include('Axioms/HL4001_2.ax').
tff(stp_o,type,(tp__o : $tType)).
tff(stp_inj_o,type,(inj__o : tp__o > $i)).
tff(stp_surj_o,type,(surj__o : $i > tp__o)).
tff(stp_inj_surj_o,axiom,( ! [X:tp__o] : (surj__o(inj__o(X)) = X))).
tff(stp_inj_mem_o,axiom,( ! [X:tp__o] : (mem(inj__o(X),bool)))).
tff(stp_iso_mem_o,axiom,( ! [X:$i] : (mem(X,bool) => (X = inj__o(surj__o(X)))))).
tff(tp_c_2Emin_2E_40,type,(c_2Emin_2E_40:del > $i)).
tff(mem_c_2Emin_2E_40,axiom,( ! [A_27a:del] : mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)))).
tff(tp_c_2Ecardinal_2Ecardeq,type,(c_2Ecardinal_2Ecardeq:(del * del) > $i)).
tff(mem_c_2Ecardinal_2Ecardeq,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ecardinal_2Ecardeq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))).
tff(tp_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: ( del * del ) > del )).
tff(tp_c_2Epred__set_2ECROSS,type,(c_2Epred__set_2ECROSS:(del * del) > $i)).
tff(mem_c_2Epred__set_2ECROSS,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : 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))))))).
tff(tp_c_2Ecardinal_2Ecardleq,type,(c_2Ecardinal_2Ecardleq:(del * del) > $i)).
tff(mem_c_2Ecardinal_2Ecardleq,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ecardinal_2Ecardleq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))).
tff(tp_c_2Ecombin_2ES,type,(c_2Ecombin_2ES:(del * del * del) > $i)).
tff(mem_c_2Ecombin_2ES,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : 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)))))))).
tff(tp_c_2Ecombin_2EC,type,(c_2Ecombin_2EC:(del * del * del) > $i)).
tff(mem_c_2Ecombin_2EC,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : 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)))))))).
tff(tp_c_2Ecombin_2EI,type,(c_2Ecombin_2EI:del > $i)).
tff(mem_c_2Ecombin_2EI,axiom,( ! [A_27a:del] : mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)))).
tff(tp_c_2Ecombin_2Eo,type,(c_2Ecombin_2Eo:(del * del * del) > $i)).
tff(mem_c_2Ecombin_2Eo,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : 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)))))))).
tff(tp_ty_2Erealax_2Ereal,type,( ty_2Erealax_2Ereal: del )).
tff(stp_ty_2Erealax_2Ereal,type,(tp__ty_2Erealax_2Ereal : $tType)).
tff(stp_inj_ty_2Erealax_2Ereal,type,(inj__ty_2Erealax_2Ereal : tp__ty_2Erealax_2Ereal > $i)).
tff(stp_surj_ty_2Erealax_2Ereal,type,(surj__ty_2Erealax_2Ereal : $i > tp__ty_2Erealax_2Ereal)).
tff(stp_inj_surj_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X)) = X))).
tff(stp_inj_mem_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : (mem(inj__ty_2Erealax_2Ereal(X),ty_2Erealax_2Ereal)))).
tff(stp_iso_mem_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : (mem(X,ty_2Erealax_2Ereal) => (X = inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X)))))).
tff(tp_c_2Ereal_2Esup,type,(c_2Ereal_2Esup:$i)).
tff(mem_c_2Ereal_2Esup,axiom,mem(c_2Ereal_2Esup,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal))).
tff(tp_c_2Epred__set_2EINSERT,type,(c_2Epred__set_2EINSERT:del > $i)).
tff(mem_c_2Epred__set_2EINSERT,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))))).
tff(tp_c_2Epred__set_2EDIFF,type,(c_2Epred__set_2EDIFF:del > $i)).
tff(mem_c_2Epred__set_2EDIFF,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EDIFF(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))).
tff(tp_ty_2Enum_2Enum,type,( ty_2Enum_2Enum: del )).
tff(stp_ty_2Enum_2Enum,type,(tp__ty_2Enum_2Enum : $tType)).
tff(stp_inj_ty_2Enum_2Enum,type,(inj__ty_2Enum_2Enum : tp__ty_2Enum_2Enum > $i)).
tff(stp_surj_ty_2Enum_2Enum,type,(surj__ty_2Enum_2Enum : $i > tp__ty_2Enum_2Enum)).
