x,V1P)) = ap(f738(A_27a,A_27c,V1P),V10x)))) # label(lameq_f738) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4364 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V5x ap(f584(A_27b,V1P),V5x) = ap(V1P,V5x)))) # label(lameq_f584) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4365 (all A_27b all A_27a all V0i (mem(V0i,arr(ty_2Epair_2Eprod(A_27a,ty_2Eone_2Eone),A_27b)) -> (all V2x ap(f751(A_27b,A_27a,V0i),V2x) = ap(V0i,ap(ap(c_2Epair_2E_2C(A_27a,ty_2Eone_2Eone),V2x),c_2Eone_2Eone))))) # label(lameq_f751) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4366 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1Q (mem(V1Q,arr(A_27b,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (exists V3fv (mem(V3fv,A_27b) & ap(V1Q,V3fv) = V2x)) | V0y = V2x)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27a),V1Q),f596(A_27a,V0y)))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__TWO__CASES) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4367 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V5x ap(c_2Ebool_2E_3F(A_27a),f704(A_27c,A_27a,V5x,V1P)) = ap(f737(A_27a,A_27c,V1P),V5x)))) # label(lameq_f737) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4368 (all A_27b all V3P1 (mem(V3P1,arr(A_27b,bool)) -> (all V26x ap(V3P1,V26x) = ap(f668(A_27b,V3P1),V26x)))) # label(lameq_f668) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4369 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27a,A_27b)) -> (all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3iK (mem(V3iK,A_27b) -> (all V4q (mem(V4q,bool) -> (all V5p (mem(V5p,bool) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f601(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f640(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f610(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f641(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f612(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f605(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f642(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f628(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f649(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f626(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f648(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V0i),f623(A_27b,V1P))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f624(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V0i),f647(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f621(A_27b,V2Q))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f646(A_27b,V2Q,V5p)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),f619(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),f645(A_27b,V1P,V4q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f617(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f616(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(ty_2Eone_2Eone,A_27b),k(ty_2Eone_2Eone,V3iK)),f644(A_27b,V1P,V2Q)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f614(A_27b,V2Q))) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V0i),f592(A_27b,V1P))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V0i),f643(A_27b,V1P,V2Q)))))))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__IMP) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4370 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V12x ap(ap(c_2Ebool_2E_5C_2F,ap(V1P,V12x)),ap(V2Q,V12x)) = ap(f613(A_27b,V1P,V2Q),V12x)))))) # label(lameq_f613) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4371 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V17y (mem(V17y,A_27a) -> (all V19x ap(f721(A_27a,A_27c,V1P,V17y),V19x) = ap(ap(V1P,V19x),V17y)))))) # label(lameq_f721) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4372 (all A_27b all V3b (mem(V3b,arr(A_27b,bool)) -> (all V23x ap(V3b,V23x) = ap(f680(A_27b,V3b),V23x)))) # label(lameq_f680) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4373 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V7x ap(f651(A_27b,V1P,V2Q),V7x) = ap(ap(c_2Emin_2E_3D(bool),ap(V1P,V7x)),ap(V2Q,V7x))))))) # label(lameq_f651) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4374 (all A_27a all A_27c all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V17x ap(f730(A_27a,A_27c,V1P),V17x) = ap(c_2Ebool_2E_21(A_27a),f729(A_27c,A_27a,V17x,V1P))))) # label(lameq_f730) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4375 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0i (mem(V0i,arr(A_27b,A_27c)) -> (all V1P (mem(V1P,arr(A_27c,arr(A_27a,bool))) -> (all V2iK (mem(V2iK,A_27c) -> ((all V3y (mem(V3y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f722(A_27a,A_27c,V1P,V3y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27c),V0i),f705(A_27a,A_27c,V1P)))) & ((all V15y (mem(V15y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f728(A_27a,A_27c,V1P,V15y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b,A_27c),V0i),f730(A_27a,A_27c,V1P)))) & ((all V19y (mem(V19y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f731(A_27a,A_27c,V1P,V19y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(ty_2Eone_2Eone,A_27c),k(ty_2Eone_2Eone,V2iK)),f733(A_27a,A_27c,V1P)))) & ((all V25y (mem(V25y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f734(A_27a,A_27c,V1P,V25y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b,A_27c),V0i),f736(A_27a,A_27c,V1P)))) & ((all V11y (mem(V11y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f725(A_27a,A_27c,V1P,V11y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b,A_27c),V0i),f727(A_27a,A_27c,V1P)))) & ((all V7y (mem(V7y,A_27a) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),V0i),f706(A_27a,A_27c,V1P,V7y))))) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b,A_27c),V0i),f724(A_27a,A_27c,V1P)))))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__FORALL) # label(axiom) # label(non_clause). [assumption]. 