0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n029.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % DateTime : Tue Jul 13 15:38:55 EDT 2021 0.13/0.34 % CPUTime : 5.29/5.35 ============================== Prover9 =============================== 5.29/5.35 Prover9 (32) version 2009-11A, November 2009. 5.29/5.35 Process 23811 was started by sandbox2 on n029.cluster.edu, 5.29/5.35 Tue Jul 13 15:39:00 2021 5.29/5.35 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_23658_n029.cluster.edu". 5.29/5.35 ============================== end of head =========================== 5.29/5.35 5.29/5.35 ============================== INPUT ================================= 5.29/5.35 5.29/5.35 % Reading from file /tmp/Prover9_23658_n029.cluster.edu 5.29/5.35 5.29/5.35 set(prolog_style_variables). 5.29/5.35 set(auto2). 5.29/5.35 % set(auto2) -> set(auto). 5.29/5.35 % set(auto) -> set(auto_inference). 5.29/5.35 % set(auto) -> set(auto_setup). 5.29/5.35 % set(auto_setup) -> set(predicate_elim). 5.29/5.35 % set(auto_setup) -> assign(eq_defs, unfold). 5.29/5.35 % set(auto) -> set(auto_limits). 5.29/5.35 % set(auto_limits) -> assign(max_weight, "100.000"). 5.29/5.35 % set(auto_limits) -> assign(sos_limit, 20000). 5.29/5.35 % set(auto) -> set(auto_denials). 5.29/5.35 % set(auto) -> set(auto_process). 5.29/5.35 % set(auto2) -> assign(new_constants, 1). 5.29/5.35 % set(auto2) -> assign(fold_denial_max, 3). 5.29/5.35 % set(auto2) -> assign(max_weight, "200.000"). 5.29/5.35 % set(auto2) -> assign(max_hours, 1). 5.29/5.35 % assign(max_hours, 1) -> assign(max_seconds, 3600). 5.29/5.35 % set(auto2) -> assign(max_seconds, 0). 5.29/5.35 % set(auto2) -> assign(max_minutes, 5). 5.29/5.35 % assign(max_minutes, 5) -> assign(max_seconds, 300). 5.29/5.35 % set(auto2) -> set(sort_initial_sos). 5.29/5.35 % set(auto2) -> assign(sos_limit, -1). 5.29/5.35 % set(auto2) -> assign(lrs_ticks, 3000). 5.29/5.35 % set(auto2) -> assign(max_megs, 400). 5.29/5.35 % set(auto2) -> assign(stats, some). 5.29/5.35 % set(auto2) -> clear(echo_input). 5.29/5.35 % set(auto2) -> set(quiet). 5.29/5.35 % set(auto2) -> clear(print_initial_clauses). 5.29/5.35 % set(auto2) -> clear(print_given). 5.29/5.35 assign(lrs_ticks,-1). 5.29/5.35 assign(sos_limit,10000). 5.29/5.35 assign(order,kbo). 5.29/5.35 set(lex_order_vars). 5.29/5.35 clear(print_given). 5.29/5.35 5.29/5.35 % formulas(sos). % not echoed (3294 formulas) 5.29/5.35 5.29/5.35 ============================== end of input ========================== 5.29/5.35 5.29/5.35 % From the command line: assign(max_seconds, 1200). 5.29/5.35 5.29/5.35 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 5.29/5.35 5.29/5.35 % Formulas that are not ordinary clauses: 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 4 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 6 (all A all Y all X (mem(X,A) -> ap(k(A,Y),X) = Y)) # label(kbeta) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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 <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 33 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 41 (all A_27a all V0p f43(A_27a,V0p) = ap(f44(A_27a),V0p)) # label(lameq_f44) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 48 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(A_27a),V0x))))))) # label(conj_thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 49 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V3x ap(f53(A_27b,A_27a,V1N),V3x) = ap(V1N,V3x)))) # label(lameq_f53) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 50 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x ((p(ap(V0P,V2x)) | p(ap(V1Q,V2x))) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x)))) | (exists V4x (mem(V4x,A_27a) & p(ap(V1Q,V4x))))))))))) # label(conj_thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 51 (all V0bool (mem(V0bool,arr(bool,arr(bool,bool))) -> ($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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 77 (all V4b ap(f65,V4b) = ap(c_2Ebool_2E_7E,V4b)) # label(lameq_f65) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 80 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 81 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 82 (all A_27a (ne(A_27a) -> k(A_27a,c_2Ebool_2ET) = c_2Ebool_2EDATATYPE(A_27a))) # label(ax_thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 83 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V2z) -> p(V3w)) & (p(V0y) -> p(V1x)) -> ((p(V1x) -> p(V2z)) -> (p(V0y) -> p(V3w)))))))))))) # label(conj_thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 84 (all V1t2 (mem(V1t2,bool) -> (all V0t1 (mem(V0t1,bool) -> (all V2t ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t)))))) # label(lameq_f3) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 85 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> V3y = V2x)))) & p(V0t) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),k(A_27a,V0t)))))))) # label(conj_thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 86 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_21(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 87 (all V0t1 f7(V0t1) = ap(f8,V0t1)) # label(lameq_f8) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 88 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t) & p(V0t)) & ($F & p(V0t) <-> $F) & ($F <-> p(V0t) & $F))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 89 i(bool) = i(bool) <-> $T # label(ax_thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 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]. 5.29/5.35 100 (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]. 5.29/5.35 101 (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]. 5.29/5.35 102 (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]. 5.29/5.35 103 (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]. 5.29/5.35 104 (all A_27a all V0t ap(f18(A_27a),V0t) = f17(A_27a,V0t)) # label(lameq_f18) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 105 (all A_27a all V0p f38(A_27a,V0p) = ap(f39(A_27a),V0p)) # label(lameq_f39) # label(axiom) # label(non_clause). [assumption]. 5.29/5.35 106 (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]. 5.29/5.35 107 (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]. 5.29/5.35 108 (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]. 5.29/5.35 109 (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]. 5.29/5.35 110 (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]. 5.29/5.35 111 (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]. 5.29/5.35 112 (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]. 5.29/5.35 113 (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]. 5.29/5.36 114 (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]. 5.29/5.36 115 (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]. 5.29/5.36 116 (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]. 5.29/5.36 117 (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]. 5.29/5.36 118 (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]. 5.29/5.36 119 (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]. 5.29/5.36 120 (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]. 5.29/5.36 121 (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]. 5.29/5.36 122 (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]. 5.29/5.36 123 (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]. 5.29/5.36 124 (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]. 5.29/5.36 125 (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]. 5.29/5.36 126 (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]. 5.29/5.36 127 (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]. 5.29/5.36 128 (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]. 5.29/5.36 129 (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]. 5.29/5.36 130 (all V0t (mem(V0t,bool) -> (-p(V0t) -> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 131 (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]. 5.29/5.36 132 (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]. 5.29/5.36 133 (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]. 5.29/5.36 134 (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]. 5.29/5.36 135 (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]. 5.29/5.36 136 (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]. 5.29/5.36 137 (all V0t (mem(V0t,bool) -> -(p(V0t) & -p(V0t)))) # label(conj_thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 138 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 139 (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]. 5.29/5.36 140 (all V0t (mem(V0t,bool) -> p(V0t))) <-> $F # label(ax_thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 141 (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]. 5.29/5.36 142 (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]. 5.29/5.36 143 (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]. 5.29/5.36 144 (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]. 5.29/5.36 145 (all A0 (ne(A0) -> ne(ty_2Ebool_2Eitself(A0)))) # label(ne_ty_2Ebool_2Eitself) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 146 (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]. 5.29/5.36 147 (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]. 5.29/5.36 148 (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]. 5.29/5.36 149 (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]. 5.29/5.36 150 (all A_27a all V0p f45(A_27a,V0p) = ap(f46(A_27a),V0p)) # label(lameq_f46) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 151 (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]. 5.29/5.36 152 (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]. 5.29/5.36 153 (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]. 5.29/5.36 154 (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]. 5.29/5.36 155 (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]. 5.29/5.36 156 (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]. 5.29/5.36 157 (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]. 5.29/5.36 158 (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]. 5.29/5.36 159 (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]. 5.29/5.36 160 (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]. 5.29/5.36 161 (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]. 5.29/5.36 162 (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]. 5.29/5.36 163 (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]. 5.29/5.36 164 (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]. 5.29/5.36 165 (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]. 5.29/5.36 166 (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]. 5.29/5.36 167 (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]. 5.29/5.36 168 (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]. 5.29/5.36 169 (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]. 5.29/5.36 170 (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]. 5.29/5.36 171 (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]. 5.29/5.36 172 (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]. 5.29/5.36 173 (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]. 5.29/5.36 174 (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]. 5.29/5.36 175 (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]. 5.29/5.36 176 (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]. 5.29/5.36 177 (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]. 5.29/5.36 178 (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]. 5.29/5.36 179 (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]. 5.29/5.36 180 (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]. 5.29/5.36 181 (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]. 5.29/5.36 182 (all V0v (mem(V0v,bool) -> ($T <-> p(ap(c_2Ebool_2EBOUNDED,V0v))))) # label(conj_thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 183 (all A_27a (ne(A_27a) -> f33(A_27a) = c_2Ebool_2EIN(A_27a))) # label(ax_thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2Eliteral__case) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 185 (all A_27a all V0P ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P)))) # label(lameq_f12) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 186 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((exists X (mem(X,A) & p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_3F(A),Q))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 187 -($F <-> $T) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 188 -($T <-> $F) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 189 (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]. 5.29/5.36 190 (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]. 5.29/5.36 191 (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]. 5.29/5.36 192 (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]. 5.29/5.36 193 (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]. 5.29/5.36 194 (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]. 5.29/5.36 195 (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]. 5.29/5.36 196 (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]. 5.29/5.36 197 (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]. 5.29/5.36 198 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 199 $T <-> -$F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 200 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 201 (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]. 5.29/5.36 202 (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]. 5.29/5.36 203 (all V0t1 ap(f5,V0t1) = f4(V0t1)) # label(lameq_f5) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 204 (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]. 5.29/5.36 205 (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]. 5.29/5.36 206 (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]. 5.29/5.36 207 (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]. 5.29/5.36 208 (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]. 5.29/5.36 209 (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]. 5.29/5.36 210 (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]. 5.29/5.36 211 (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]. 5.29/5.36 212 (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]. 5.29/5.36 213 (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]. 5.29/5.36 214 (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]. 5.29/5.36 215 (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]. 5.29/5.36 216 (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]. 5.29/5.36 217 (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]. 5.29/5.36 218 (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]. 5.29/5.36 219 (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]. 