tff(stp_inj_surj_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X)) = X))).
tff(stp_inj_mem_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (mem(inj__ty_2Enum_2Enum(X),ty_2Enum_2Enum)))).
tff(stp_iso_mem_ty_2Enum_2Enum,axiom,( ! [X:$i] : (mem(X,ty_2Enum_2Enum) => (X = inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X)))))).
tff(tp_c_2Eiterate_2E_2E_2E,type,(c_2Eiterate_2E_2E_2E:$i)).
tff(mem_c_2Eiterate_2E_2E_2E,axiom,mem(c_2Eiterate_2E_2E_2E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))))).
tff(stp_fo_c_2Eiterate_2E_2E_2E,type,(fo__c_2Eiterate_2E_2E_2E:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Eiterate_2E_2E_2E,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ( ! [X2:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Eiterate_2E_2E_2E(X0,X1,X2)) = ap(ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X2))))))).
tff(tp_c_2Eiterate_2ESum,type,(c_2Eiterate_2ESum:del > $i)).
tff(mem_c_2Eiterate_2ESum,axiom,( ! [A_27a:del] : mem(c_2Eiterate_2ESum(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))))).
tff(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
tff(mem_c_2Earithmetic_2E_3E_3D,axiom,mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))).
tff(stp_fo_c_2Earithmetic_2E_3E_3D,type,(fo__c_2Earithmetic_2E_3E_3D:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Earithmetic_2E_3E_3D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3E_3D(X0,X1)) = ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$i)).
tff(mem_c_2Earithmetic_2E_3E,axiom,mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))).
tff(stp_fo_c_2Earithmetic_2E_3E,type,(fo__c_2Earithmetic_2E_3E:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Earithmetic_2E_3E,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3E(X0,X1)) = ap(ap(c_2Earithmetic_2E_3E,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Enumeral_2EiiSUC,type,(c_2Enumeral_2EiiSUC:$i)).
tff(mem_c_2Enumeral_2EiiSUC,axiom,mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Enumeral_2EiiSUC,type,(fo__c_2Enumeral_2EiiSUC:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2EiiSUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiiSUC(X0)) = ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
tff(mem_c_2Earithmetic_2EEVEN,axiom,mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool))).
tff(stp_fo_c_2Earithmetic_2EEVEN,type,(fo__c_2Earithmetic_2EEVEN:(tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Earithmetic_2EEVEN,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2EEVEN(X0)) = ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Enumeral_2Eonecount,type,(c_2Enumeral_2Eonecount:$i)).
tff(mem_c_2Enumeral_2Eonecount,axiom,mem(c_2Enumeral_2Eonecount,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Enumeral_2Eonecount,type,(fo__c_2Enumeral_2Eonecount:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2Eonecount,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2Eonecount(X0,X1)) = ap(ap(c_2Enumeral_2Eonecount,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Enumeral_2Eexactlog,type,(c_2Enumeral_2Eexactlog:$i)).
tff(mem_c_2Enumeral_2Eexactlog,axiom,mem(c_2Enumeral_2Eexactlog,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Enumeral_2Eexactlog,type,(fo__c_2Enumeral_2Eexactlog:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2Eexactlog,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2Eexactlog(X0)) = ap(c_2Enumeral_2Eexactlog,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
tff(mem_c_2Eprim__rec_2EPRE,axiom,mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Eprim__rec_2EPRE(X0)) = ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Earithmetic_2EDIV2,type,(c_2Earithmetic_2EDIV2:$i)).
tff(mem_c_2Earithmetic_2EDIV2,axiom,mem(c_2Earithmetic_2EDIV2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Earithmetic_2EDIV2,type,(fo__c_2Earithmetic_2EDIV2:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2EDIV2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EDIV2(X0)) = ap(c_2Earithmetic_2EDIV2,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Enumeral_2Etexp__help,type,(c_2Enumeral_2Etexp__help:$i)).
tff(mem_c_2Enumeral_2Etexp__help,axiom,mem(c_2Enumeral_2Etexp__help,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Enumeral_2Etexp__help,type,(fo__c_2Enumeral_2Etexp__help:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2Etexp__help,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2Etexp__help(X0,X1)) = ap(ap(c_2Enumeral_2Etexp__help,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Ebool_2ELET,type,(c_2Ebool_2ELET:(del * del) > $i)).
tff(mem_c_2Ebool_2ELET,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))))).