6.43/6.43 4376 (all A_27b all V1P (mem(V1P,arr(A_27b,bool)) -> (all V8x ap(V1P,V8x) = ap(f603(A_27b,V1P),V8x)))) # label(lameq_f603) # label(axiom) # label(non_clause). [assumption]. 14.96/14.94 4377 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))))))) # label(mem_c_2EquantHeuristics_2EGUESS__EXISTS__GAP) # label(axiom) # label(non_clause). [assumption]. 14.96/14.94 4378 -(all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0i (mem(V0i,arr(A_27b,A_27a)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V2Q,V3x)) -> p(ap(V1P,V3x))))) -> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V1P)) -> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V2Q)))))))))))))) # label(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) # label(negated_conjecture) # label(non_clause). [assumption]. 14.96/14.94 14.96/14.94 ============================== end of process non-clausal formulas === 14.96/14.94 14.96/14.94 ============================== PROCESS INITIAL CLAUSES =============== 14.96/14.94 14.96/14.94 ============================== PREDICATE ELIMINATION ================= 14.96/14.94 14.96/14.94 ============================== end predicate elimination ============= 14.96/14.94 14.96/14.94 Auto_denials: (non-Horn, no changes). 14.96/14.94 14.96/14.94 Term ordering decisions: 14.96/14.94 Function symbol KB weights: bool=1. ty_2Enum_2Enum=1. c_2Enum_2E0=1. c_2Earithmetic_2ENUMERAL=1. c_2Eprim__rec_2E_3C=1. c_2Earithmetic_2EZERO=1. c_2Earithmetic_2EBIT1=1. ty_2Eone_2Eone=1. c_2Earithmetic_2E_2B=1. c_2Earithmetic_2E_3C_3D=1. c_2Enum_2ESUC=1. c_2Earithmetic_2EBIT2=1. c_2Earithmetic_2E_2A=1. c_2Earithmetic_2E_2D=1. c_2Earithmetic_2EEXP=1. c_2Earithmetic_2EMOD=1. c_2Ebit_2EBIT=1. c_2Earithmetic_2EDIV=1. c_2Ebool_2E_2F_5C=1. c_2Ebit_2EBITS=1. c_2Edivides_2Edivides=1. c_2Ebool_2ET=1. c_2Earithmetic_2EODD=1. c_2Egcd_2Egcd=1. c_2Eprim__rec_2EPRE=1. c_2Ebool_2E_7E=1. c_2Ebool_2EF=1. c_2Emin_2E_3D_3D_3E=1. c_2Earithmetic_2EEVEN=1. c_2Enumeral_2EiDUB=1. c_2Earithmetic_2EMODEQ=1. c_2Earithmetic_2EMIN=1. c_2Enumpair_2Etri=1. c_2Earithmetic_2EMAX=1. c_2Ebit_2ESLICE=1. c_2Epred__set_2Ecount=1. c_2Earithmetic_2E_3E=1. c_2Enumeral__bit_2EFDUB=1. c_2Enumeral_2EiSUB=1. ind=1. c_2Ebool_2E_5C_2F=1. c_2Elist_2ESUM=1. c_2Elogroot_2ELOG=1. c_2Eone_2Eone=1. c_2Ewhile_2ELEAST=1. c_2Earithmetic_2EABS__DIFF=1. c_2Earithmetic_2EDIV2=1. c_2Earithmetic_2E_3E_3D=1. c_2Epred__set_2EMAX__SET=1. c_2Edivides_2Eprime=1. c_2Enumeral__bit_2ESFUNPOW=1. c_2Egcd_2Eis__gcd=1. c_2Enumeral__bit_2EiDIV2=1. c_2Ewhile_2EOLEAST=1. c_2Edivides_2EPRIMES=1. c_2Ebit_2EBITWISE=1. c_2Enumpair_2Encons=1. c_2Elogroot_2ESQRTd=1. c_2Epred__set_2EMIN__SET=1. c_2Enumeral_2EiiSUC=1. c_2Enumeral_2Etexp__help=1. c_2Epred__set_2ESUM__SET=1. c_2Ebit_2ESBIT=1. c_2Elogroot_2EROOT=1. c_2Enumeral__bit_2EBIT__MODF=1. c_2Enumeral__bit_2EBIT__REV=1. c_2Ebit_2ELOG2=1. c_2Ebit_2EMOD__2EXP=1. c_2Eind__type_2ENUMSUM=1. c_2Enumeral_2EiZ=1. c_2Enumpair_2Enpair=1. c_2Ebit_2EMOD__2EXP__EQ=1. c_2Egcd_2Elcm=1. c_2Enumeral__bit_2EiMOD__2EXP=1. c_2Earithmetic_2EDIVMOD=1. c_2Earithmetic_2EFACT=1. c_2Eind__type_2ENUMPAIR=1. c_2ElistRange_2ElistRangeLHI=1. c_2Enumeral_2Einternal__mult=1. c_2Enum_2EIS__NUM__REP=1. c_2Enumeral__bit_2EiBITWISE=1. c_2Enumeral__bit_2EiSUC=1. c_2Enumpair_2Einvtri=1. c_2Earithmetic_2Efindq=1. c_2Ebit_2EBIT__MODIFY=1. c_2Ebit_2EBIT__REVERSE=1. c_2Ebit_2EMOD__2EXP__MAX=1. c_2Egcdset_2Egcdset=1. c_2ElistRange_2ElistRangeINC=1. c_2Enumeral_2Eexactlog=1. c_2Enumeral__bit_2EiLOG2=1. c_2Enumpair_2Ensnd=1. c_2Enumeral_2Eonecount=1. c_2Enumpair_2Einvtri0=1. c_2Epred__set_2EPROD__SET=1. c_2Ebit_2EDIV__2EXP=1. c_2Ebit_2ELOWEST__SET__BIT=1. c_2Emarker_2EAbbrev=1. c_2Enumpair_2Enfst=1. c_2Eoption_2EOPTION__GUARD=1. c_2Elist_2ESUM__ACC=1. c_2Enum_2EABS__num=1. c_2Enum_2EZERO__REP=1. c_2Enum_2EREP__num=1. c_2Enum_2ESUC__REP=1. c_2Enumeral_2EiSQR=1. c_2Enumpair_2Enapp=1. c_2Enumpair_2Enlen=1. c_2Enumpair_2Enmap=1. c_2Epred__set_2Epair__to__num=1. c_2EConseqConv_2EASM__MARKER=1. c_2Ebit_2ESIGN__EXTEND=1. c_2Ebit_2ETIMES__2EXP=1. c_2Eind__type_2ENUMLEFT=1. c_2Eind__type_2ENUMRIGHT=1. c_2Elogroot_2EiSQRT0=1. c_2Elogroot_2EiSQRT1=1. c_2Elogroot_2EiSQRT2=1. c_2Elogroot_2EiSQRT3=1. c_2Emarker_2EAC=1. c_2Epred__set_2Enum__to__pair=1. f159=1. c_2Ebit_2EBITV=1. c_2Ebit_2EDIVMOD__2EXP=1. c_2Ebool_2EBOUNDED=1. c_2Eind__type_2ENUMFST=1. c_2Eind__type_2ENUMSND=1. c_2Emarker_2ECong=1. c_2Emarker_2E_3A_2D=1. f151=1. f153=1. f65=1. c_2Earithmetic_2Enat__elim____magic=1. c_2EbasicSize_2Ebool__size=1. c_2EbasicSize_2Eone__size=1. c_2Elist_2ELIST__GUARD=1. c_2Emarker_2EIfCases=1. f173=1. f178=1. f184=1. f202=1. f230=1. f232=1. f236=1. f240=1. f241=1. f