5.29/5.36 220 (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]. 5.29/5.36 221 (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]. 5.29/5.36 222 (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]. 5.29/5.36 223 (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]. 5.29/5.36 224 (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]. 5.29/5.36 225 (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]. 5.29/5.36 226 (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]. 5.29/5.36 227 (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]. 5.29/5.36 228 (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]. 5.29/5.36 229 (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]. 5.29/5.36 230 (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]. 5.29/5.36 231 (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]. 5.29/5.36 232 (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]. 5.29/5.36 233 (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]. 5.29/5.36 234 (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]. 5.29/5.36 235 (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]. 5.29/5.36 236 (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]. 5.29/5.36 237 (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]. 5.29/5.36 238 (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]. 5.29/5.36 239 (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]. 5.29/5.36 240 (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]. 5.29/5.36 241 (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]. 5.29/5.36 242 (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]. 5.29/5.36 243 (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]. 5.29/5.36 244 (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]. 5.29/5.36 245 (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]. 5.29/5.36 246 (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]. 5.29/5.36 247 (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]. 5.29/5.36 248 (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]. 5.29/5.36 249 (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]. 5.29/5.36 250 (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]. 5.29/5.36 251 (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]. 5.29/5.36 252 (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]. 5.29/5.36 253 (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]. 5.29/5.36 254 (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]. 5.29/5.36 255 (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]. 5.29/5.36 256 (all A_27a all V0p f35(A_27a,V0p) = ap(f36(A_27a),V0p)) # label(lameq_f36) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 257 (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]. 5.29/5.36 258 (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]. 5.29/5.36 259 (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]. 5.29/5.36 260 (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]. 5.29/5.36 261 (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]. 5.29/5.36 262 (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]. 5.29/5.36 263 (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]. 5.29/5.36 264 (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]. 5.29/5.36 265 (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]. 5.29/5.36 266 (all A_27a all V0x f32(A_27a,V0x) = ap(f33(A_27a),V0x)) # label(lameq_f33) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 267 (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]. 5.29/5.36 268 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $T) | ($F <-> p(V0t)))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 269 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 270 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 271 (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]. 5.29/5.36 272 (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]. 5.29/5.36 273 (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]. 5.29/5.36 274 (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]. 5.29/5.36 275 (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]. 5.29/5.36 276 (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]. 5.29/5.36 277 (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]. 5.29/5.36 278 (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]. 5.29/5.36 279 (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]. 5.29/5.36 280 (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]. 5.29/5.36 281 (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]. 5.29/5.36 282 (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]. 5.29/5.36 283 (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]. 5.29/5.36 284 (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]. 5.29/5.36 285 (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]. 5.29/5.36 286 (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]. 5.29/5.36 287 (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]. 5.29/5.36 288 (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]. 5.29/5.36 289 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 290 (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]. 5.29/5.36 291 (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]. 5.29/5.36 292 (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]. 5.29/5.36 293 (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]. 5.29/5.36 294 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 295 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 296 (all V0t (mem(V0t,bool) -> (p(V0t) -> $T))) # label(conj_thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 297 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2ET)) <-> (p(V0c) -> p(V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 298 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V2y) -> (p(V0x) -> p(V1x_27))) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> (p(V0x) & p(V2y) -> p(V3y_27) & p(V1x_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 299 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V3y_27) -> p(V2y))) & (p(V2y) -> (p(V1x_27) -> p(V0x))) -> (p(V3y_27) & p(V1x_27) -> p(V2y) & p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 300 (all V0t (mem(V0t,bool) -> ($F & p(V0t) <-> $F))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 301 -$F <-> $T # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 302 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> p(V0x)) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 5.29/5.36 303 (all V0t (mem(V0t,bool) -> ($F <-> $F & p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 304 (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]. 5.29/5.37 305 (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]. 5.29/5.37 306 (all V0t (mem(V0t,bool) -> (p(V0t) & p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 307 (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]. 5.29/5.37 308 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 309 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 310 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 311 -$T <-> $F # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 312 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> V1t = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 313 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> $T)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 314 (all V0t (mem(V0t,bool) -> (-p(V0t) <-> -p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 315 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 316 (all V0t (mem(V0t,bool) -> (p(V0t) | p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 317 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2EF),V1x)) <-> p(V1x) & -p(V0c)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 318 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 319 (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]. 5.29/5.37 320 (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]. 5.29/5.37 321 (all V0t (mem(V0t,bool) -> ($T <-> ($F -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 322 (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]. 5.29/5.37 323 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 324 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 325 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 326 (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]. 5.29/5.37 327 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 328 (all V0A (mem(V0A,bool) -> (--p(V0A) <-> p(V0A)))) # label(conj_thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 329 (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]. 5.29/5.37 330 (all V0A (mem(V0A,bool) -> (-p(V0A) & p(V0A) <-> $F))) # label(conj_thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 331 (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]. 5.29/5.37 332 (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]. 5.29/5.37 333 (all V0b (mem(V0b,bool) -> (p(V0b) -> (p(V0b) <-> $T)))) # label(conj_thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 334 (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]. 5.29/5.37 335 (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]. 5.29/5.37 336 (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]. 5.29/5.37 337 (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]. 5.29/5.37 338 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 339 (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]. 5.29/5.37 340 (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]. 5.29/5.37 341 (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]. 5.29/5.37 342 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 343 (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]. 5.29/5.37 344 (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]. 5.29/5.37 345 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 346 (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]. 5.29/5.37 347 (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]. 5.29/5.37 348 (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]. 5.29/5.37 349 (all V0b (mem(V0b,bool) -> (-p(V0b) -> (p(V0b) <-> $F)))) # label(conj_thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 350 (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]. 5.29/5.37 351 (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]. 5.29/5.37 352 (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]. 5.29/5.37 353 (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]. 5.29/5.37 354 (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]. 5.29/5.37 355 (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]. 5.29/5.37 356 (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]. 5.29/5.37 357 (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]. 5.29/5.37 358 (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]. 5.29/5.37 359 (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]. 5.29/5.37 360 (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]. 5.29/5.37 361 (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]. 5.29/5.37 362 p(c_2Emarker_2EIfCases) <-> $T # label(ax_thm_2Emarker_2EIfCases__def) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 363 (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]. 5.29/5.37 364 (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]. 5.29/5.37 365 (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]. 5.29/5.37 366 (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]. 5.29/5.37 367 (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]. 5.29/5.37 368 (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]. 5.29/5.37 369 (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]. 5.29/5.37 370 (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]. 5.29/5.37 371 (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]. 5.29/5.37 372 (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]. 5.29/5.37 373 (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]. 5.29/5.37 374 (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]. 5.29/5.37 375 (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]. 5.29/5.37 376 (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]. 5.29/5.37 377 (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]. 5.29/5.37 378 (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]. 5.29/5.37 379 (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]. 5.29/5.37 380 (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]. 5.29/5.37 381 (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]. 5.29/5.37 382 (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]. 5.29/5.37 383 (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]. 5.29/5.37 384 (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]. 5.29/5.37 385 (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]. 5.29/5.37 386 (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]. 5.29/5.37 387 (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]. 5.29/5.37 388 (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]. 5.29/5.37 389 (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]. 5.29/5.37 390 (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]. 5.29/5.37 391 (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]. 5.29/5.37 392 (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]. 5.29/5.37 393 (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]. 5.29/5.37 394 (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]. 5.29/5.37 395 (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]. 5.29/5.37 396 (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]. 5.29/5.37 397 (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]. 5.29/5.37 398 (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]. 5.29/5.37 399 (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]. 5.29/5.37 400 (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]. 5.29/5.37 401 (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]. 5.29/5.37 402 (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]. 5.29/5.37 403 (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]. 5.29/5.37 404 (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]. 5.29/5.37 405 (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]. 5.29/5.37 406 (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]. 5.29/5.37 407 (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]. 5.29/5.37 408 (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]. 5.29/5.37 409 (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]. 5.29/5.37 410 (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]. 5.29/5.37 411 (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]. 5.29/5.37 412 (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]. 