tff(tp_c_2Enumeral_2EiDUB,type,(c_2Enumeral_2EiDUB:$i)).
tff(mem_c_2Enumeral_2EiDUB,axiom,mem(c_2Enumeral_2EiDUB,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Enumeral_2EiDUB,type,(fo__c_2Enumeral_2EiDUB:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiDUB(X0)) = ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
tff(mem_c_2Enumeral_2EiZ,axiom,mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2EiZ(X0)) = ap(c_2Enumeral_2EiZ,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Enumeral_2Einternal__mult,type,(c_2Enumeral_2Einternal__mult:$i)).
tff(mem_c_2Enumeral_2Einternal__mult,axiom,mem(c_2Enumeral_2Einternal__mult,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Enumeral_2Einternal__mult,type,(fo__c_2Enumeral_2Einternal__mult:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enumeral_2Einternal__mult,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enumeral_2Einternal__mult(X0,X1)) = ap(ap(c_2Enumeral_2Einternal__mult,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Epair_2EFST,type,(c_2Epair_2EFST:(del * del) > $i)).
tff(mem_c_2Epair_2EFST,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Epair_2EFST(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27a))))).
tff(tp_c_2Epair_2ESND,type,(c_2Epair_2ESND:(del * del) > $i)).
tff(mem_c_2Epair_2ESND,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Epair_2ESND(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27b))))).
tff(tp_c_2Epred__set_2EEMPTY,type,(c_2Epred__set_2EEMPTY:del > $i)).
tff(mem_c_2Epred__set_2EEMPTY,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)))).
tff(tp_c_2Epred__set_2EUNIV,type,(c_2Epred__set_2EUNIV:del > $i)).
tff(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)))).
tff(tp_c_2Epred__set_2ESUBSET,type,(c_2Epred__set_2ESUBSET:del > $i)).
tff(mem_c_2Epred__set_2ESUBSET,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))).
tff(tp_c_2Epred__set_2EINTER,type,(c_2Epred__set_2EINTER:del > $i)).
tff(mem_c_2Epred__set_2EINTER,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EINTER(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))).
tff(tp_c_2Epred__set_2EFINITE,type,(c_2Epred__set_2EFINITE:del > $i)).
tff(mem_c_2Epred__set_2EFINITE,axiom,( ! [A_27a:del] : mem(c_2Epred__set_2EFINITE(A_27a),arr(arr(A_27a,bool),bool)))).
tff(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$i)).
tff(mem_c_2Ereal_2Ereal__sub,axiom,mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Ereal__sub,type,(fo__c_2Ereal_2Ereal__sub:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__sub(X0,X1)) = ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Erealax_2Einv,type,(c_2Erealax_2Einv:$i)).
tff(mem_c_2Erealax_2Einv,axiom,mem(c_2Erealax_2Einv,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Erealax_2Einv,type,(fo__c_2Erealax_2Einv:(tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Erealax_2Einv,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Einv(X0)) = ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ereal_2Eabs,type,(c_2Ereal_2Eabs:$i)).
tff(mem_c_2Ereal_2Eabs,axiom,mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ereal_2Eabs,type,(fo__c_2Ereal_2Eabs:(tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Eabs,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Eabs(X0)) = ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
tff(mem_c_2Enum_2ESUC,axiom,mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Enum_2ESUC(X0)) = ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Ebool_2E_3F,type,(c_2Ebool_2E_3F:del > $i)).
tff(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a:del] : mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))).
tff(ax_ex_p,axiom,( ! [A:del] : ( ! [Q:$i] : (mem(Q,arr(A,bool)) => (p(ap(c_2Ebool_2E_3F(A),Q)) <=> (? [X:$i] : (mem(X,A) & p(ap(Q,X))))))))).
tff(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
tff(mem_c_2Earithmetic_2E_2D,axiom,mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0,X1)) = ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
tff(mem_c_2Earithmetic_2E_2B,axiom,mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2B(X0,X1)) = ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Erealax_2Ereal__add,type,(c_2Erealax_2Ereal__add:$i)).
tff(mem_c_2Erealax_2Ereal__add,axiom,mem(c_2Erealax_2Ereal__add,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Erealax_2Ereal__add,type,(fo__c_2Erealax_2Ereal__add:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Erealax_2Ereal__add,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__add(X0,X1)) = ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
tff(mem_c_2Earithmetic_2E_2A,axiom,mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2A(X0,X1)) = ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Earithmetic_2EODD,type,(c_2Earithmetic_2EODD:$i)).