248=1. f251=1. f306=1. f5=1. f8=1. f9=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. ap=1. arr=1. ty_2Epair_2Eprod=1. c_2Epair_2E_2C=1. c_2Epair_2ELEX=1. c_2Elist_2ELIST__REL=1. c_2Epred__set_2EGSPEC=1. ty_2Esum_2Esum=1. c_2Epred__set_2EIMAGE=1. c_2Elist_2EMAP=1. c_2Epred__set_2EBIJ=1. k=1. c_2Epair_2EPROD__ALL=1. c_2Epred__set_2EINJ=1. c_2Eset__relation_2Efinite__prefixes=1. c_2Esum_2ESUM__ALL=1. c_2EquantHeuristics_2EGUESS__FORALL__GAP=1. c_2Epair_2EFST=1. c_2Epair_2ESND=1. c_2EquantHeuristics_2EGUESS__EXISTS__GAP=1. c_2Eset__relation_2Ereln__to__rel=1. c_2EquantHeuristics_2EGUESS__EXISTS__POINT=1. c_2EquantHeuristics_2EGUESS__EXISTS=1. c_2EquantHeuristics_2EGUESS__FORALL=1. c_2Esum_2EINL=1. c_2Esum_2EINR=1. c_2EquantHeuristics_2EGUESS__FORALL__POINT=1. f360=1. f364=1. c_2Ebool_2ELET=1. c_2Eset__relation_2Erange=1. c_2Eset__relation_2Edomain=1. c_2Elist_2EZIP=1. c_2Ecombin_2EUPDATE=1. c_2Epred__set_2ECROSS=1. c_2Erelation_2Einv=1. c_2Epred__set_2ESURJ=1. c_2Elist_2Elist__CASE=1. c_2Eoption_2Eoption__CASE=1. c_2Epred__set_2EPREIMAGE=1. c_2Ebool_2ETYPE__DEFINITION=1. c_2Erelation_2ERSUBSET=1. c_2Eoption_2EOPTION__MAP=1. c_2Eset__relation_2Erel__to__reln=1. c_2Estate__transformer_2EUNIT=1. c_2Ecombin_2EK=1. c_2EfixedPoint_2Emonotone=1. c_2Ebool_2ERES__ABSTRACT=1. c_2Epred__set_2EITSET=1. c_2EerrorStateMonad_2EUNIT=1. c_2Erelation_2ERDOM=1. c_2Epred__set_2EFUNSET=1. c_2Eoption_2EOPTION__BIND=1. c_2Eoption_2EOPTREL=1. c_2Elist_2EFOLDL=1. c_2Elist_2ELIST__BIND=1. c_2Eind__type_2EISO=1. c_2Ebool_2Eliteral__case=1. f108=1. c_2Elist_2EFOLDR=1. c_2Erelation_2EWFREC=1. c_2Ebool_2EONE__ONE=1. c_2EfixedPoint_2Efnsum=1. c_2Erelation_2ERUNION=1. c_2Eposet_2Efunction=1. c_2Erelation_2ERINTER=1. c_2Estate__transformer_2EJOIN=1. c_2EerrorStateMonad_2EES__FAIL=1. c_2Elist_2EUNZIP=1. f49=1. c_2Elist_2ELIST__APPLY=1. c_2Eoption_2EOPTION__APPLY=1. c_2Erelation_2EINDUCTIVE__INVARIANT__ON=1. c_2EerrorStateMonad_2EJOIN=1. c_2Eoption_2EOPTION__IGNORE__BIND=1. c_2Epred__set_2EDFUNSET=1. c_2Epred__set_2ELINV__OPT=1. c_2Erelation_2ERESTRICT=1. c_2Ewhile_2EHOARE__SPEC=1. c_2Elist_2EOPT__MMAP=1. c_2Elist_2EsplitAtPki=1. c_2Erelation_2EINDUCTIVE__INVARIANT=1. c_2Erelation_2Einv__image=1. c_2Erelation_2ERRANGE=1. c_2Eset__relation_2Eupper__bounds=1. c_2Esum_2EIS__SUM__REP=1. f469=1. c_2EerrorStateMonad_2EES__CHOICE=1. c_2EnormalForms_2EEXT__POINT=1. c_2Epair_2ESWAP=1. c_2Erelation_2ERRESTRICT=1. c_2Erelation_2ERUNIV=1. c_2Esum_2EISL=1. f471=1. f482=1. c_2Ebool_2EONTO=1. c_2Ecombin_2ECOMM=1. c_2Ecombin_2ELEFT__ID=1. c_2Ecombin_2ERIGHT__ID=1. c_2Esum_2EABS__sum=1. c_2Esum_2EISR=1. f592=1. c_2EerrorStateMonad_2EFOREACH=1. c_2EfixedPoint_2Eempty=1. c_2Epair_2EABS__prod=1. c_2Epred__set_2ELINV=1. c_2Erelation_2ERDOM__DELETE=1. c_2Estate__transformer_2EFOREACH=1. f392=1. f394=1. f468=1. f472=1. f473=1. f484=1. f486=1. f584=1. f590=1. f601=1. f605=1. f61=1. f616=1. f621=1. f624=1. c_2Ecombin_2EFAIL=1. c_2EerrorStateMonad_2Esequence=1. c_2Epair_2EREP__prod=1. c_2Erelation_2Eapprox=1. c_2Estate__transformer_2Esequence=1. c_2Esum_2EOUTL=1. c_2Esum_2EOUTR=1. c_2Esum_2EREP__sum=1. f262=1. f282=1. f596=1. f603=1. f610=1. f612=1. f614=1. f617=1. f619=1. f623=1. f626=1. f628=1. c_2EbasicSize_2Esum__size=1. c_2Ecombin_2EW=1. c_2Epair_2ERPROD=1. c_2Eposet_2Epointwise__lift=1. c_2Epred__set_2ERINV=1. c_2Erelation_2ERCOMPL=1. c_2Erelation_2Enf=1. c_2Erelation_2Ethe__fun=1. c_2Estate__transformer_2EMWHILE=1. f120=1. f14=1. f155=1. f157=1. f252=1. f256=1. f297=1. f298=1. f440=1. f450=1. f481=1. f485=1. f492=1. f494=1. f581=1. f582=1. f583=1. f585=1. f586=1. f587=1. f588=1. f589=1. f591=1. f650=1. f652=1. f654=1. f656=1. f657=1. f68=1. c_2EbasicSize_2Epair__size=1. c_2Ebool_2Eitself__case=1. c_2Ecombin_2E_3A_3E=1. c_2EerrorStateMonad_2EREAD=1. c_2Elist_2ELIST__IGNORE__BIND=1. c_2Estate__transformer_2EREAD=1. f109=1. f11=1. f110=1. f115=1. f163=1. f17=1. f176=1. f179=1. f182=1. f203=1. f204=1. f206=1. f208=1. f209=1. f21=1. f210=1. f217=1. f218=1. f220=1. f228=1. f233=1. f237=1. f24=1. f242=1. f246=1. f253=1. f278=1. f280=1. f281=1. f285=1. f288=1. f289=1. f290=1. f293=1. f294=1. f295=1. f3=1. f30=1. f307=1. f308=1. f310=1. f311=1. f315=1. f32=1. f327=1. f329=1. f342=1. f348=1. f35=1. f350=1. f356=1. f368=1. f370=1. f373=1. f38=1. f380=1. f384=1. f385=1. f399=1. f40=1. f418=1. f419=1. f421=1. f428=1. f43=1. f449=1. f45=1. f461=1. f466=1. f50=1. f500=1. f505=1. f506=1. f51=1. f511=1. f517=1. f519=1. f530=1. f542=1. f547=1. f548=1. f553=1. f559=1. f561=1. f57=1. f574=1. f59=1. f595=1. f597=1. f598=1. f599=1. f6=1. f60=1. f600=1. f602=1. f604=1. f606=1. f607=1. f608=1. f659=1. f660=1. f662=1. f663=1. f665=1. f666=1. f668=1. f669=1. f675=1. f677=1. f678=1. f680=1. f682=1. f684=1. f685=1. f687=1. f688=1. f690=1. f691=1. f693=1. f694=1. f696=1. f697=1. f699=1. f700=1. f76=1. f87=1. c_2EquantHeuristics_2EIS__REMOVABLE__QUANT__FUN=1. f5=1. f23=1. f28=1. f34=1. f36=1. f39=1. f46=1. f47=1. f48=1. f73=1. f74=1. f85=1. f86=1. f88=1. f89=1. f90=1. f100=1. f101=1. f102=1. f111=1. f124=1. f126=1. f154=1. f156=1. f164=1. f173=1. f174=1. f175=1. f177=1. f178=1. f180=1. f185=1. f188=1. f191=1. f234=1. f235=1. f250=1. f254=1. f268=1. f270=1. f271=1. f291=1. f292=1. f296=1. f304=1. f306=1. f314=1. f316=1. f317