5.29/5.37 413 (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]. 5.29/5.37 414 (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]. 5.29/5.37 415 (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]. 5.29/5.37 416 (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]. 5.29/5.37 417 (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]. 5.29/5.37 418 (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]. 5.29/5.37 419 (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]. 5.29/5.37 420 (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]. 5.29/5.37 421 (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]. 5.29/5.37 422 (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]. 5.29/5.37 423 (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]. 5.29/5.37 424 (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]. 5.29/5.37 425 (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]. 5.29/5.37 426 (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]. 5.32/5.37 427 (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]. 5.32/5.37 428 (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]. 5.32/5.37 429 (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]. 5.32/5.37 430 (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]. 5.32/5.37 431 (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]. 5.32/5.37 432 (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]. 5.32/5.37 433 (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]. 5.32/5.37 434 (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]. 5.32/5.37 435 (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]. 5.32/5.37 436 (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]. 5.32/5.37 437 (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]. 5.32/5.37 438 (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]. 5.32/5.37 439 (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]. 5.32/5.37 440 (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]. 5.32/5.37 441 (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]. 5.32/5.37 442 (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]. 5.32/5.37 443 (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]. 5.32/5.37 444 (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]. 5.32/5.37 445 (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]. 5.32/5.37 446 (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]. 5.32/5.37 447 (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]. 5.32/5.37 448 (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]. 5.32/5.37 449 (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]. 5.32/5.37 450 (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]. 5.32/5.37 451 (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]. 5.32/5.37 452 (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]. 5.32/5.37 453 (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]. 5.32/5.37 454 (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]. 5.32/5.37 455 (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]. 5.32/5.37 456 (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]. 5.32/5.37 457 (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]. 5.32/5.37 458 (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]. 5.32/5.37 459 (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]. 5.32/5.37 460 (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]. 5.32/5.37 461 (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]. 5.32/5.37 462 (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]. 5.32/5.37 463 (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]. 5.32/5.37 464 (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]. 5.32/5.37 465 (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]. 5.32/5.37 466 (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]. 5.32/5.37 467 (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]. 5.32/5.37 468 (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]. 5.32/5.37 469 (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]. 5.32/5.37 470 (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]. 5.32/5.37 471 (all V0v (mem(V0v,ty_2Eone_2Eone) -> c_2Eone_2Eone = V0v)) # label(conj_thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 5.32/5.37 472 (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]. 5.32/5.37 473 (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]. 5.32/5.37 474 (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]. 5.32/5.37 475 (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]. 5.32/5.37 476 (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]. 5.32/5.37 477 (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]. 5.32/5.37 478 (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]. 5.32/5.37 479 (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]. 5.32/5.37 480 (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]. 5.32/5.37 481 (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]. 5.32/5.37 482 (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]. 5.32/5.37 483 (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]. 5.32/5.37 484 (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]. 5.32/5.37 485 (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]. 5.32/5.37 486 (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]. 5.32/5.37 487 (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]. 5.32/5.37 488 (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]. 5.32/5.37 489 (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]. 5.32/5.37 490 (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]. 5.32/5.37 491 (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]. 5.32/5.37 492 (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]. 5.32/5.38 493 (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]. 5.32/5.38 494 (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]. 5.32/5.38 495 (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]. 5.32/5.38 496 (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]. 5.32/5.38 497 (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]. 5.32/5.38 498 (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]. 5.32/5.38 499 (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]. 5.32/5.38 500 (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]. 5.32/5.38 501 (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]. 5.32/5.38 502 (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]. 5.32/5.38 503 (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]. 5.32/5.38 504 (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]. 5.32/5.38 505 (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]. 5.32/5.38 506 (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]. 5.32/5.38 507 (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]. 5.32/5.38 508 (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]. 5.32/5.38 509 (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]. 5.32/5.38 510 (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]. 5.32/5.38 511 (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]. 5.32/5.38 512 (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]. 5.32/5.38 513 (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]. 5.32/5.38 514 (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]. 5.32/5.38 515 (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]. 5.32/5.38 516 (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]. 5.32/5.38 517 (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]. 5.32/5.38 518 (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]. 5.32/5.38 519 (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]. 5.32/5.38 520 (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]. 5.32/5.38 521 (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]. 5.32/5.38 522 (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]. 5.32/5.38 523 (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]. 5.32/5.38 524 (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]. 5.32/5.38 525 (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]. 5.32/5.38 526 (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]. 5.32/5.38 527 (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]. 5.32/5.38 528 (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]. 5.32/5.38 529 (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]. 5.32/5.38 530 (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]. 5.32/5.38 531 (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]. 5.32/5.38 532 (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]. 5.32/5.38 533 (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]. 5.32/5.38 534 (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]. 5.32/5.38 535 (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]. 5.32/5.38 536 (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]. 5.32/5.38 537 (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]. 5.32/5.38 538 (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]. 5.32/5.38 539 (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]. 5.32/5.38 540 (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]. 5.32/5.38 541 (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]. 5.32/5.38 542 (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]. 5.32/5.38 543 (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]. 5.32/5.38 544 (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]. 5.32/5.38 545 (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]. 5.32/5.38 546 (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]. 5.32/5.38 547 (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]. 5.32/5.38 548 (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]. 5.32/5.38 549 (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]. 5.32/5.38 550 (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]. 5.32/5.38 551 (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]. 5.32/5.38 552 (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]. 5.32/5.38 553 (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]. 5.32/5.38 554 (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]. 5.32/5.38 555 (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]. 5.32/5.38 556 (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]. 5.32/5.38 557 (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]. 5.32/5.38 558 (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]. 5.32/5.38 559 (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]. 5.32/5.38 560 (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]. 5.32/5.38 561 (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]. 5.32/5.38 562 (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]. 5.32/5.38 563 (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]. 5.32/5.38 564 (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]. 5.32/5.38 565 (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]. 5.32/5.38 566 (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]. 5.32/5.38 567 (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]. 5.32/5.38 568 (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]. 5.32/5.38 569 (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]. 5.32/5.38 570 (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]. 5.32/5.38 571 (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]. 5.32/5.38 572 (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]. 5.32/5.38 573 (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]. 5.32/5.38 574 (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]. 5.32/5.38 575 (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]. 5.32/5.38 576 (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]. 5.32/5.38 577 (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]. 5.32/5.38 578 (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]. 5.32/5.38 579 (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]. 5.32/5.38 580 (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]. 5.32/5.38 581 (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]. 5.32/5.38 582 (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]. 5.32/5.38 583 (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]. 5.32/5.38 584 (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]. 5.32/5.38 585 (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]. 5.32/5.38 586 (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]. 5.32/5.38 587 (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]. 5.32/5.38 588 (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]. 5.32/5.38 589 (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]. 5.32/5.38 590 (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]. 5.32/5.38 591 (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]. 5.32/5.38 592 (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]. 5.32/5.38 593 (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]. 5.32/5.38 594 (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]. 5.32/5.38 595 (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]. 5.32/5.38 596 (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]. 5.32/5.38 597 (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]. 5.32/5.38 598 (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]. 5.32/5.38 599 (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]. 5.32/5.38 600 (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]. 5.32/5.38 601 (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]. 5.32/5.38 602 (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]. 5.32/5.38 603 (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]. 5.32/5.38 604 (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]. 5.32/5.38 605 (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]. 5.32/5.38 606 (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]. 5.32/5.38 607 (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]. 5.32/5.38 608 (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]. 5.32/5.38 609 (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]. 5.32/5.38 610 (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]. 5.32/5.38 611 (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]. 5.32/5.38 612 (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]. 5.32/5.38 613 (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]. 5.32/5.38 614 (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]. 5.32/5.38 615 (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]. 5.32/5.38 616 (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]. 5.32/5.38 617 (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]. 5.32/5.38 618 (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]. 5.32/5.38 619 (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]. 