tff(mem_c_2Earithmetic_2EODD,axiom,mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool))).
tff(stp_fo_c_2Earithmetic_2EODD,type,(fo__c_2Earithmetic_2EODD:(tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Earithmetic_2EODD,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2EODD(X0)) = ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
tff(mem_c_2Earithmetic_2EEXP,axiom,mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))).
tff(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EEXP(X0,X1)) = ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
tff(mem_c_2Earithmetic_2EBIT2,axiom,mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EBIT2(X0)) = ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
tff(mem_c_2Ereal_2Epow,axiom,mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Epow(X0,X1)) = ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Erealax_2Ereal__mul,type,(c_2Erealax_2Ereal__mul:$i)).
tff(mem_c_2Erealax_2Ereal__mul,axiom,mem(c_2Erealax_2Ereal__mul,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Erealax_2Ereal__mul,type,(fo__c_2Erealax_2Ereal__mul:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Erealax_2Ereal__mul,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__mul(X0,X1)) = ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Emarker_2Eunint,type,(c_2Emarker_2Eunint:del > $i)).
tff(mem_c_2Emarker_2Eunint,axiom,( ! [A_27a:del] : mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)))).
tff(tp_c_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:del > $i)).
tff(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))))).
tff(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
tff(mem_c_2Ereal_2E_2F,axiom,mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2E_2F,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2E_2F(X0,X1)) = ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
tff(mem_c_2Ebool_2ET,axiom,mem(c_2Ebool_2ET,bool)).
tff(stp_fo_c_2Ebool_2ET,type,(fo__c_2Ebool_2ET:tp__o)).
tff(stp_eq_fo_c_2Ebool_2ET,axiom,(inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET)).
tff(ax_true_p,axiom,p(c_2Ebool_2ET)).
tff(tp_c_2Ereal_2Ereal__lte,type,(c_2Ereal_2Ereal__lte:$i)).
tff(mem_c_2Ereal_2Ereal__lte,axiom,mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))).
tff(stp_fo_c_2Ereal_2Ereal__lte,type,(fo__c_2Ereal_2Ereal__lte:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Ereal_2Ereal__lte,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Ereal_2Ereal__lte(X0,X1)) = ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Erealax_2Ereal__neg,type,(c_2Erealax_2Ereal__neg:$i)).
tff(mem_c_2Erealax_2Ereal__neg,axiom,mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Erealax_2Ereal__neg,type,(fo__c_2Erealax_2Ereal__neg:(tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Erealax_2Ereal__neg,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Erealax_2Ereal__neg(X0)) = ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
tff(mem_c_2Ereal_2Ereal__of__num,axiom,mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__of__num(X0)) = ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Epair_2EUNCURRY,type,(c_2Epair_2EUNCURRY:(del * del * del) > $i)).
tff(mem_c_2Epair_2EUNCURRY,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : 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))))))).
tff(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del * del) > $i)).
tff(mem_c_2Epair_2E_2C,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))))))).
tff(tp_c_2Epred__set_2EGSPEC,type,(c_2Epred__set_2EGSPEC:(del * del) > $i)).
tff(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool)))))).
tff(tp_c_2Ebool_2EIN,type,(c_2Ebool_2EIN:del > $i)).
tff(mem_c_2Ebool_2EIN,axiom,( ! [A_27a:del] : mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))))).
tff(tp_c_2Erealax_2Ereal__lt,type,(c_2Erealax_2Ereal__lt:$i)).
tff(mem_c_2Erealax_2Ereal__lt,axiom,mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))).
tff(stp_fo_c_2Erealax_2Ereal__lt,type,(fo__c_2Erealax_2Ereal__lt:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Erealax_2Ereal__lt,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Erealax_2Ereal__lt(X0,X1)) = ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
tff(mem_c_2Earithmetic_2EZERO,axiom,mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum)).
tff(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,(inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
tff(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
tff(mem_c_2Earithmetic_2EBIT1,axiom,mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EBIT1(X0)) = ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Earithmetic_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
tff(mem_c_2Earithmetic_2ENUMERAL,axiom,mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))).
tff(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2ENUMERAL(X0)) = ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
tff(mem_c_2Earithmetic_2E_3C_3D,axiom,mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))).
tff(stp_fo_c_2Earithmetic_2E_3C_3D,type,(fo__c_2Earithmetic_2E_3C_3D:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Earithmetic_2E_3C_3D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0,X1)) = ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$i)).