=1. f374=1. f375=1. f376=1. f408=1. f409=1. f410=1. f416=1. f417=1. f445=1. f446=1. f448=1. f451=1. f452=1. f460=1. f462=1. f463=1. f464=1. f474=1. f475=1. f476=1. f483=1. f487=1. f490=1. f495=1. f498=1. f501=1. f502=1. f503=1. f507=1. f510=1. f543=1. f593=1. f609=1. f615=1. f620=1. f670=1. f679=1. f681=1. f683=1. f686=1. f689=1. f692=1. f695=1. f710=1. f711=1. f714=1. f718=1. f719=1. f720=1. f749=1. f750=1. f751=1. f760=1. f761=1. f762=1. f764=1. f765=1. f766=1. f773=1. f774=1. f776=1. f791=1. f797=1. f798=1. f799=1. f807=1. f808=1. f809=1. f816=1. f817=1. f818=1. f820=1. f821=1. f822=1. f825=1. f826=1. f827=1. f833=1. f834=1. f843=1. f844=1. f845=1. f853=1. f854=1. f855=1. f858=1. f859=1. f860=1. f862=1. f877=1. f880=1. f889=1. f899=1. f905=1. f906=1. f912=1. f914=1. f916=1. f917=1. f918=1. f919=1. f922=1. f927=1. f933=1. f946=1. f957=1. f959=1. f966=1. f967=1. f972=1. f973=1. f974=1. f975=1. f977=1. f978=1. f984=1. f988=1. f989=1. f991=1. f992=1. f999=1. f1008=1. f1026=1. f1027=1. f1028=1. f1046=1. f1049=1. f1050=1. f1051=1. f1066=1. f1067=1. f1068=1. f1070=1. f1071=1. f1073=1. f1074=1. f1075=1. f1076=1. f1077=1. f1078=1. f1079=1. f1107=1. f1139=1. f1140=1. f1141=1. f1173=1. f1174=1. f1175=1. f1190=1. f1191=1. f1192=1. f1195=1. f1196=1. f1200=1. f1207=1. f1208=1. f1209=1. f1210=1. f1212=1. f1213=1. f1214=1. f1215=1. f1222=1. f1223=1. f1255=1. f1256=1. f1262=1. f1263=1. f1287=1. f1288=1. f1291=1. f1292=1. f1297=1. f1335=1. f1349=1. f1350=1. f1351=1. f1356=1. f1357=1. f1358=1. ty_2Elist_2Elist=1. c_2Ebool_2EIN=1. ty_2Eoption_2Eoption=1. c_2Erelation_2EEQC=1. c_2Elist_2ENIL=1. c_2Elist_2ECONS=1. c_2Epred__set_2EFINITE=1. c_2Elist_2ELENGTH=1. c_2Epred__set_2EEMPTY=1. c_2Erelation_2ETC=1. c_2Epred__set_2ESUBSET=1. c_2Elist_2EAPPEND=1. c_2Ebool_2ECOND=1. c_2Eoption_2ESOME=1. c_2Eset__relation_2Etc=1. c_2Elist_2ELIST__TO__SET=1. c_2Epred__set_2EINSERT=1. c_2Eoption_2ENONE=1. c_2Eposet_2Eposet=1. c_2Erelation_2ERTC=1. c_2Emin_2E_3D=1. c_2Epred__set_2Eequiv__on=1. c_2Epred__set_2EUNION=1. c_2Epred__set_2EUNIV=1. c_2Epred__set_2ECARD=1. c_2Epred__set_2EBIGUNION=1. c_2Epred__set_2EDISJOINT=1. c_2Elist_2EEVERY=1. c_2Erelation_2EWF=1. c_2Eset__relation_2Elinear__order=1. c_2Ebool_2ERES__FORALL=1. c_2Epred__set_2Ecountable=1. c_2Elist_2EEL=1. c_2Epred__set_2EDELETE=1. c_2Epred__set_2EINTER=1. c_2Ebool_2ERES__EXISTS=1. c_2Ebool_2E_21=1. c_2Elist_2EALL__DISTINCT=1. c_2Erelation_2ERC=1. c_2Epred__set_2EDIFF=1. c_2Elist_2EFILTER=1. c_2Elist_2EGENLIST=1. c_2Ebool_2E_3F=1. c_2Erelation_2Etransitive=1. c_2Elist_2EEXISTS=1. c_2Epred__set_2ESUM__IMAGE=1. c_2Eset__relation_2Eacyclic=1. ty_2Eind__type_2Erecspace=1. c_2Elist_2ELLEX=1. c_2Elist_2EREVERSE=1. c_2Ebool_2E_3F_21=1. c_2Epred__set_2EBIGINTER=1. c_2Earithmetic_2ENRC=1. c_2Elist_2ELUPDATE=1. c_2Elist_2ESNOC=1. c_2Erelation_2Ereflexive=1. c_2Ecombin_2EI=1. c_2Erelation_2ESC=1. c_2Eset__relation_2Etransitive=1. c_2Elist_2ETAKE=1. c_2Eset__relation_2Estrict__linear__order=1. c_2Eset__relation_2Epartial__order=1. c_2Elist_2EDROP=1. c_2Eposet_2Eglb=1. c_2Eposet_2Elub=1. c_2Eset__relation_2Eminimal__elements=1. c_2Eind__type_2EZRECSPACE=1. c_2Emin_2E_40=1. c_2Epred__set_2EREST=1. c_2Epred__set_2ESING=1. c_2Eset__relation_2Errestrict=1. c_2Epred__set_2Epairwise=1. c_2Erelation_2Eantisymmetric=1. c_2Erelation_2Esymmetric=1. c_2Earithmetic_2EFUNPOW=1. c_2Elist_2ESHORTLEX=1. c_2Epred__set_2EPSUBSET=1. c_2Erelation_2EWFP=1. c_2Elist_2EFLAT=1. c_2Ewhile_2EOWHILE=1. c_2Eoption_2EOPTION__ALL=1. c_2Erelation_2EWeakOrder=1. c_2Eposet_2Ecomplete=1. c_2Erelation_2Eirreflexive=1. c_2Earithmetic_2Enum__CASE=1. c_2Ebool_2ERES__EXISTS__UNIQUE=1. c_2Epred__set_2ECOMPL=1. c_2Eset__relation_2Eantisym=1. c_2Eind__type_2EZBOT=1. c_2Elist_2ELAST=1. c_2Elist_2ELRC=1. c_2Elist_2ENULL=1. c_2Eoption_2EIS__SOME=1. c_2Epred__set_2EREL__RESTRICT=1. c_2Erelation_2Etrichotomous=1. c_2Elist_2EisPREFIX=1. c_2Eset__relation_2Emaximal__elements=1. i=1. c_2Epred__set_2ECHOICE=1. c_2Erelation_2Ediamond=1. ty_2Ebool_2Eitself=1. c_2Ecombin_2EASSOC=1. c_2Eposet_2Ecarrier=1. c_2EfixedPoint_2Elfp=1. c_2Eoption_2ETHE=1. c_2Eoption_2Esome=1. c_2Eposet_2Emonotonic=1. c_2Epred__set_2EPOW=1. c_2Elist_2EFRONT=1. c_2Elist_2ESET__TO__LIST=1. c_2Elist_2ETL=1. c_2Erelation_2Etotal=1. c_2Eind__type_2ECONSTR=1. c_2Elist_2EdropWhile=1. c_2Elist_2EoEL=1. c_2Eposet_2Echain=1. c_2Erelation_2EWeakLinearOrder=1. c_2Eset__relation_2Eper=1. c_2Elist_2EHD=1. c_2Elist_2Enub=1. c_2Epred__set_2Eis__measure__maximal=1. c_2Erelation_2ESTRORD=1. c_2Erelation_2Eequivalence=1. c_2Erelation_2Ercdiamond=1. c_2Eset__relation_2Ereflexive=1. c_2Eposet_2Egfp=1. c_2Eposet_2Elfp=1. c_2Erelation_2EINVOL=1. c_2Erelation_2EOrder=1. c_2Eset__relation_2Echain=1. c_2Eset__relation_2Estrict=1. c_2Ebool_2Ethe__value=1. c_2Eind__type_2EINJP=1. c_2Eind__type_2EZCONSTR=1. c_2Elist_2EGENLIST__AUX=1. c_2Epred__set_2Eschroeder__close=1. c_2Eprim__rec_2ESIMP__REC__REL=1. c_2Erelation_2EIDEM=1. c_2Erelation_2EStrongOrder=1. c_2Erelation_2EWCR=1. c_2Eset__relation_2ERREFL__EXP=1. c_2Eset__relation_2Eget__min=1. c_2Ebool_2ERES__SELECT=1. c_2EfixedPoint_2Egfp=1. c_2Elist_2Elist__size=1. c_2Enumpair_2Enlistrec=1. c_2Epred__set_2Epartition=1. c_2Eset__relation_2Eirreflexive=1. c_2Ebool_2EDATATYPE=1. c_2Eind__type