5.32/5.40 620 (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]. 5.32/5.40 621 (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]. 5.32/5.40 622 (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]. 5.32/5.40 623 (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]. 5.32/5.40 624 (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]. 5.32/5.40 625 (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]. 5.32/5.40 626 (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]. 5.32/5.40 627 (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]. 5.32/5.40 628 (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]. 5.32/5.40 629 (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]. 5.32/5.40 630 (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]. 5.32/5.40 631 (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]. 5.32/5.40 632 (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]. 5.32/5.40 633 (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]. 5.32/5.40 634 (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]. 5.32/5.40 635 (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]. 5.32/5.40 636 (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]. 5.32/5.40 637 (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]. 5.32/5.40 638 (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]. 5.32/5.40 639 (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]. 5.32/5.40 640 (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]. 5.32/5.40 641 (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]. 5.32/5.40 642 (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]. 5.32/5.40 643 (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]. 5.32/5.40 644 (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]. 5.32/5.40 645 (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]. 5.32/5.40 646 (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]. 5.32/5.40 647 (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]. 5.32/5.40 648 (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]. 5.32/5.40 649 (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]. 5.32/5.40 650 (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]. 5.32/5.40 651 (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]. 5.32/5.40 652 (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]. 5.32/5.40 653 (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]. 5.32/5.40 654 (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]. 5.32/5.40 655 (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]. 5.32/5.40 656 (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]. 5.32/5.40 657 (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]. 5.32/5.40 658 (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]. 5.32/5.40 659 (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]. 5.32/5.40 660 (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]. 5.32/5.40 661 (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]. 5.32/5.40 662 (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]. 5.32/5.40 663 (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]. 5.32/5.40 664 (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]. 5.32/5.40 665 (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]. 5.32/5.40 666 (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]. 5.32/5.40 667 (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]. 5.32/5.40 668 (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]. 5.32/5.40 669 (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]. 5.32/5.40 670 (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]. 5.32/5.40 671 (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]. 5.32/5.40 672 (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]. 5.32/5.40 673 (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]. 5.32/5.40 674 (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]. 5.32/5.40 675 (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]. 5.32/5.40 676 (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]. 5.32/5.40 677 (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]. 5.32/5.40 678 (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]. 5.32/5.40 679 (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]. 5.32/5.40 680 (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]. 5.32/5.40 681 (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]. 5.32/5.40 682 (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]. 5.32/5.40 683 (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]. 5.32/5.40 684 (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]. 5.32/5.40 685 (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]. 5.32/5.40 686 (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]. 5.32/5.40 687 (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]. 5.32/5.40 688 (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]. 5.32/5.40 689 (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]. 5.32/5.40 690 (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]. 5.32/5.40 691 (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]. 5.32/5.40 692 (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]. 5.32/5.40 693 (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]. 5.32/5.40 694 (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]. 5.32/5.40 695 (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]. 5.32/5.40 696 (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]. 5.32/5.40 697 (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]. 5.32/5.40 698 (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]. 5.32/5.40 699 (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]. 5.32/5.40 700 (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]. 5.32/5.40 701 (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]. 5.32/5.40 702 (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]. 5.32/5.40 703 (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]. 5.32/5.40 704 (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]. 5.32/5.40 705 (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]. 5.32/5.40 706 (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]. 5.32/5.40 707 (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]. 5.32/5.40 708 (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]. 5.32/5.40 709 (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]. 5.32/5.40 710 (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]. 5.32/5.40 711 (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]. 5.32/5.40 712 (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]. 5.32/5.40 713 (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]. 5.32/5.40 714 (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]. 5.32/5.40 715 (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]. 5.32/5.40 716 (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]. 5.32/5.41 717 (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]. 5.32/5.41 718 (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]. 5.32/5.41 719 (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]. 5.32/5.41 720 (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]. 5.32/5.41 721 (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]. 5.32/5.41 722 (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]. 5.32/5.41 723 (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]. 5.32/5.41 724 (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]. 5.32/5.41 725 (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]. 5.32/5.41 726 (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]. 5.32/5.41 727 (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]. 5.32/5.41 728 (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]. 5.32/5.41 729 (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]. 5.32/5.41 730 (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]. 5.32/5.41 731 (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]. 5.32/5.41 732 (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]. 5.32/5.41 733 (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]. 5.32/5.41 734 (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]. 5.32/5.41 735 (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]. 5.32/5.41 736 (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]. 5.32/5.41 737 (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]. 5.32/5.41 738 (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]. 5.32/5.41 739 (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]. 5.32/5.41 740 (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]. 5.32/5.41 741 (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]. 5.32/5.41 742 (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]. 5.32/5.41 743 (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]. 5.32/5.41 744 (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]. 5.32/5.41 745 (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]. 5.32/5.41 746 (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]. 5.32/5.41 747 (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]. 5.32/5.41 748 (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]. 5.32/5.41 749 (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]. 5.32/5.41 750 (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]. 5.32/5.41 751 (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]. 5.32/5.41 752 (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]. 5.32/5.41 753 (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]. 5.32/5.41 754 (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]. 5.32/5.41 755 (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]. 5.32/5.41 756 (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]. 5.32/5.41 757 (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]. 5.32/5.41 758 (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]. 5.32/5.41 759 (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]. 5.32/5.41 760 (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]. 5.32/5.41 761 (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]. 5.32/5.41 762 (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]. 5.32/5.41 763 (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]. 5.32/5.41 764 (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]. 5.32/5.41 765 (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]. 5.32/5.41 766 (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]. 5.32/5.41 767 (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]. 5.32/5.41 768 (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]. 5.32/5.41 769 (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]. 5.32/5.41 770 (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]. 5.32/5.41 771 (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]. 5.32/5.41 772 (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]. 5.32/5.41 773 (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]. 5.32/5.41 774 (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]. 5.32/5.41 775 (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]. 5.32/5.41 776 (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]. 5.32/5.41 777 (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]. 5.32/5.41 778 (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]. 5.32/5.41 779 (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]. 5.32/5.41 780 (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]. 5.32/5.42 781 (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]. 5.32/5.42 782 (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]. 5.32/5.42 783 (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]. 5.32/5.42 784 (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]. 5.32/5.42 785 (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]. 5.32/5.42 786 (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]. 5.32/5.42 787 (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]. 5.32/5.42 788 (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]. 5.32/5.42 789 (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]. 5.32/5.42 790 (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]. 5.32/5.42 791 (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]. 5.32/5.42 792 (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]. 5.32/5.42 793 (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]. 5.32/5.42 794 (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]. 5.32/5.42 795 (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]. 5.32/5.42 796 (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]. 5.32/5.42 797 (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]. 5.32/5.42 798 (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]. 5.32/5.42 799 (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]. 5.32/5.42 800 (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]. 5.32/5.42 801 (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]. 5.32/5.42 802 (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]. 5.32/5.42 803 (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]. 5.32/5.42 804 (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]. 5.32/5.42 805 (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]. 5.32/5.42 806 (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]. 5.32/5.42 807 (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]. 5.32/5.42 808 (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]. 5.32/5.42 809 (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]. 5.32/5.42 810 (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]. 5.32/5.42 811 (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]. 5.32/5.42 812 (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]. 5.32/5.42 813 (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]. 5.32/5.42 814 (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]. 5.32/5.42 815 (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]. 5.32/5.42 816 (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]. 5.32/5.42 817 (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]. 5.32/5.42 818 (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]. 5.32/5.42 819 (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]. 5.32/5.42 820 (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]. 5.32/5.42 821 (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]. 5.32/5.42 822 (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]. 5.32/5.42 823 (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]. 5.32/5.42 824 (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]. 5.32/5.42 825 (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]. 5.32/5.42 826 (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]. 5.32/5.42 827 (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]. 