tff(mem_c_2Eprim__rec_2E_3C,axiom,mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool)))).
tff(stp_fo_c_2Eprim__rec_2E_3C,type,(fo__c_2Eprim__rec_2E_3C:(tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum) > tp__o)).
tff(stp_eq_fo_c_2Eprim__rec_2E_3C,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1)) = ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
tff(mem_c_2Enum_2E0,axiom,mem(c_2Enum_2E0,ty_2Enum_2Enum)).
tff(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Enum_2E0,axiom,(inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0)).
tff(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
tff(mem_c_2Ebool_2EF,axiom,mem(c_2Ebool_2EF,bool)).
tff(stp_fo_c_2Ebool_2EF,type,(fo__c_2Ebool_2EF:tp__o)).
tff(stp_eq_fo_c_2Ebool_2EF,axiom,(inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF)).
tff(ax_false_p,axiom,(~ p(c_2Ebool_2EF))).
tff(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$i)).
tff(mem_c_2Ebool_2E_2F_5C,axiom,mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool)))).
tff(stp_fo_c_2Ebool_2E_2F_5C,type,(fo__c_2Ebool_2E_2F_5C:(tp__o * tp__o) > tp__o)).
tff(stp_eq_fo_c_2Ebool_2E_2F_5C,axiom,( ! [X0:tp__o] : ( ! [X1:tp__o] : (inj__o(fo__c_2Ebool_2E_2F_5C(X0,X1)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X0)),inj__o(X1)))))).
tff(ax_and_p,axiom,( ! [Q:$i] : (mem(Q,bool) => ( ! [R:$i] : (mem(R,bool) => (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <=> (p(Q) & p(R)))))))).
tff(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:del > $i)).
tff(mem_c_2Emin_2E_3D,axiom,( ! [A_27a:del] : mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))).
tff(ax_eq_p,axiom,( ! [A:del] : ( ! [X:$i] : (mem(X,A) => ( ! [Y:$i] : (mem(Y,A) => (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <=> (X = Y)))))))).
tff(tp_c_2Ebool_2E_5C_2F,type,(c_2Ebool_2E_5C_2F:$i)).
tff(mem_c_2Ebool_2E_5C_2F,axiom,mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool)))).
tff(stp_fo_c_2Ebool_2E_5C_2F,type,(fo__c_2Ebool_2E_5C_2F:(tp__o * tp__o) > tp__o)).
tff(stp_eq_fo_c_2Ebool_2E_5C_2F,axiom,( ! [X0:tp__o] : ( ! [X1:tp__o] : (inj__o(fo__c_2Ebool_2E_5C_2F(X0,X1)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(X0)),inj__o(X1)))))).
tff(ax_or_p,axiom,( ! [Q:$i] : (mem(Q,bool) => ( ! [R:$i] : (mem(R,bool) => (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <=> (p(Q) | p(R)))))))).
tff(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
tff(mem_c_2Ebool_2E_7E,axiom,mem(c_2Ebool_2E_7E,arr(bool,bool))).
tff(stp_fo_c_2Ebool_2E_7E,type,(fo__c_2Ebool_2E_7E:(tp__o) > tp__o)).
tff(stp_eq_fo_c_2Ebool_2E_7E,axiom,( ! [X0:tp__o] : (inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0))))).
tff(ax_neg_p,axiom,( ! [Q:$i] : (mem(Q,bool) => (p(ap(c_2Ebool_2E_7E,Q)) <=> (~ p(Q)))))).
tff(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$i)).
tff(mem_c_2Emin_2E_3D_3D_3E,axiom,mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool)))).
tff(stp_fo_c_2Emin_2E_3D_3D_3E,type,(fo__c_2Emin_2E_3D_3D_3E:(tp__o * tp__o) > tp__o)).
tff(stp_eq_fo_c_2Emin_2E_3D_3D_3E,axiom,( ! [X0:tp__o] : ( ! [X1:tp__o] : (inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)))))).
tff(ax_imp_p,axiom,( ! [Q:$i] : (mem(Q,bool) => ( ! [R:$i] : (mem(R,bool) => (p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <=> (p(Q) => p(R)))))))).
tff(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:del > $i)).
tff(mem_c_2Ebool_2E_21,axiom,( ! [A_27a:del] : mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))).