_2EBOTTOM=1. c_2Eind__type_2Edest__rec=1. c_2Elist_2EEVERYi=1. c_2Elist_2EUNIQUE=1. c_2Eoption_2EIS__NONE=1. c_2Eposet_2Edown__continuous=1. c_2Eposet_2Eup__continuous=1. c_2Epred__set_2Echooser=1. c_2Eset__relation_2Enth__min=1. c_2Eind__type_2EINJN=1. c_2Eind__type_2Emk__rec=1. c_2Enumeral_2EiBIT__cases=1. c_2Eprim__rec_2Emeasure=1. c_2Erelation_2EEMPTY__REL=1. c_2Erelation_2EStrongLinearOrder=1. c_2Ewhile_2EWHILE=1. c_2Ebool_2EARB=1. c_2Ecombin_2EMONOID=1. c_2Eind__type_2EINJA=1. c_2Eind__type_2EINJF=1. c_2Eoption_2EOPTION__CHOICE=1. c_2Eoption_2EOPTION__JOIN=1. c_2Eposet_2Ebottom=1. c_2Eposet_2Etop=1. c_2Epred__set_2Eenumerate=1. c_2EerrorStateMonad_2EES__GUARD=1. c_2Elist_2EINDEX__FIND=1. c_2Elist_2ELEN=1. c_2Elist_2EREV=1. c_2Eoption_2Eoption__ABS=1. c_2Epred__set_2EPROD__IMAGE=1. c_2Eprim__rec_2EPRIM__REC__FUN=1. c_2Eprim__rec_2ESIMP__REC=1. c_2Eprim__rec_2Ewellfounded=1. c_2Erelation_2ECR=1. c_2Erelation_2Ediag=1. c_2Eset__relation_2ERRUNIV=1. c_2EfixedPoint_2Eclosed=1. c_2EfixedPoint_2Edense=1. c_2Eind__type_2EFCONS=1. c_2EnormalForms_2EUNIV__POINT=1. c_2Enumpair_2Enfoldl=1. c_2Eprim__rec_2EPRIM__REC=1. c_2Eset__relation_2Eall__choices=1. c_2EerrorStateMonad_2EFOR=1. c_2Elist_2EoHD=1. c_2Eoption_2Eoption__REP=1. c_2Eposet_2Econtinuous=1. c_2Erelation_2ELinearOrder=1. c_2Erelation_2EPreOrder=1. c_2Erelation_2ESN=1. c_2Eset__relation_2Enum__order=1. c_2Eset__relation_2Euniv__reln=1. c_2Estate__transformer_2EFOR=1. c_2EbasicSize_2Eoption__size=1. c_2Eone_2Eone__CASE=1. c_2Eset__relation_2Eper__restrict=1. f188=1. f189=1. f535=1. c_2EerrorStateMonad_2EWRITE=1. c_2Eind__type_2EFNIL=1. c_2Elist_2EFIND=1. c_2Elist_2EINDEX__OF=1. c_2Elist_2EPAD__LEFT=1. c_2Elist_2EPAD__RIGHT=1. c_2Emarker_2Estmarker=1. c_2Emarker_2Eunint=1. c_2Eposet_2Erelation=1. c_2Eset__relation_2Efchains=1. c_2Estate__transformer_2EWRITE=1. f1=1. f12=1. f149=1. f150=1. f152=1. f158=1. f172=1. f177=1. f18=1. f183=1. f190=1. f191=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f2=1. f200=1. f201=1. f207=1. f219=1. f229=1. f231=1. f234=1. f235=1. f238=1. f239=1. f243=1. f247=1. f249=1. f275=1. f291=1. f292=1. f314=1. f316=1. f33=1. f343=1. f36=1. f376=1. f381=1. f386=1. f39=1. f4=1. f400=1. f420=1. f422=1. f44=1. f443=1. f46=1. f463=1. f501=1. f507=1. f543=1. f549=1. f578=1. f7=1. c_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS=1. c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL=1. f9=1. f125=1. f184=1. f186=1. f187=1. f494=1. f680=1. f684=1. f696=1. f700=1. f701=1. f712=1. f715=1. f716=1. f717=1. f721=1. f722=1. f723=1. f724=1. f726=1. f730=1. f731=1. f732=1. f736=1. f737=1. f738=1. f752=1. f753=1. f768=1. f778=1. f779=1. f780=1. f786=1. f787=1. f789=1. f790=1. f792=1. f793=1. f794=1. f795=1. f796=1. f811=1. f828=1. f829=1. f830=1. f831=1. f835=1. f836=1. f837=1. f838=1. f839=1. f840=1. f841=1. f842=1. f846=1. f847=1. f848=1. f849=1. f850=1. f851=1. f856=1. f907=1. f908=1. f915=1. f920=1. f921=1. f1031=1. f1254=1. f1310=1. c_2Epair_2EUNCURRY=1. c_2Ecombin_2Eo=1. c_2EerrorStateMonad_2EBIND=1. c_2Eoption_2EOPTION__MAP2=1. c_2Epair_2Epair__CASE=1. c_2Elist_2EMAP2=1. c_2Estate__transformer_2EBIND=1. c_2Esum_2Esum__CASE=1. c_2Erelation_2EO=1. c_2Elist_2EFOLDL2=1. c_2Ecombin_2EC=1. c_2Estate__transformer_2EMMAP=1. c_2EerrorStateMonad_2EMMAP=1. c_2Estate__transformer_2EEXT=1. c_2Ecombin_2ES=1. c_2Epair_2ECURRY=1. c_2Eoption_2EOPTION__MCOMP=1. f128=1. f304=1. c_2Ecombin_2EFCOMM=1. f129=1. f705=1. f737=1. c_2EerrorStateMonad_2EIGNORE__BIND=1. c_2EerrorStateMonad_2EES__APPLY=1. c_2EerrorStateMonad_2EmapM=1. c_2Eset__relation_2Ercomp=1. c_2Estate__transformer_2EmapM=1. f166=1. f303=1. f63=1. f709=1. f713=1. f717=1. f738=1. f739=1. f740=1. f186=1. f187=1. f390=1. f467=1. f470=1. f476=1. f487=1. f488=1. f53=1. c_2EerrorStateMonad_2EEXT=1. c_2Estate__transformer_2EIGNORE__BIND=1. f185=1. f258=1. f37=1. f397=1. f404=1. f406=1. f408=1. f424=1. f452=1. f459=1. f460=1. f483=1. f491=1. f493=1. f496=1. f64=1. f724=1. f727=1. f730=1. f733=1. f736=1. f741=1. f742=1. f743=1. f744=1. f745=1. f747=1. f750=1. f751=1. f752=1. f753=1. f754=1. f755=1. f756=1. f82=1. f89=1. f91=1. c_2EerrorStateMonad_2ENARROW=1. c_2EerrorStateMonad_2EWIDEN=1. c_2Elist_2ELIST__LIFT2=1. c_2Estate__transformer_2ENARROW=1. c_2Estate__transformer_2EWIDEN=1. f10=1. f107=1. f114=1. f119=1. f13=1. f154=1. f156=1. f16=1. f162=1. f164=1. f165=1. f174=1. f175=1. f181=1. f20=1. f205=1. f212=1. f213=1. f216=1. f23=1. f245=1. f250=1. f255=1. f26=1. f263=1. f264=1. f265=1. f266=1. f276=1. f277=1. f279=1. f284=1. f286=1. f287=1. f29=1. f296=1. f299=1. f302=1. f305=1. f31=1. f312=1. f313=1. f318=1. f320=1. f322=1. f326=1. f328=1. f336=1. f339=1. f34=1. f340=1. f341=1. f344=1. f346=1. f347=1. f349=1. f352=1. f354=1. f355=1. f359=1. f363=1. f367=1. f369=1. f371=1. f372=1. f375=1. f383=1. f393=1. f396=1. f398=1. f41=1. f42=1. f425=1. f427=1. f429=1. f431=1. f436=1. f437=1. f441=1. f444=1. f453=1. f465=1. f47=1. f48=1. f495=1. f497=1. f499=1. f503=1. f504=1. f510=1. f515=1. f516=1. f518=1. f521=1. f527=1. f528=1. f529=1. f533=1. f536=1. f541=1. f545=1. f546=1. f552=1. f557=1. f558=1. f560=1. f563=1. f564=1. f571=1. f572=1. f573=1. f576=1. f58=1. f609=1. f611=1. f613=1. f615=1. f618=1. f62=1. f620=1. f622=1. f625=1. f627