5.32/5.42 828 (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]. 5.32/5.42 829 (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]. 5.32/5.42 830 (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]. 5.32/5.42 831 (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]. 5.32/5.42 832 (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]. 5.32/5.42 833 (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]. 5.32/5.42 834 (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]. 5.32/5.42 835 (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]. 5.32/5.42 836 (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]. 5.32/5.42 837 (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]. 5.32/5.42 838 (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]. 5.32/5.42 839 (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]. 5.32/5.42 840 (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]. 5.32/5.42 841 (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]. 5.32/5.42 842 (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]. 5.32/5.42 843 (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]. 5.32/5.42 844 (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]. 5.32/5.42 845 (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]. 5.37/5.42 846 (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]. 5.37/5.42 847 (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]. 5.37/5.42 848 (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]. 5.37/5.42 849 (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]. 5.37/5.42 850 (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]. 5.37/5.42 851 (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]. 5.37/5.42 852 (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]. 5.37/5.42 853 (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]. 5.37/5.42 854 (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]. 5.37/5.42 855 (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]. 5.37/5.42 856 (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]. 5.37/5.42 857 (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]. 5.37/5.42 858 (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]. 5.37/5.42 859 (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]. 5.37/5.42 860 (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]. 5.37/5.42 861 (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]. 5.37/5.42 862 (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]. 5.37/5.42 863 (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]. 5.37/5.42 864 (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]. 5.37/5.42 865 (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]. 5.37/5.42 866 (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]. 5.37/5.42 867 (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]. 5.37/5.42 868 (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]. 5.37/5.42 869 (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]. 5.37/5.42 870 (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]. 5.37/5.42 871 (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]. 5.37/5.42 872 (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]. 5.37/5.42 873 (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]. 5.37/5.42 874 (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]. 5.37/5.42 875 (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]. 5.37/5.42 876 (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]. 5.37/5.42 877 (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]. 5.37/5.42 878 (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]. 5.37/5.42 879 (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]. 5.37/5.42 880 (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]. 5.37/5.42 881 (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]. 5.37/5.42 882 (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]. 5.37/5.42 883 (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]. 5.37/5.42 884 (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]. 5.37/5.42 885 (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]. 5.37/5.42 886 (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]. 5.37/5.42 887 (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]. 5.37/5.42 888 (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]. 5.37/5.42 889 (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]. 5.37/5.42 890 (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]. 5.37/5.42 891 (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]. 5.37/5.42 892 (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]. 5.37/5.42 893 (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]. 5.37/5.42 894 (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]. 5.37/5.42 895 (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]. 5.37/5.42 896 (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]. 5.37/5.42 897 (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]. 5.37/5.42 898 (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]. 5.37/5.42 899 (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]. 5.37/5.42 900 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 901 (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]. 5.37/5.42 902 (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]. 5.37/5.42 903 (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]. 5.37/5.42 904 (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]. 5.37/5.42 905 (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]. 5.37/5.42 906 (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]. 5.37/5.42 907 (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]. 5.37/5.42 908 (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]. 5.37/5.43 909 (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]. 5.37/5.43 910 (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]. 5.37/5.43 911 (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]. 5.37/5.43 912 (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]. 5.37/5.43 913 (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]. 5.37/5.43 914 (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]. 5.37/5.43 915 (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]. 5.37/5.43 916 (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]. 5.37/5.43 917 (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]. 5.37/5.43 918 (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]. 5.37/5.43 919 (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]. 5.37/5.43 920 (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]. 5.37/5.43 921 (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]. 5.37/5.43 922 (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]. 5.37/5.43 923 (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]. 5.37/5.43 924 (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]. 5.37/5.43 925 (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]. 5.37/5.43 926 (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]. 5.37/5.43 927 (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]. 5.37/5.43 928 (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]. 5.37/5.43 929 (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]. 5.37/5.43 930 (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]. 5.37/5.43 931 (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]. 5.37/5.43 932 (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]. 5.37/5.43 933 (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]. 5.37/5.43 934 (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]. 5.37/5.43 935 (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]. 5.37/5.43 936 (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]. 5.37/5.43 937 (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]. 5.37/5.43 938 (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]. 5.37/5.43 939 (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]. 5.37/5.43 940 (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]. 5.37/5.43 941 (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]. 5.37/5.43 942 (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]. 5.37/5.43 943 (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]. 5.37/5.43 944 (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]. 5.37/5.43 945 (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]. 5.37/5.43 946 (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]. 5.37/5.43 947 (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]. 5.37/5.43 948 (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]. 5.37/5.43 949 (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]. 5.37/5.43 950 (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]. 5.37/5.43 951 (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]. 5.37/5.43 952 (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]. 5.37/5.43 953 (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]. 5.37/5.43 954 (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]. 5.37/5.43 955 (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]. 5.37/5.43 956 (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]. 5.37/5.43 957 (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]. 5.37/5.43 958 (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]. 5.37/5.43 959 (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]. 5.37/5.43 960 (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]. 5.37/5.43 961 (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]. 5.37/5.43 962 (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]. 5.37/5.43 963 (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]. 5.37/5.43 964 (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]. 5.37/5.43 965 (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]. 5.37/5.43 966 (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]. 5.37/5.43 967 (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]. 5.37/5.43 968 (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]. 5.37/5.43 969 (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]. 5.37/5.43 970 (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]. 5.37/5.43 971 (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]. 5.37/5.43 972 (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]. 5.37/5.43 973 (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]. 5.37/5.43 974 (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]. 5.37/5.43 975 (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]. 5.37/5.43 976 (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]. 5.37/5.43 977 (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]. 5.37/5.43 978 (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]. 5.37/5.43 979 (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]. 5.37/5.43 980 (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]. 5.37/5.43 981 (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]. 5.37/5.43 982 (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]. 5.37/5.43 983 (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]. 5.37/5.43 984 (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]. 5.37/5.43 985 (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]. 5.37/5.43 986 (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]. 5.37/5.43 987 (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]. 5.37/5.43 988 (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]. 5.37/5.43 989 (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]. 5.37/5.43 990 (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]. 5.37/5.43 991 (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]. 5.37/5.43 992 (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]. 5.37/5.43 993 (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]. 5.37/5.43 994 (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]. 5.37/5.43 995 (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]. 5.37/5.43 996 (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]. 5.37/5.43 997 (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]. 5.37/5.43 998 (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]. 5.37/5.43 999 (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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.37/5.43 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 1064 (all V2x ap(f151,V2x) = f150(V2x)) # label(lameq_f151) # label(axiom) # label(non_clause). [assumption]. 5.39/5.45 1065 (all V4x ap(f153,V4x) = f152(V4x)) # label(lameq_f153) # label(axiom) # label(non_clause). [assumption]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 1101 (all V0x ap(f159,V0x) = f158(V0x)) # label(lameq_f159) # label(axiom) # label(non_clause). [assumption]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.45 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.46 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.47 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 1330 $F <-> p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2EODD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 1370 p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) <-> $T # label(ax_thm_2Earithmetic_2EEVEN_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.48 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 1591 (all V1m ap(f173,V1m) = f172(V1m)) # label(lameq_f173) # label(axiom) # label(non_clause). [assumption]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.49 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.50 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 1830 (all A0 (ne(A0) -> ne(ty_2Eind__type_2Erecspace(A0)))) # label(ne_ty_2Eind__type_2Erecspace) # label(axiom) # label(non_clause). [assumption]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 1972 (all V2n k(ty_2Enum_2Enum,f247(V2n)) = ap(f248,V2n)) # label(lameq_f248) # label(axiom) # label(non_clause). [assumption]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.51 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.39/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 2100 (all V3x ap(f251,V3x) = k(bool,ap(c_2Ebool_2E_7E,V3x))) # label(lameq_f251) # label(axiom) # label(non_clause). [assumption]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.52 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.53 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.54 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.55 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.56 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.57 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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)) <-> $T))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.48/5.58 2920 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,ap(c_2Enum_2ESUC,V2n)),V3a),V4b)) <-> p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V2n),ap(c_2Earithmetic_2EDIV2,V3a)),ap(c_2Earithmetic_2EDIV2,V4b))) & (p(ap(c_2Earithmetic_2EODD,V4b)) <-> p(ap(c_2Earithmetic_2EODD,V3a)))))))))) # label(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 5.48/5.58 2921 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ($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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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]. 5.48/5.58 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)) -> 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]. 5.48/5.58 2941 (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_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),V0r),V2s)) -> 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]. 5.48/5.59 2942 (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]. 5.48/5.59 2943 (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]. 5.48/5.59 2944 (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_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) & 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),ap(ap(c_2Epred__set_2EUNION(A_27b),V1s),V2t)))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__range) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2945 (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(c_2Eset__relation_2Eacyclic(A_27a),V1r_27)) & p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r)) & 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),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]. 5.48/5.59 2946 (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_2Epred__set_2EGSPEC(A_27a,A_27a),f320(A_27b,A_27a,V0r)) = ap(c_2Eset__relation_2Erange(A_27a,A_27b),V0r))))))) # label(ax_thm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2947 (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),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)),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]. 5.48/5.59 2948 (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)) -> (V0s = V1t <-> (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)))))))))))))))) # label(conj_thm_2Eset__relation_2Erextension) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2949 (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(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)) = ap(f330(A_27b,A_27a,V0r,V2e),V3e_27)))))) # label(lameq_f330) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2950 (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(f317(A_27a,A_27b,V1x,V0r),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)))))) # label(lameq_f317) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2951 (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_2Eset__relation_2Efinite__prefixes(A_27a,A_27b),V0r),V1s)) & 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),V2s_27))))))))))))) # label(conj_thm_2Eset__relation_2Efinite__prefixes__subset__s) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2952 (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]. 5.48/5.59 2953 (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]. 5.48/5.59 2954 (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]. 5.48/5.59 2955 (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]. 5.48/5.59 2956 (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]. 5.48/5.59 2957 (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)),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)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & p(ap(ap(V1tc_27,V6z),V5y)))) -> 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__left) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2958 (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(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(A_27a),V1y),V3s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),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)),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V2r),V3s)))))))))))))) # label(conj_thm_2Eset__relation_2Ein__rrestrict) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2959 (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]. 5.48/5.59 2960 (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]. 5.48/5.59 2961 (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]. 5.48/5.59 2962 (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]. 5.48/5.59 2963 (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_2Etransitive(A_27a),ap(c_2Eset__relation_2Estrict(A_27a),V0r))) & p(ap(c_2Eset__relation_2Eantisym(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)) & 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))))))))) # label(conj_thm_2Eset__relation_2Estrict__partial__order) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2964 (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]. 5.48/5.59 2965 (all A_27a all V1x (mem(V1x,A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all 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)) = ap(f347(A_27a,V1x,V0s),V2y)))))) # label(lameq_f347) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2966 (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]. 5.48/5.59 2967 (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]. 5.48/5.59 2968 (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]. 5.48/5.59 2969 (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]. 5.48/5.59 2970 (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]. 5.48/5.59 2971 (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_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s_27),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]. 5.48/5.59 2972 (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_2Epred__set_2EGSPEC(A_27a,A_27a),f318(A_27b,A_27a,V0r)) = ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V0r))))))) # label(ax_thm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2973 (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]. 5.48/5.59 2974 (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]. 5.48/5.59 2975 (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]. 5.48/5.59 2976 (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(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)))))))))))) # label(conj_thm_2Eset__relation_2Ein__rel__to__reln) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2977 (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_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))) = ap(ap(c_2Eset__relation_2Ercomp(A_27a,A_27b,A_27c),V0r1),V1r2))))))))))) # label(ax_thm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2978 (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]. 5.48/5.59 2979 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x ap(f350(A_27a,V1s),V2x) = f349(A_27a,V1s,V2x)))) # label(lameq_f350) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2980 (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]. 5.48/5.59 2981 (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)) -> ((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))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Eset__relation_2Edomain(A_27a,A_27b),V1r)))))))))))) # label(conj_thm_2Eset__relation_2Ein__domain) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2982 (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]. 5.48/5.59 2983 (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]. 5.48/5.59 2984 (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]. 5.48/5.59 2985 (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 f321(A_27a,V1s,V0r,V2x) = ap(f322(A_27a,V1s,V0r),V2x)))))) # label(lameq_f322) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2986 (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]. 5.48/5.59 2987 (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),V0r1),V2s1)) & 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),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]. 5.48/5.59 2988 (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_2Erelation_2ERUNION(A_27a,A_27a),V0R),f350(A_27a,V1s)) = ap(ap(c_2Eset__relation_2ERREFL__EXP(A_27a),V0R),V1s))))))) # label(ax_thm_2Eset__relation_2ERREFL__EXP__def) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2989 (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]. 5.48/5.59 2990 (all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)) -> (all V1a0 ap(f342(A_27a,V0r),V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool)),f341(A_27a,V0r,V1a0))))) # label(lameq_f342) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2991 (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]. 5.48/5.59 2992 (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]. 5.48/5.59 2993 (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)) -> (p(ap(ap(c_2Eset__relation_2Efinite__prefixes(A_27a,A_27a),V1r),V2s)) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(V0f,V3x) = ap(V0f,V4y) -> V3x = V4y))))) -> 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]. 5.48/5.59 2994 (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(ap(c_2Epair_2E_2C(A_27b,bool),V4x),ap(c_2Ebool_2E_3F(A_27c),f331(A_27b,A_27c,V1r2,V4x,V3s2))) = ap(f332(A_27c,A_27b,V1r2,V3s2),V4x)))))) # label(lameq_f332) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2995 (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) -> (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 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 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]. 5.48/5.59 2996 (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]. 5.48/5.59 2997 (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(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))) = ap(f335(A_27a,V3a0,V4x,V0r),V5y)))))))) # label(lameq_f335) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2998 (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)),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)))))))) & (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),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),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),V3x),V4y)),ap(c_2Eset__relation_2Etc(A_27a),V0r)))))))))))) # label(conj_thm_2Eset__relation_2Etc__rules) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 2999 (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 f333(A_27b,A_27a,V0f,V5x,V1r) = ap(f334(A_27b,A_27a,V0f,V1r),V5x)))))) # label(lameq_f334) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3000 (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]. 5.48/5.59 3001 (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]. 5.48/5.59 3002 (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]. 5.48/5.59 3003 (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]. 5.48/5.59 3004 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> f348(A_27a,V0s) = ap(c_2Eset__relation_2ERRUNIV(A_27a),V0s))))) # label(ax_thm_2Eset__relation_2ERRUNIV__def) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3005 (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]. 5.48/5.59 3006 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> V0R = ap(ap(c_2Epred__set_2EREL__RESTRICT(A_27a),V0R),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Eset__relation_2EREL__RESTRICT__UNIV) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3007 (all A_27b all A_27a all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> (all V1x ap(f344(A_27b,A_27a,V0r),V1x) = f317(A_27a,A_27b,V1x,V0r)))) # label(lameq_f344) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3008 (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]. 5.57/5.59 3009 (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)),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))) <-> 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__cases__left) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3010 (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]. 5.57/5.59 3011 (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)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Eset__relation_2Erange(A_27a,A_27b),V1r))) <-> (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)))))))))))) # label(conj_thm_2Eset__relation_2Ein__range) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3012 (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]. 5.57/5.59 3013 (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(f341(A_27a,V0r,V1a0),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))))))) # label(lameq_f341) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3014 (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),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1x)),V2y) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),ap(ap(c_2Epred__set_2EINTER(A_27a),V1x),V2y)))))))))) # label(conj_thm_2Eset__relation_2Errestrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3015 (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]. 5.57/5.59 3016 (all A_27a (ne(A_27a) -> (all V0rs (mem(V0rs,arr(arr(ty_2Epair_2Eprod(A_27a,A_27a),bool),bool)) -> ((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)) & V1r != V2r_27 & 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))))))))) & (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))))) -> 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]. 5.57/5.59 3017 (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(f321(A_27a,V1s,V0r,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),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))))))))))) # label(lameq_f321) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3018 (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]. 5.57/5.59 3019 (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]. 5.57/5.59 3020 (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),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))) <-> p(ap(c_2Eset__relation_2Eacyclic(A_27a),V0r))))))) # label(conj_thm_2Eset__relation_2Eacyclic__SWAP) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3021 (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]. 5.57/5.59 3022 (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]. 5.57/5.59 3023 (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]. 5.57/5.59 3024 (all A_27a all V0xs (mem(V0xs,arr(A_27a,bool)) -> (all V1x1 f328(A_27a,V0xs,V1x1) = ap(f329(A_27a,V0xs),V1x1)))) # label(lameq_f329) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3025 (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]. 5.57/5.59 3026 (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]. 5.57/5.59 3027 (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)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s)) & 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),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)) <-> p(ap(ap(c_2Eset__relation_2Elinear__order(A_27a),V0r),V1s))))))))) # label(ax_thm_2Eset__relation_2Elinear__order__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3028 (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]. 