=1. f629=1. f630=1. f631=1. f632=1. f633=1. f634=1. f635=1. f636=1. f637=1. f638=1. f639=1. f640=1. f641=1. f642=1. f643=1. f644=1. f645=1. f646=1. f647=1. f648=1. f649=1. f651=1. f653=1. f655=1. f658=1. f661=1. f664=1. f667=1. f670=1. f71=1. f74=1. f75=1. f80=1. f90=1. f93=1. f94=1. f95=1. f2=1. f3=1. f4=1. f6=1. f7=1. f8=1. f11=1. f12=1. f14=1. f15=1. f17=1. f19=1. f21=1. f22=1. f25=1. f27=1. f30=1. f32=1. f33=1. f38=1. f40=1. f43=1. f44=1. f45=1. f54=1. f55=1. f56=1. f57=1. f59=1. f60=1. f61=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f72=1. f76=1. f77=1. f78=1. f79=1. f81=1. f83=1. f84=1. f92=1. f96=1. f97=1. f98=1. f99=1. f103=1. f104=1. f105=1. f106=1. f108=1. f112=1. f113=1. f115=1. f116=1. f117=1. f118=1. f120=1. f121=1. f127=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. f138=1. f139=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f150=1. f151=1. f152=1. f153=1. f157=1. f158=1. f159=1. f160=1. f161=1. f163=1. f167=1. f168=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f200=1. f201=1. f202=1. f203=1. f206=1. f207=1. f217=1. f218=1. f220=1. f224=1. f225=1. f226=1. f231=1. f232=1. f233=1. f236=1. f239=1. f240=1. f241=1. f242=1. f243=1. f251=1. f256=1. f267=1. f269=1. f272=1. f273=1. f274=1. f275=1. f278=1. f280=1. f281=1. f282=1. f283=1. f285=1. f288=1. f289=1. f307=1. f308=1. f309=1. f310=1. f311=1. f319=1. f321=1. f323=1. f324=1. f325=1. f327=1. f329=1. f330=1. f331=1. f332=1. f337=1. f338=1. f342=1. f343=1. f345=1. f348=1. f350=1. f351=1. f353=1. f356=1. f360=1. f361=1. f366=1. f382=1. f384=1. f385=1. f386=1. f400=1. f401=1. f411=1. f412=1. f413=1. f414=1. f415=1. f420=1. f421=1. f422=1. f423=1. f426=1. f428=1. f430=1. f432=1. f433=1. f434=1. f435=1. f438=1. f442=1. f443=1. f447=1. f454=1. f455=1. f456=1. f457=1. f480=1. f500=1. f522=1. f530=1. f531=1. f532=1. f534=1. f535=1. f537=1. f538=1. f539=1. f540=1. f542=1. f544=1. f547=1. f548=1. f549=1. f550=1. f559=1. f561=1. f570=1. f574=1. f575=1. f578=1. f582=1. f583=1. f585=1. f594=1. f610=1. f616=1. f617=1. f621=1. f624=1. f626=1. f650=1. f652=1. f654=1. f656=1. f657=1. f659=1. f660=1. f662=1. f666=1. f668=1. f671=1. f690=1. f691=1. f702=1. f703=1. f706=1. f707=1. f708=1. f725=1. f728=1. f729=1. f734=1. f746=1. f748=1. f757=1. f758=1. f767=1. f781=1. f819=1. f832=1. f857=1. f861=1. f863=1. f870=1. f871=1. f872=1. f873=1. f881=1. f882=1. f883=1. f884=1. f885=1. f886=1. f887=1. f888=1. f890=1. f891=1. f895=1. f896=1. f904=1. f913=1. f924=1. f925=1. f926=1. f931=1. f932=1. f934=1. f935=1. f942=1. f947=1. f948=1. f950=1. f955=1. f956=1. f963=1. f976=1. f979=1. f980=1. f985=1. f993=1. f1003=1. f1009=1. f1012=1. f1019=1. f1020=1. f1021=1. f1022=1. f1023=1. f1024=1. f1025=1. f1029=1. f1033=1. f1034=1. f1035=1. f1036=1. f1044=1. f1045=1. f1047=1. f1048=1. f1052=1. f1053=1. f1054=1. f1055=1. f1056=1. f1057=1. f1058=1. f1059=1. f1060=1. f1061=1. f1063=1. f1064=1. f1065=1. f1072=1. f1080=1. f1081=1. f1082=1. f1083=1. f1084=1. f1085=1. f1086=1. f1087=1. f1088=1. f1089=1. f1093=1. f1094=1. f1095=1. f1096=1. f1097=1. f1098=1. f1102=1. f1103=1. f1104=1. f1105=1. f1106=1. f1108=1. f1109=1. f1110=1. f1111=1. f1112=1. f1113=1. f1116=1. f1117=1. f1118=1. f1119=1. f1122=1. f1123=1. f1124=1. f1125=1. f1126=1. f1127=1. f1128=1. f1130=1. f1131=1. f1134=1. f1135=1. f1136=1. f1137=1. f1138=1. f1142=1. f1143=1. f1146=1. f1147=1. f1150=1. f1151=1. f1159=1. f1160=1. f1164=1. f1171=1. f1172=1. f1188=1. f1189=1. f1199=1. f1235=1. f1236=1. f1237=1. f1238=1. f1239=1. f1240=1. f1244=1. f1267=1. f1273=1. f1278=1. f1279=1. f1281=1. f1282=1. f1302=1. f1303=1. f1307=1. f1311=1. f1312=1. f1315=1. f1336=1. f1343=1. f1344=1. f1345=1. f1347=1. f1348=1. f1352=1. f1353=1. f1354=1. f1355=1. f1359=1. f1360=1. f1361=1. f1362=1. c_2Estate__transformer_2EMCOMP=1. c_2Esum_2E_2B_2B=1. c_2Epair_2E_23_23=1. f171=1. f334=1. f391=1. f703=1. f706=1. f707=1. f711=1. f715=1. f260=1. f261=1. f402=1. f702=1. f138=1. f140=1. f274=1. f317=1. f330=1. f446=1. f448=1. f454=1. f474=1. f477=1. f478=1. f479=1. f480=1. f489=1. f490=1. f54=1. f55=1. f594=1. f704=1. f708=1. f710=1. f712=1. f714=1. f716=1. f718=1. f719=1. f720=1. f721=1. f722=1. f723=1. f725=1. f726=1. f728=1. f729=1. f731=1. f732=1. f734=1. f735=1. f84=1. c_2EerrorStateMonad_2EES__LIFT2=1. f103=1. f104=1. f106=1. f112=1. f113=1. f117=1. f118=1. f122=1. f123=1. f124=1. f126=1. f127=1. f131=1. f139=1. f144=1. f148=1. f15=1. f161=1. f169=1. f180=1. f19=1. f192=1. f193=1. f211=1. f215=1. f22=1. f221=1. f227=1. f244=1. f25=1. f254=1. f257=1. f259=1. f267=1. f269=1. f27=1. f271=1. f28=1. f283=1. f300=1. f301=1. f309=1. f319=1. f321=1. f332=1. f335=1. f337=1. f338=1. f345=1. f351=1. f353=1. f358=1. f362=1. f366=1. f374=1. f382=1. f388=1. f389=1. f395=1. f403=1. f405=1. f407=1. f412=1. f413=1. f414=1. f415=1. f423=1. f426=1. f430=1. f434=1. f435=1. f439=1. f442=1. f451=1. f462=1. f464=1. f475=1. f498=1. f502=1. f509=1. f513=1. f514=1. f520=1. f524=1. f526=1. f531=1. f538=1. f539=1. f540=1. f544=1. f551=1. f555=1. f556=1. f562=1. f567=1. f568=1. f570=1. f579=1. f580=1. f593=1. f671=1. f672=1. f673=1. f674=1. f676=1. f679=1. f681=1. f683=1. f686=1. f689=1. f692=1. f695=1. f698=1. f70=1. f701=1. f73=1. f746=1. f748=1. f749=1. f79=1. f88=1. f92=1. f98=1. f1=1. f24=1. f49