5.57/5.59 3029 (all A_27a (ne(A_27a) -> (all V0r (mem(V0r,arr(ty_2Epair_2Eprod(A_27a,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)),f327(A_27a,V0r))) = ap(c_2Eset__relation_2Estrict(A_27a),V0r))))) # label(ax_thm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3030 (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_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))) = ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R))))))) # label(ax_thm_2Eset__relation_2Erel__to__reln__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3031 (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]. 5.57/5.59 3032 (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]. 5.57/5.59 3033 (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]. 5.57/5.59 3034 (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]. 5.57/5.59 3035 (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]. 5.57/5.59 3036 (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]. 5.57/5.59 3037 (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)),ap(c_2Eset__relation_2Etc(A_27a),V0r))) & 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__strongind__right) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3038 (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]. 5.57/5.59 3039 (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]. 5.57/5.59 3040 (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]. 5.57/5.59 3041 (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]. 5.57/5.59 3042 (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]. 5.57/5.59 3043 (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]. 5.57/5.59 3044 (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]. 5.57/5.59 3045 (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_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_2Eset__relation_2Elinear__order(A_27a),V0r),V1s)) -> 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]. 5.57/5.59 3046 (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]. 5.57/5.59 3047 (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]. 5.57/5.59 3048 (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]. 5.57/5.59 3049 (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),ap(c_2Eset__relation_2Etc(A_27a),V0r)) = ap(c_2Eset__relation_2Etc(A_27a),V0r))))) # label(conj_thm_2Eset__relation_2Etc__idemp) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3050 (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]. 5.57/5.59 3051 (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]. 5.57/5.59 3052 (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]. 5.57/5.59 3053 (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]. 5.57/5.59 3054 (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]. 5.57/5.59 3055 (all A_27a all V0r f342(A_27a,V0r) = ap(f343(A_27a),V0r)) # label(lameq_f343) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3056 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x f345(A_27a,A_27b,V0R,V1x) = ap(f346(A_27b,A_27a,V0R),V1x)))) # label(lameq_f346) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3057 (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]. 5.57/5.59 3058 (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]. 5.57/5.59 3059 (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(f323(A_27b,A_27a,A_27c,V2x,V0r1,V3y,V1r2),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))))))))))) # label(lameq_f323) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3060 (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]. 5.57/5.59 3061 (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]. 5.57/5.59 3062 (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]. 5.57/5.59 3063 (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(V1tc_27,V4x),V6z)) & 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))) & 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) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3064 (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 (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)),V0r)) & p(ap(ap(V1tc_27,V6z),V5y)))) -> 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__ind__left) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3065 (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]. 5.57/5.59 3066 (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),V2x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),V1s))))))))))))) # label(conj_thm_2Eset__relation_2Estrict__linear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3067 (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(c_2Ebool_2E_3F(A_27a),f338(A_27a,V3a0,V2tc_27,V6x)) = ap(f339(A_27a,V2tc_27,V3a0),V6x)))))) # label(lameq_f339) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3068 (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)) <-> (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)))))))))))))) # label(ax_thm_2Eset__relation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3069 (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(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)) = ap(f333(A_27b,A_27a,V0f,V5x,V1r),V6y)))))))) # label(lameq_f333) # label(axiom) # label(non_clause). [assumption]. 5.57/5.59 3070 (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_2Etransitive(A_27a),V0r)) & p(ap(c_2Eset__relation_2Eantisym(A_27a),V0r)) & p(ap(ap(c_2Eset__relation_2Ereflexive(A_27a),V0r),V1s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s)) & 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]. 5.57/5.60 3071 (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]. 5.57/5.60 3072 (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]. 5.57/5.60 3073 (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(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),ap(ap(c_2Eset__relation_2Errestrict(A_27a),V1r),V2s))) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),V0x),V1r)) & 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))))))))))) # label(conj_thm_2Eset__relation_2Ein__rrestrict__alt) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3074 (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 (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),V6z),V5y)),V0r)) & p(ap(ap(V1tc_27,V4x),V6z)))) -> 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__ind__right) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3075 (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]. 5.57/5.60 3076 (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)) -> V2y = V1x)))))))))) # label(ax_thm_2Eset__relation_2Eantisym__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3077 (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_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_2Eset__relation_2Epartial__order(A_27a),V0r),V1s)) -> 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]. 5.57/5.60 3078 (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]. 5.57/5.60 3079 (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]. 5.57/5.60 3080 (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_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 V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V1s)) & V4y != V3x & 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))))))) & (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)))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Eset__relation_2Erange(A_27a,A_27a),V0r)),V1s))))))))) # label(ax_thm_2Eset__relation_2Estrict__linear__order__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3081 (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]. 5.57/5.60 3082 (all A_27a (ne(A_27a) -> c_2Eset__relation_2Etc(A_27a) = f343(A_27a))) # label(ax_thm_2Eset__relation_2Etc__def) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3083 (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]. 5.57/5.60 3084 (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(f324(A_27a,A_27c,A_27b,V0r1,V1r2,V2x),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)))))))))) # label(lameq_f324) # label(axiom) # label(non_clause). [assumption]. 5.57/5.60 3085 (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]. 5.57/5.60 3086 (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]. 5.57/5.60 3087 (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(V1tc_27,V4x),V6z)) & p(ap(ap(V1tc_27,V6z),V5y)) & 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__ind) # label(axiom) # label(non_clause). [assumption]. 16.39/16.51 3088 (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]. 16.39/16.51 3089 (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]. 16.39/16.51 3090 (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]. 16.39/16.51 3091 (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]. 16.39/16.51 3092 (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_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))) = ap(ap(c_2Eset__relation_2Errestrict(A_27a),V0r),V1s))))))) # label(ax_thm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 16.39/16.51 3093 -(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_2Ereln__to__rel(A_27a,A_27b),ap(c_2Eset__relation_2Erel__to__reln(A_27a,A_27b),V0R)) = V0R)))))) # label(conj_thm_2Eset__relation_2Erel__to__reln__inv) # label(negated_conjecture) # label(non_clause). [assumption]. 16.39/16.51 16.39/16.51 ============================== end of process non-clausal formulas === 16.39/16.51 16.39/16.51 ============================== PROCESS INITIAL CLAUSES =============== 16.39/16.51 16.39/16.51 ============================== PREDICATE ELIMINATION ================= 16.39/16.51 16.39/16.51 ============================== end predicate elimination ============= 16.39/16.51 16.39/16.51 Auto_denials: (non-Horn, no changes). 16.39/16.51 16.39/16.51 Term ordering decisions: 16.39/16.51 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. c_2Earithmetic_2E_3C_3D=1. c_2Enum_2ESUC=1. c_2Earithmetic_2E_2B=1. c_2Earithmetic_2EBIT2=1. c_2Earithmetic_2E_2A=1. c_2Earithmetic_2EEXP=1. c_2Earithmetic_2E_2D=1. c_2Earithmetic_2EMOD=1. c_2Ebit_2EBIT=1. c_2Earithmetic_2EDIV=1. c_2Ebit_2EBITS=1. c_2Edivides_2Edivides=1. c_2Earithmetic_2EODD=1. c_2Egcd_2Egcd=1. c_2Ebool_2ET=1. c_2Ebool_2E_2F_5C=1. c_2Eprim__rec_2EPRE=1. c_2Earithmetic_2EEVEN=1. c_2Enumeral_2EiDUB=1. c_2Ebool_2EF=1. ty_2Eone_2Eone=1. c_2Earithmetic_2EMODEQ=1. c_2Enumpair_2Etri=1. c_2Earithmetic_2EMIN=1. c_2Earithmetic_2EMAX=1. c_2Ebit_2ESLICE=1. c_2Emin_2E_3D_3D_3E=1. c_2Earithmetic_2E_3E=1. c_2Enumeral__bit_2EFDUB=1. c_2Enumeral_2EiSUB=1. c_2Epred__set_2Ecount=1. ind=1. c_2Elogroot_2ELOG=1. c_2Ewhile_2ELEAST=1. c_2Earithmetic_2EABS__DIFF=1. c_2Earithmetic_2EDIV2=1. c_2Epred__set_2EMAX__SET=1. c_2Edivides_2Eprime=1. c_2Enumeral__bit_2ESFUNPOW=1. c_2Earithmetic_2E_3E_3D=1. c_2Egcd_2Eis__gcd=1. c_2Enumeral__bit_2EiDIV2=1. c_2Edivides_2EPRIMES=1. c_2Ewhile_2EOLEAST=1. c_2Ebit_2EBITWISE=1. c_2Enumpair_2Encons=1. c_2Elogroot_2ESQRTd=1. c_2Epred__set_2EMIN__SET=1. c_2Ebool_2E_5C_2F=1. c_2Ebool_2E_7E=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_2Eone_2Eone=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_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_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_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_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. ap=1. arr=1. ty_2Epair_2Eprod=1. c_2Epair_2E_2C=1. c_2Epair_2ELEX=1. ty_2Esum_2Esum=1. c_2Epred__set_2EIMAGE=1. c_2Epred__set_2EBIJ=1. c_2Epair_2EPROD__ALL=1. c_2Epred__set_2EINJ=1. c_2Esum_2ESUM__ALL=1. c_2Epred__set_2EGSPEC=1. c_2Esum_2EINL=1. c_2Esum_2EINR=1. c_2Epair_2EFST=1. c_2Epair_2ESND=1. c_2Ebool_2ELET=1. c_2Eset__relation_2Erange=1. c_2Ecombin_2EUPDATE=1. c_2Epred__set_2ECROSS=1. c_2Eset__relation_2Edomain=1. c_2Erelation_2Einv=1. c_2Epred__set_2ESURJ=1. k=1. c_2Epred__set_2EPREIMAGE=1. c_2Ebool_2ETYPE__DEFINITION=1. c_2Eoption_2Eoption__CASE=1. c_2Erelation_2ERSUBSET=1. c_2Eset__relation_2Efinite__prefixes=1. c_2EfixedPoint_2Emonotone=1. c_2Eoption_2EOPTION__MAP=1. c_2Epred__set_2EITSET=1. c_2Epred__set_2EFUNSET=1. c_2Eoption_2EOPTREL=1. c_2Erelation_2ERDOM=1. c_2Eind__type_2EISO=1. c_2Eoption_2EOPTION__BIND=1. c_2Ebool_2Eliteral__case=1. c_2Ecombin_2EK=1. c_2Ebool_2EONE__ONE=1. c_2EfixedPoint_2Efnsum=1. c_2Erelation_2ERUNION=1. c_2Eposet_2Efunction=1. c_2Erelation_2ERINTER=1. f49=1. c_2Eoption_2EOPTION__APPLY=1. c_2Erelation_2EINDUCTIVE__INVARIANT__ON=1. c_2Eoption_2EOPTION__IGNORE__BIND=1. c_2Epred__set_2EDFUNSET=1. c_2Epred__set_2ELINV__OPT=1. c_2Erelation_2ERESTRICT=1. c_2Erelation_2EWFREC=1. c_2Ewhile_2EHOARE__SPEC=1. c_2Erelation_2EINDUCTIVE__INVARIANT=1. c_2Erelation_2Einv__image=1. c_2Esum_2EIS__SUM__REP=1. c_2Ebool_2ERES__ABSTRACT=1. c_2EnormalForms_2EEXT__POINT=1. c_2Erelation_2ERRANGE=1. c_2Erelation_2ERRESTRICT=1. c_2Erelation_2ERUNIV=1. c_2Esum_2EISL=1. c_2Ebool_2EONTO=1. c_2Ecombin_2ELEFT__ID=1. c_2Ecombin_2ERIGHT__ID=1. c_2Epair_2ESWAP=1. c_2Esum_2EABS__sum=1. c_2Esum_2EISR=1. c_2Ecombin_2ECOMM=1. c_2EfixedPoint_2Eempty=1. c_2Epair_2EABS__prod=1. c_2Epred__set_2ELINV=1. c_2Erelation_2ERDOM__DELETE=1. c_2Eset__relation_2Erel__to__reln=1. c_2Eset__relation_2Ereln__to__rel=1. c_2Ecombin_2EFAIL=1. c_2Epair_2EREP__prod=1. c_2Erelation_2Eapprox=1. c_2Esum_2EOUTL=1. c_2Esum_2EOUTR=1. c_2Esum_2EREP__sum=1. f262=1. f282=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. f120=1. f14=1. f155=1. f157=1. f252=1. f256=1. f297=1. f298=1. f61=1. f68=1. c_2EbasicSize_2Epair__size=1. c_2Ebool_2Eitself__case=1. c_2Ecombin_2E_3A_3E=1. f108=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. f38=1. f40=1. f43=1. f45=1. f50=1. f51=1. f57=1. f59=1. f6=1. f60=1. f76=1. f87=1. c_2Eset__relation_2Eupper__bounds=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. f368=1. f369=1. f370=1. f396=1. f397=1. f398=1. f404=1. f405=1. f424=1. f425=1. f427=1. f428=1. f429=1. f436=1. f437=1. f438=1. f439=1. f446=1. f447=1. f448=1. f453=1. f454=1. f457=1. f462=1. f465=1. f468=1. f469=1. f470=1. f472=1. f474=1. f502=1. f535=1. f537=1. f543=1. f548=1. f575=1. f581=1. f583=1. f584=1. f586=1. f587=1. f590=1. f591=1. f604=1. f605=1. f608=1. f612=1. f613=1. f614=1. f633=1. f634=1. f635=1. f641=1. f642=1. f643=1. f645=1. f646=1. f647=1. f654=1. f655=1. f657=1. f672=1. f678=1. f679=1. f680=1. f688=1. f689=1. f690=1. f697=1. f698=1. f699=1. f701=1. f702=1. f703=1. f706=1. f707=1. f708=1. f714=1. f715=1. f724=1. f725=1. f726=1. f734=1. f735=1. f736=1. f739=1. f740=1. f741=1. f743=1. f758=1. f761=1. f770=1. f780=1. f786=1. f787=1. f793=1. f795=1. f797=1. f798=1. f799=1. f800=1. f803=1. f808=1. f814=1. f827=1. f838=1. f840=1. f847=1. f848=1. f853=1. f854=1. f855=1. f856=1. f858=1. f859=1. f865=1. f869=1. f870=1. f872=1. f873=1. f880=1. f889=1. f907=1. f908=1. f909=1. f927=1. f945=1. f946=1. f947=1. f957=1. f970=1. f971=1. f972=1. f980=1. f981=1. c_2Ebool_2EIN=1. c_2Erelation_2EEQC=1. ty_2Eoption_2Eoption=1. c_2Epred__set_2EFINITE=1. c_2Erelation_2ETC=1. c_2Epred__set_2ESUBSET=1. c_2Epred__set_2EEMPTY=1. c_2Eset__relation_2Etc=1. c_2Ebool_2ECOND=1. c_2Eposet_2Eposet=1. c_2Epred__set_2EINSERT=1. c_2Erelation_2ERTC=1. c_2Eoption_2ESOME=1. c_2Epred__set_2Eequiv__on=1. c_2Eoption_2ENONE=1. c_2Epred__set_2EUNION=1. c_2Epred__set_2ECARD=1. c_2Emin_2E_3D=1. c_2Epred__set_2EUNIV=1. c_2Epred__set_2EBIGUNION=1. c_2Epred__set_2EDISJOINT=1. c_2Epred__set_2Ecountable=1. c_2Epred__set_2EINTER=1. c_2Epred__set_2EDELETE=1. c_2Erelation_2EWF=1. c_2Erelation_2ERC=1. c_2Epred__set_2EDIFF=1. c_2Epred__set_2ESUM__IMAGE=1. c_2Erelation_2Etransitive=1. c_2Ebool_2E_21=1. c_2Ebool_2E_3F=1. c_2Earithmetic_2ENRC=1. c_2Erelation_2ESC=1. ty_2Eind__type_2Erecspace=1. c_2Eset__relation_2Eacyclic=1. c_2Epred__set_2EBIGINTER=1. c_2Erelation_2Ereflexive=1. c_2Eset__relation_2Etransitive=1. c_2Eposet_2Eglb=1. c_2Eposet_2Elub=1. c_2Eind__type_2EZRECSPACE=1. c_2Ebool_2E_3F_21=1. c_2Epred__set_2Epairwise=1. c_2Erelation_2Esymmetric=1. c_2Earithmetic_2EFUNPOW=1. c_2Epred__set_2EPSUBSET=1. c_2Epred__set_2ESING=1. c_2Erelation_2EWFP=1. c_2Ebool_2ERES__FORALL=1. c_2Epred__set_2EREST=1. c_2Ewhile_2EOWHILE=1. c_2Eoption_2EOPTION__ALL=1. c_2Erelation_2Eantisymmetric=1. c_2Eset__relation_2Errestrict=1. c_2Ebool_2ERES__EXISTS=1. c_2Eposet_2Ecomplete=1. c_2Earithmetic_2Enum__CASE=1. c_2Emin_2E_40=1. c_2Epred__set_2ECOMPL=1. c_2Eind__type_2EZBOT=1. c_2Eoption_2EIS__SOME=1. c_2Erelation_2Etrichotomous=1. c_2Eset__relation_2Estrict__linear__order=1. c_2Erelation_2EWeakOrder=1. c_2Erelation_2Ediamond=1. c_2Eset__relation_2Eantisym=1. ty_2Ebool_2Eitself=1. c_2Eposet_2Ecarrier=1. c_2Ecombin_2EASSOC=1. c_2Ecombin_2EI=1. c_2EfixedPoint_2Elfp=1. c_2Eoption_2Esome=1. c_2Eset__relation_2Elinear__order=1. c_2Eset__relation_2Epartial__order=1. c_2Eposet_2Emonotonic=1. c_2Epred__set_2EPOW=1. c_2Epred__set_2ECHOICE=1. c_2Epred__set_2EREL__RESTRICT=1. c_2Erelation_2Eirreflexive=1. c_2Eposet_2Echain=1. i=1. c_2Epred__set_2Eis__measure__maximal=1. c_2Erelation_2Eequivalence=1. c_2Erelation_2Ercdiamond=1. c_2Eind__type_2ECONSTR=1. c_2Eposet_2Egfp=1. c_2Eposet_2Elfp=1. c_2Erelation_2EINVOL=1. c_2Erelation_2EOrder=1. c_2Ebool_2Ethe__value=1. c_2Eind__type_2EINJP=1. c_2Eind__type_2EZCONSTR=1. c_2Epred__set_2Eschroeder__close=1. c_2Eprim__rec_2ESIMP__REC__REL=1. c_2Erelation_2EIDEM=1. c_2Erelation_2ESTRORD=1. c_2Erelation_2EStrongOrder=1. c_2Erelation_2EWCR=1. c_2Erelation_2Etotal=1. c_2EfixedPoint_2Egfp=1. c_2Enumpair_2Enlistrec=1. c_2Eoption_2ETHE=1. c_2Epred__set_2Epartition=1. c_2Erelation_2EWeakLinearOrder=1. c_2Eind__type_2Edest__rec=1. c_2Eoption_2EIS__NONE=1. c_2Eposet_2Edown__continuous=1. c_2Eposet_2Eup__continuous=1. c_2Epred__set_2Echooser=1. c_2Eset__relation_2Estrict=1. c_2Ebool_2EDATATYPE=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_2Ewhile_2EWHILE=1. c_2Ecombin_2EMONOID=1. c_2Eind__type_2EBOTTOM=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_2Eset__relation_2Ereflexive=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_2Ebool_2EARB=1. c_2Ebool_2ERES__EXISTS__UNIQUE=1. c_2EfixedPoint_2Eclosed=1. c_2EfixedPoint_2Edense=1. c_2EnormalForms_2EUNIV__POINT=1. c_2Enumpair_2Enfoldl=1. c_2Eprim__rec_2EPRIM__REC=1. c_2Eind__type_2EFCONS=1. c_2Eoption_2Eoption__REP=1. c_2Eposet_2Econtinuous=1. c_2Erelation_2ELinearOrder=1. c_2Erelation_2EPreOrder=1. c_2Erelation_2ESN=1. c_2Erelation_2EStrongLinearOrder=1. c_2Eset__relation_2ERREFL__EXP=1. c_2Eset__relation_2Eirreflexive=1. c_2EbasicSize_2Eoption__size=1. c_2Ebool_2ERES__SELECT=1. c_2Eone_2Eone__CASE=1. f188=1. f189=1. c_2Eind__type_2EFNIL=1. c_2Emarker_2Estmarker=1. c_2Emarker_2Eunint=1. c_2Eposet_2Erelation=1. c_2Eset__relation_2ERRUNIV=1. c_2Eset__relation_2Euniv__reln=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. f39=1. f4=1. f44=1. f46=1. f7=1. c_2Eset__relation_2Eall__choices=1. c_2Eset__relation_2Echain=1. c_2Eset__relation_2Efchains=1. c_2Eset__relation_2Eget__min=1. c_2Eset__relation_2Emaximal__elements=1. c_2Eset__relation_2Eminimal__elements=1. c_2Eset__relation_2Enth__min=1. c_2Eset__relation_2Enum__order=1. c_2Eset__relation_2Eper=1. c_2Eset__relation_2Eper__restrict=1. f9=1. f125=1. f184=1. f186=1. f187=1. f461=1. f582=1. f585=1. f592=1. f595=1. f596=1. f606=1. f609=1. f610=1. f611=1. f615=1. f616=1. f617=1. f618=1. f620=1. f623=1. f624=1. f625=1. f628=1. f629=1. f630=1. f636=1. f637=1. f649=1. f659=1. f660=1. f661=1. f667=1. f668=1. f670=1. f671=1. f673=1. f674=1. f675=1. f676=1. f677=1. f692=1. f709=1. f710=1. f711=1. f712=1. f716=1. f717=1. f718=1. f719=1. f720=1. f721=1. f722=1. f723=1. f727=1. f728=1. f729=1. f730=1. f731=1. f732=1. f737=1. f788=1. f789=1. f796=1. f801=1. f802=1. f912=1. c_2Epair_2EUNCURRY=1. c_2Ecombin_2Eo=1. c_2Eoption_2EOPTION__MAP2=1. c_2Esum_2Esum__CASE=1. c_2Epair_2Epair__CASE=1. c_2Erelation_2EO=1. c_2Ecombin_2EC=1. c_2Ecombin_2ES=1. c_2Epair_2ECURRY=1. f128=1. f304=1. c_2Ecombin_2EFCOMM=1. c_2Eoption_2EOPTION__MCOMP=1. f129=1. f166=1. f303=1. f186=1. f187=1. f53=1. c_2Eset__relation_2Ercomp=1. f185=1. f258=1. f37=1. f63=1. f82=1. f89=1. f91=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. f41=1. f42=1. f47=1. f48=1. f58=1. f62=1. f64=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. f352=1. f353=1. f356=1. f357=1. f361=1. f376=1. f377=1. f378=1. f379=1. f390=1. f391=1. f399=1. f400=1. f401=1. f402=1. f403=1. f408=1. f409=1. f410=1. f411=1. f412=1. f413=1. f414=1. f415=1. f416=1. f417=1. f418=1. f419=1. f421=1. f422=1. f426=1. f430=1. f431=1. f432=1. f433=1. f452=1. f467=1. f485=1. f492=1. f493=1. f494=1. f495=1. f496=1. f497=1. f498=1. f499=1. f500=1. f501=1. f503=1. f504=1. f505=1. f506=1. f507=1. f514=1. f515=1. f524=1. f525=1. f526=1. f529=1. f531=1. f532=1. f534=1. f536=1. f538=1. f544=1. f545=1. f549=1. f552=1. f553=1. f561=1. f563=1. f564=1. f565=1. f566=1. f567=1. f568=1. f569=1. f573=1. f574=1. f576=1. f588=1. f589=1. f597=1. f598=1. f600=1. f601=1. f602=1. f619=1. f621=1. f622=1. f626=1. f631=1. f632=1. f638=1. f639=1. f648=1. f662=1. f700=1. f713=1. f738=1. f742=1. f744=1. f751=1. f752=1. f753=1. f754=1. f762=1. f763=1. f764=1. f765=1. f766=1. f767=1. f768=1. f769=1. f771=1. f772=1. f776=1. f777=1. f785=1. f794=1. f805=1. f806=1. f807=1. f812=1. f813=1. f815=1. f816=1. f823=1. f828=1. f829=1. f831=1. f836=1. f837=1. f844=1. f857=1. f860=1. f861=1. f866=1. f874=1. f884=1. f890=1. f893=1. f900=1. f901=1. f902=1. f903=1. f904=1. f905=1. f906=1. f910=1. f914=1. f915=1. f916=1. f917=1. f925=1. f926=1. f931=1. f932=1. f933=1. f934=1. f935=1. f939=1. f940=1. f941=1. f942=1. f948=1. f949=1. f950=1. f951=1. f952=1. f953=1. f954=1. f955=1. f956=1. f958=1. f959=1. f960=1. f961=1. f962=1. f963=1. f964=1. f965=1. f966=1. f967=1. f968=1. f969=1. f974=1. f975=1. f976=1. f977=1. f978=1. f982=1. f983=1. f984=1. f985=1. f986=1. f987=1. f988=1. f989=1. c_2Esum_2E_2B_2B=1. c_2Epair_2E_23_23=1. f171=1. f334=1. f260=1. f261=1. f138=1. f140=1. f274=1. f317=1. f330=1. f54=1. f55=1. f84=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. f70=1. f73=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. f358=1. f359=1. f360=1. f367=1. f371=1. f372=1. f373=1. f374=1. f375=1. f380=1. f381=1. f382=1. f383=1. f384=1. f392=1. f420=1. f423=1. f434=1. f435=1. f444=1. f466=1. f478=1. f508=1. f513=1. f530=1. f533=1. f539=1. f540=1. f541=1. f546=1. f547=1. f550=1. f551=1. f559=1. f560=1. f562=1. f577=1. f579=1. f580=1. f594=1. f599=1. f650=1. f651=1. f652=1. f653=1. f658=1. f665=1. f669=1. f681=1. f682=1. f683=1. f684=1. f685=1. f686=1. f687=1. f704=1. f705=1. f733=1. f748=1. f749=1. f750=1. f755=1. f756=1. f757=1. f759=1. f760=1. f773=1. f774=1. f781=1. f782=1. f783=1. f784=1. f790=1. f791=1. f792=1. f809=1. f810=1. f811=1. f822=1. f824=1. f825=1. f830=1. f839=1. f841=1. f845=1. f846=1. f862=1. f863=1. f864=1. f867=1. f871=1. f875=1. f876=1. f881=1. f885=1. f886=1. f911=1. f921=1. f923=1. f928=1. f929=1. f930=1. f936=1. f943=1. f944=1. f973=1. f979=1. f100=1. f272=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. f52=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. f354=1. f355=1. f362=1. f363=1. f364=1. f365=1. f366=1. f385=1. f386=1. f388=1. f389=1. f393=1. f394=1. f395=1. f406=1. f407=1. f440=1. f441=1. f442=1. f443=1. f445=1. f450=1. f459=1. f460=1. f463=1. f464=1. f473=1. f475=1. f542=1. f554=1. f556=1. f557=1. f558=1. f570=1. f571=1. f578=1. f593=1. f607=1. f644=1. f656=1. f663=1. f664=1. f666=1. f691=1. f693=1. f694=1. f695=1. f696=1. f775=1. f778=1. f779=1. f804=1. f817=1. f818=1. f819=1. f820=1. f821=1. f832=1. f833=1. f834=1. f842=1. f849=1. f850=1. f851=1. f868=1. f877=1. f879=1. f882=1. f883=1. f887=1. f888=1. f891=1. f892=1. f894=1. f895=1. f896=1. f913=1. f918=1. f919=1. f920=1. f922=1. f924=1. f937=1. f938=1. f133=1. f134=1. f137=1. f142=1. f146=1. f167=1. f223=1. f225=1. f324=1. f122=1. f149=1. f244=1. f245=1. f449=1. f451=1. f471=1. f476=1. f477=1. f486=1. f487=1. f555=1. f572=1. f603=1. f640=1. f745=1. f746=1. f747=1. f826=1. f835=1. f843=1. f852=1. f878=1. f897=1. f898=1. f899=1. f132=1. f136=1. f141=1. f145=1. f222=1. f224=1. f323=1. f189=1. f190=1. f210=1. f387=1. f479=1. f480=1. f509=1. f510=1. f511=1. f512=1. f527=1. f528=1. f627=1. f192=1. f193=1. f246=1. f458=1. f481=1. f482=1. f483=1. f484=1. f488=1. f489=1. f490=1. f491=1. f208=1. f209=1. f455=1. f456=1. f516=1. f517=1. f518=1. f519=1. f520=1. f521=1. f522=1. f523=1. 16.39/16.51 16.39/16.51 ============================== STATISTICS ============================ 16.39/16.51 16.39/16.51 Given=0. Generated=7143. Kept=6816. proofs=0. 16.39/16.51 Usable=0. Sos=0. Demods=79. Limbo=6815, Disabled=7143. Hints=0. 16.39/16.51 Kept_by_rule=0, Deleted_by_rule=0. 16.39/16.51 Forward_subsumed=327. Back_subsumed=0. 16.39/16.51 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 16.39/16.51 New_demodulators=79 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 16.39/16.51 Demod_attempts=300804. Demod_rewrites=1092. 16.39/16.51 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 16.39/16.51 Nonunit_fsub_feature_tests=7186. Nonunit_bsub_feature_tests=0. 16.39/16.51 Megabytes=419.43. 16.39/16.51 User_CPU=11.63, System_CPU=0.12, Wall_clock=12. 16.39/16.51 16.39/16.51 Megs malloced by palloc(): 400. 16.39/16.51 type (bytes each) gets frees in use bytes 16.39/16.51 chunk ( 104) 185354 185354 0 0.0 K 16.39/16.51 string_buf ( 8) 162229 162229 0 0.0 K 16.39/16.51 token ( 20) 455770 455770 0 0.0 K 16.39/16.51 pterm ( 16) 266625 266625 0 0.0 K 16.39/16.51 hashtab ( 8) 3093 3093 0 0.0 K 16.39/16.51 hashnode ( 8) 29571 29571 0 0.0 K 16.39/16.51 term ( 20) 2632303 2109003 523300 10220.7 K 16.39/16.51 term arg arrays: 2625.9 K 16.39/16.51 attribute ( 12) 37259 566 36693 430.0 K 16.39/16.51 ilist ( 8) 92426931 92417790 9141 71.4 K 16.39/16.51 plist ( 8) 117699 64296 53403 417.2 K 16.39/16.51 i2list ( 12) 678790 678790 0 0.0 K 16.39/16.51 just ( 12) 25300 6525 18775 220.0 K 16.39/16.51 parajust ( 16) 0 0 0 0.0 K 16.39/16.51 instancejust ( 8) 0 0 0 0.0 K 16.39/16.51 ivyjust ( 24) 0 0 0 0.0 K 16.39/16.51 formula ( 28) 312627 233267 79360 2170.0 K 16.39/16.51 formula arg arrays: 285.8 K 16.39/16.51 topform ( 52) 18074 327 17747 901.2 K 16.39/16.51 clist_pos ( 20) 21875 7143 14732 287.7 K 16.39/16.51 clist ( 16) 8 0 8 0.1 K 16.39/16.51 context ( 808) 168635 168635 0 0.0 K 16.39/16.51 trail ( 12) 1044065 1044065 0 0.0 K 16.39/16.51 ac_match_pos (70044) 0 0 0 0.0 K 16.39/16.51 ac_match_free_vars_pos (20020) 16.39/16.51 0 0 0 0.0 K 16.39/16.51 btm_state ( 60) 0 0 0 0.0 K 16.39/16.51 btu_state ( 60) 0 0 0 0.0 K 16.39/16.51 ac_position (285432) 0 0 0 0.0 K 16.39/16.51 fpa_trie ( 20) 33777 0 33777 659.7 K 16.39/16.51 fpa_state ( 28) 2 2 0 0.0 K 16.39/16.51 fpa_index ( 12) 10 0 10 0.1 K 16.39/16.51 fpa_chunk ( 20) 29005 8084 20921 408.6 K 16.39/16.51 fpa_list ( 16) 14890 0 14890 232.7 K 16.39/16.51 fpa_list chunks: 763.5 K 16.39/16.51 discrim ( 12) 1712 0 1712 20.1 K 16.39/16.51 discrim_pos ( 16) 1099 1099 0 0.0 K 16.39/16.51 flat2 ( 32) 409749 409749 0 0.0 K 16.39/16.51 flat ( 48) 0 0 0 0.0 K 16.39/16.51 flatterm ( 32) 575367 575367 0 0.0 K 16.39/16.51 mindex ( 28) 13 0 13 0.4 K 16.39/16.51 mindex_pos ( 56) 145050 145050 0 0.0 K 16.39/16.51 lindex ( 12) 5 0 5 0.1 K 16.39/16.51 clash ( 40) 0 0 0 0.0 K 16.39/16.51 di_tree ( 12) 33164278 0 33164278 388643.9 K 16.39/16.51 avl_node ( 20) 0 0 0 0.0 K 16.39/16.51 16.39/16.51 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 16.39/16.51 List 1, length 13, 0.1 K 16.39/16.51 List 4, length 2, 0.0 K 16.39/16.51 List 8, length 18, 0.6 K 16.39/16.51 List 14, length 8, 0.4 K 16.39/16.51 List 17, length 52, 3.5 K 16.39/16.51 List 18, length 7, 0.5 K 16.39/16.51 List 19, length 2, 0.1 K 16.39/16.51 List 20, length 2, 0.2 K 16.39/16.51 List 21, length 2, 0.2 K 16.39/16.51 List 22, length 2, 0.2 K 16.39/16.51 List 23, length 2, 0.2 K 16.39/16.51 List 24, length 2, 0.2 K 16.39/16.51 List 26, length 520, 52.8 K 16.39/16.51 List 27, length 2, 0.2 K 16.39/16.51 List 28, length 2, 0.2 K 16.39/16.51 List 32, length 33, 4.1 K 16.39/16.51 List 40, length 2, 0.3 K 16.39/16.51 List 48, length 2, 0.4 K 16.39/16.51 List 50, length 2, 0.4 K 16.39/16.51 List 54, length 2, 0.4 K 16.39/16.51 List 63, length 2, 0.5 K 16.39/16.51 List 64, length 7, 1.8 K 16.39/16.51 List 72, length 2, 0.6 K 16.39/16.51 List 80, length 2, 0.6 K 16.39/16.51 List 81, length 2, 0.6 K 16.39/16.51 List 86, length 2, 0.7 K 16.39/16.51 List 96, length 2, 0.8 K 16.39/16.51 List 128, length 76, 38.0 K 16.39/16.51 List 144, length 2, 1.1 K 16.39/16.51 List 162, length 2, 1.3 K 16.39/16.51 List 166, length 2, 1.3 K 16.39/16.51 List 189, length 2, 1.5 K 16.39/16.51 List 192, length 2, 1.5 K 16.39/16.51 List 194, length 2, 1.5 K 16.49/16.52 List 202, length 2, 1.6 K 16.49/16.52 List 320, length 2, 2.5 K 16.49/16.52 16.49/16.52 ============================== SELECTOR REPORT ======================= 16.49/16.52 Sos_deleted=0, Sos_displaced=0, Sos_size=0 16.49/16.52 SELECTOR PART PRIORITY ORDER SIZE SELECTED 16.49/16.52 I 2147483647 high age 0 0 16.49/16.52 H 1 high weight 0 0 16.49/16.52 A 1 low age 0 0 16.49/16.52 F 4 low weight 0 0 16.49/16.52 T 4 low weight 0 0 16.49/16.52 ============================== end of selector report ================ 16.49/16.52 16.49/16.52 ============================== end of statistics ===================== 16.49/16.52 16.49/16.52 Exiting with failure. 16.49/16.52 16.49/16.52 Process 23811 exit (max_megs) Tue Jul 13 15:39:12 2021 16.49/16.52 Prover9 interrupted 16.49/16.52 EOF