=1. f50=1. f51=1. f52=1. f58=1. f93=1. f136=1. f137=1. f181=1. f182=1. f212=1. f213=1. f214=1. f216=1. f219=1. f222=1. f223=1. f228=1. f229=1. f230=1. f247=1. f248=1. f249=1. f262=1. f302=1. f303=1. f305=1. f318=1. f333=1. f336=1. f363=1. f364=1. f365=1. f372=1. f377=1. f378=1. f379=1. f380=1. f381=1. f387=1. f390=1. f392=1. f393=1. f394=1. f404=1. f440=1. f444=1. f458=1. f459=1. f469=1. f499=1. f515=1. f552=1. f557=1. f581=1. f584=1. f611=1. f612=1. f613=1. f618=1. f619=1. f622=1. f623=1. f632=1. f633=1. f651=1. f675=1. f677=1. f678=1. f699=1. f705=1. f769=1. f770=1. f771=1. f772=1. f777=1. f784=1. f788=1. f800=1. f801=1. f802=1. f803=1. f804=1. f805=1. f806=1. f823=1. f824=1. f852=1. f867=1. f868=1. f869=1. f874=1. f875=1. f876=1. f878=1. f879=1. f892=1. f893=1. f900=1. f901=1. f902=1. f903=1. f909=1. f910=1. f911=1. f928=1. f929=1. f930=1. f941=1. f943=1. f944=1. f949=1. f958=1. f960=1. f964=1. f965=1. f981=1. f982=1. f983=1. f986=1. f990=1. f994=1. f995=1. f1000=1. f1004=1. f1005=1. f1030=1. f1040=1. f1042=1. f1062=1. f1069=1. f1090=1. f1091=1. f1092=1. f1101=1. f1114=1. f1115=1. f1121=1. f1129=1. f1132=1. f1133=1. f1148=1. f1149=1. f1156=1. f1165=1. f1166=1. f1167=1. f1168=1. f1169=1. f1170=1. f1176=1. f1177=1. f1178=1. f1179=1. f1180=1. f1181=1. f1182=1. f1183=1. f1184=1. f1185=1. f1201=1. f1202=1. f1203=1. f1204=1. f1206=1. f1229=1. f1230=1. f1233=1. f1241=1. f1245=1. f1246=1. f1264=1. f1265=1. f1266=1. f1270=1. f1271=1. f1272=1. f1280=1. f1283=1. f1293=1. f1316=1. f1317=1. f1320=1. f1321=1. f1322=1. f1323=1. f1324=1. f1325=1. f1326=1. f1327=1. f1328=1. f1329=1. f1330=1. f1331=1. f1332=1. f1338=1. f1339=1. f1363=1. f1366=1. f1369=1. f1371=1. f1372=1. f1373=1. f1374=1. f1375=1. f1376=1. f1377=1. f1382=1. f1383=1. f1384=1. f1385=1. f1386=1. f1387=1. f1388=1. f1389=1. f1390=1. f1397=1. f1398=1. f1399=1. f1400=1. f1402=1. f1410=1. f1413=1. f1415=1. f1416=1. f1422=1. f1423=1. f1424=1. f1425=1. f1426=1. c_2EerrorStateMonad_2EMCOMP=1. f100=1. f272=1. f410=1. f417=1. f456=1. f458=1. f56=1. f85=1. f101=1. f102=1. f105=1. f111=1. f116=1. f121=1. f125=1. f130=1. f135=1. f143=1. f147=1. f160=1. f168=1. f170=1. f214=1. f226=1. f268=1. f270=1. f273=1. f325=1. f331=1. f333=1. f357=1. f361=1. f365=1. f377=1. f378=1. f379=1. f387=1. f401=1. f411=1. f433=1. f438=1. f445=1. f447=1. f508=1. f512=1. f52=1. f522=1. f523=1. f525=1. f534=1. f537=1. f550=1. f554=1. f565=1. f566=1. f569=1. f577=1. f66=1. f67=1. f69=1. f72=1. f77=1. f78=1. f81=1. f83=1. f86=1. f96=1. f97=1. f99=1. f18=1. f53=1. f123=1. f140=1. f169=1. f171=1. f172=1. f204=1. f237=1. f238=1. f257=1. f258=1. f276=1. f277=1. f297=1. f298=1. f299=1. f312=1. f313=1. f358=1. f359=1. f367=1. f368=1. f369=1. f370=1. f371=1. f395=1. f396=1. f398=1. f399=1. f405=1. f406=1. f407=1. f418=1. f419=1. f465=1. f466=1. f467=1. f468=1. f470=1. f478=1. f492=1. f493=1. f496=1. f497=1. f509=1. f511=1. f614=1. f627=1. f629=1. f630=1. f631=1. f663=1. f664=1. f676=1. f697=1. f713=1. f763=1. f775=1. f782=1. f783=1. f785=1. f810=1. f812=1. f813=1. f814=1. f815=1. f894=1. f897=1. f898=1. f923=1. f936=1. f937=1. f938=1. f939=1. f940=1. f951=1. f952=1. f953=1. f961=1. f968=1. f969=1. f970=1. f987=1. f996=1. f998=1. f1001=1. f1002=1. f1006=1. f1007=1. f1010=1. f1011=1. f1013=1. f1014=1. f1015=1. f1032=1. f1037=1. f1038=1. f1039=1. f1041=1. f1043=1. f1099=1. f1100=1. f1120=1. f1161=1. f1162=1. f1193=1. f1194=1. f1205=1. f1211=1. f1217=1. f1218=1. f1219=1. f1226=1. f1227=1. f1228=1. f1234=1. f1250=1. f1251=1. f1257=1. f1260=1. f1261=1. f1268=1. f1269=1. f1274=1. f1275=1. f1276=1. f1277=1. f1300=1. f1301=1. f1306=1. f1337=1. f1340=1. f1341=1. f1346=1. f1364=1. f1365=1. f1367=1. f1368=1. f1370=1. f1378=1. f1379=1. f1380=1. f1381=1. f1401=1. f1409=1. f1411=1. f1414=1. f1417=1. f1418=1. f1419=1. f1420=1. f1421=1. f133=1. f134=1. f137=1. f142=1. f146=1. f167=1. f223=1. f225=1. f324=1. f409=1. f416=1. f432=1. f455=1. f457=1. f532=1. f575=1. f122=1. f149=1. f244=1. f245=1. f477=1. f479=1. f504=1. f512=1. f513=1. f523=1. f524=1. f628=1. f665=1. f709=1. f759=1. f864=1. f865=1. f866=1. f945=1. f954=1. f962=1. f971=1. f997=1. f1016=1. f1017=1. f1018=1. f1157=1. f1158=1. f1163=1. f1186=1. f1187=1. f1197=1. f1198=1. f1216=1. f1231=1. f1232=1. f1242=1. f1243=1. f1252=1. f1253=1. f1258=1. f1259=1. f1284=1. f1294=1. f1295=1. f1296=1. f1298=1. f1299=1. f1308=1. f1309=1. f1333=1. f1334=1. f1342=1. f1391=1. f1392=1. f1393=1. f1394=1. f1395=1. f1396=1. f1404=1. f1405=1. f1407=1. f1408=1. f1412=1. f1427=1. f1428=1. f1429=1. f1430=1. f1431=1. f1432=1. f132=1. f136=1. f141=1. f145=1. f222=1. f224=1. f323=1. f189=1. f190=1. f210=1. f397=1. f516=1. f517=1. f553=1. f554=1. f555=1. f556=1. f576=1. f577=1. f735=1. f1224=1. f1225=1. f1304=1. f1305=1. f1318=1. f1319=1. f1403=1. f1406=1. f192=1. f193=1. f246=1. f491=1. f518=1. f519=1. f520=1. f521=1. f525=1. f526=1. f527=1. f528=1. f1144=1. f1145=1. f1220=1. f1221=1. f1285=1. f1286=1. f1289=1. f1290=1. f208=1. f209=1. f488=1. f489=1. f1313=1. f1314=1. f562=1. f563=1. f564=1. f565=1. f566=1. f567=1. f568=1. f569=1. f1247=1. f1248=1. f1249=1. f1152=1. f1153=1. f1154=1. f1155=1. 14.96/14.94 14.96/14.94 ============================== STATISTICS ============================ 14.96/14.94 14.96/14.94 Given=0. Generated=4235. Kept=4068. proofs=0. 14.96/14.94 Usable=0. Sos=0. Demods=44. Limbo=4067, Disabled=4235. Hints=0. 14.96/14.94 Kept_by_rule=0, Deleted_by_rule=0. 14.96/14.94 Forward_subsumed=167. Back_subsumed=0. 14.96/14.94 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 14.96/14.94 New_demodulators=44 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 14.96/14.94 Demod_attempts=181539. Demod_rewrites=178. 14.96/14.94 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 14.96/14.94 Nonunit_fsub_feature_tests=4282. Nonunit_bsub_feature_tests=0. 14.96/14.94 Megabytes=419.43. 14.96/14.94 User_CPU=9.66, System_CPU=0.11, Wall_clock=10. 14.96/14.94 14.96/14.94 Megs malloced by palloc(): 400. 14.96/14.94 type (bytes each) gets frees in use bytes 14.96/14.94 chunk ( 104) 277232 277232 0 0.0 K 14.96/14.94 string_buf ( 8) 242205 242205 0 0.0 K 14.96/14.94 token ( 20) 681161 681161 0 0.0 K 14.96/14.94 pterm ( 16) 401044 401044 0 0.0 K 14.96/14.94 hashtab ( 8) 4378 4378 0 0.0 K 14.96/14.94 hashnode ( 8) 42323 42323 0 0.0 K 14.96/14.94 term ( 20) 3888989 3243976 645013 12597.9 K 14.96/14.94 term arg arrays: 3101.8 K 14.96/14.94 attribute ( 12) 42248 318 41930 491.4 K 14.96/14.94 ilist ( 8) 82682537 82668682 13855 108.2 K 14.96/14.94 plist ( 8) 153704 90847 62857 491.1 K 14.96/14.94 i2list ( 12) 538223 538223 0 0.0 K 14.96/14.94 just ( 12) 23536 4062 19474 228.2 K 14.96/14.94 parajust ( 16) 0 0 0 0.0 K 14.96/14.94 instancejust ( 8) 0 0 0 0.0 K 14.96/14.94 ivyjust ( 24) 0 0 0 0.0 K 14.96/14.94 formula ( 28) 441399 326213 115186 3149.6 K 14.96/14.94 formula arg arrays: 415.7 K 14.96/14.94 topform ( 52) 19283 167 19116 970.7 K 14.96/14.94 clist_pos ( 20) 19016 4235 14781 288.7 K 14.96/14.94 clist ( 16) 8 0 8 0.1 K 14.96/14.94 context ( 808) 108823 108823 0 0.0 K 14.96/14.94 trail ( 12) 1008001 1008001 0 0.0 K 14.96/14.94 ac_match_pos (70044) 0 0 0 0.0 K 14.96/14.94 ac_match_free_vars_pos (20020) 14.96/14.94 0 0 0 0.0 K 14.96/14.94 btm_state ( 60) 0 0 0 0.0 K 14.96/14.94 btu_state ( 60) 0 0 0 0.0 K 14.96/14.94 ac_position (285432) 0 0 0 0.0 K 14.96/14.94 fpa_trie ( 20) 21663 0 21663 423.1 K 14.96/14.94 fpa_state ( 28) 0 0 0 0.0 K 14.96/14.94 fpa_index ( 12) 10 0 10 0.1 K 14.96/14.94 fpa_chunk ( 20) 19303 5796 13507 263.8 K 14.96/14.94 fpa_list ( 16) 9424 0 9424 147.2 K 14.96/14.94 fpa_list chunks: 502.1 K 14.96/14.94 discrim ( 12) 785 0 785 9.2 K 14.96/14.94 discrim_pos ( 16) 178 178 0 0.0 K 14.96/14.94 flat2 ( 32) 264283 264283 0 0.0 K 14.96/14.94 flat ( 48) 0 0 0 0.0 K 14.96/14.94 flatterm ( 32) 372002 372002 0 0.0 K 14.96/14.94 mindex ( 28) 13 0 13 0.4 K 14.96/14.94 mindex_pos ( 56) 94538 94538 0 0.0 K 14.96/14.94 lindex ( 12) 5 0 5 0.1 K 14.96/14.94 clash ( 40) 0 0 0 0.0 K 14.96/14.94 di_tree ( 12) 32866923 0 32866923 385159.3 K 14.96/14.94 avl_node ( 20) 0 0 0 0.0 K 14.96/14.94 14.96/14.94 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 14.96/14.94 List 1, length 26, 0.1 K 14.96/14.94 List 4, length 4, 0.1 K 14.96/14.94 List 5, length 1, 0.0 K 14.96/14.94 List 7, length 4, 0.1 K 14.96/14.94 List 8, length 50, 1.6 K 14.96/14.94 List 9, length 1, 0.0 K 14.96/14.94 List 12, length 75, 3.5 K 14.96/14.94 List 14, length 8, 0.4 K 14.96/14.94 List 16, length 2, 0.1 K 14.96/14.94 List 17, length 40, 2.7 K 14.96/14.94 List 18, length 7, 0.5 K 14.96/14.94 List 19, length 11, 0.8 K 14.96/14.94 List 20, length 24, 1.9 K 14.96/14.94 List 21, length 2, 0.2 K 14.96/14.94 List 22, length 2, 0.2 K 14.96/14.94 List 23, length 1, 0.1 K 14.96/14.94 List 24, length 2, 0.2 K 14.96/14.94 List 26, length 669, 67.9 K 14.96/14.94 List 27, length 2, 0.2 K 14.96/14.94 List 28, length 2, 0.2 K 14.96/14.94 List 32, length 5, 0.6 K 14.96/14.94 List 35, length 2, 0.3 K 14.96/14.94 List 40, length 2, 0.3 K 14.96/14.94 List 48, length 2, 0.4 K 14.96/14.94 List 50, length 2, 0.4 K 14.96/14.94 List 54, length 2, 0.4 K 14.96/14.94 List 63, length 2, 0.5 K 14.96/14.94 List 64, length 2, 0.5 K 14.96/14.94 List 72, length 2, 0.6 K 14.96/14.94 List 80, length 2, 0.6 K 14.96/14.94 List 81, length 2, 0.6 K 14.96/14.94 List 84, length 2, 0.7 K 14.96/14.94 List 86, length 2, 0.7 K 14.96/14.94 List 96, length 2, 0.8 K 14.96/14.94 List 120, length 2, 0.9 K 14.96/14.94 List 144, length 2, 1.1 K 14.96/14.94 List 160, length 2, 1.2 K 14.96/14.94 List 162, length 2, 1.3 K 14.96/14.94 List 166, length 2, 1.3 K 14.96/14.94 List 189, length 2, 1.5 K 14.96/14.94 List 192, length 2, 1.5 K 14.96/14.94 List 194, length 2, 1.5 K 14.96/14.94 List 202, length 2, 1.6 K 14.96/14.94 List 320, length 2, 2.5 K 14.96/14.94 14.96/14.94 ============================== SELECTOR REPORT ======================= 14.96/14.94 Sos_deleted=0, Sos_displaced=0, Sos_size=0 14.96/14.94 SELECTOR PART PRIORITY ORDER SIZE SELECTED 14.96/14.94 I 2147483647 high age 0 0 14.96/14.94 H 1 high weight 0 0 14.96/14.94 A 1 low age 0 0 14.96/14.94 F 4 low weight 0 0 14.96/14.94 T 4 low weight 0 0 14.96/14.94 ============================== end of selector report ================ 14.96/14.94 14.96/14.94 ============================== end of statistics ===================== 14.96/14.94 14.96/14.94 Exiting with failure. 14.96/14.94 14.96/14.94 Process 25270 exit (max_megs) Tue Jul 13 15:29:33 2021 14.96/14.94 Prover9 interrupted 14.96/14.95 EOF