tff(ax_all_p,axiom,( ! [A:del] : ( ! [Q:$i] : (mem(Q,arr(A,bool)) => (p(ap(c_2Ebool_2E_21(A),Q)) <=> ( ! [X:$i] : (mem(X,A) => p(ap(Q,X))))))))).
tff(conj_thm_2Earithmetic_2EADD__CLAUSES,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0m))) = V0m) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V0m) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0m))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))))))).
tff(conj_thm_2Earithmetic_2EADD__SYM,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m)))))))).
tff(conj_thm_2Earithmetic_2EADD__ASSOC,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(V2p))))))))).
tff(conj_thm_2Earithmetic_2EZERO__LESS__EQ,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n)))))).
tff(conj_thm_2Earithmetic_2ENOT__LESS,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m)))))))).
tff(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m)))))))).
tff(conj_thm_2Earithmetic_2EADD1,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0m))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))).
tff(conj_thm_2Earithmetic_2EMULT__RIGHT__1,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0m)))).
tff(conj_thm_2Earithmetic_2EMULT__CLAUSES,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0m))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0m))) = V0m) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0m) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0m))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(V1n)))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))))))))).
tff(conj_thm_2Earithmetic_2EADD__EQ__0,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) = fo__c_2Enum_2E0) <=> ((V0m = fo__c_2Enum_2E0) & (V1n = fo__c_2Enum_2E0))))))).
tff(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p)))) => p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V2p))))))))).
tff(conj_thm_2Earithmetic_2EWOP,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Enum_2Enum,bool)) => ((? [V1n:tp__ty_2Enum_2Enum] : p(ap(V0P,inj__ty_2Enum_2Enum(V1n)))) => (? [V2n:tp__ty_2Enum_2Enum] : (p(ap(V0P,inj__ty_2Enum_2Enum(V2n))) & ( ! [V3m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V3m)),inj__ty_2Enum_2Enum(V2n))) => (~~ p(ap(V0P,inj__ty_2Enum_2Enum(V3m))))))))))))).
tff(conj_thm_2Earithmetic_2ECOMPLETE__INDUCTION,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Enum_2Enum,bool)) => (( ! [V1n:tp__ty_2Enum_2Enum] : (( ! [V2m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V1n))) => p(ap(V0P,inj__ty_2Enum_2Enum(V2m))))) => p(ap(V0P,inj__ty_2Enum_2Enum(V1n))))) => ( ! [V3n:tp__ty_2Enum_2Enum] : p(ap(V0P,inj__ty_2Enum_2Enum(V3n))))))))).
tff(conj_thm_2Earithmetic_2EEQ__LESS__EQ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((V0m = V1n) <=> (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m))))))))).
tff(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V2p)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p))))))))).
tff(conj_thm_2Earithmetic_2ENOT__LEQ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(V0m)))))))).
tff(conj_thm_2Earithmetic_2ENOT__NUM__EQ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ (V0m = V1n)) <=> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0m))),inj__ty_2Enum_2Enum(V1n))) | p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(V0m))))))))).
tff(conj_thm_2Earithmetic_2ESUC__ONE__ADD,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0m)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V2p)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V2p))),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Earithmetic_2ELE,lemma,((( ! [V0n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> (V0n = fo__c_2Enum_2E0))) & ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) <=> ((V1m = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) | p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))))))))).
tff(conj_thm_2Earithmetic_2ESUB__ELIM__THM,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Enum_2Enum,bool)) => ( ! [V1a:tp__ty_2Enum_2Enum] : ( ! [V2b:tp__ty_2Enum_2Enum] : (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1a)),inj__ty_2Enum_2Enum(V2b)))) <=> ( ! [V3d:tp__ty_2Enum_2Enum] : (((V2b = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1a)),inj__ty_2Enum_2Enum(V3d)))) => p(ap(V0P,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((V1a = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2b)),inj__ty_2Enum_2Enum(V3d)))) => p(ap(V0P,inj__ty_2Enum_2Enum(V3d))))))))))))).
tff(conj_thm_2Earithmetic_2EEXP__1,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0n))))).
tff(ax_thm_2Ebool_2EEXISTS__DEF,axiom,( ! [A_27a:del]: (c_2Ebool_2E_3F(A_27a) = f2(A_27a)))).
tff(ax_thm_2Ebool_2ELET__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: (c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a))))).
tff(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0t:$i] : (mem(V0t,arr(A_27a,A_27b)) => (f31(A_27b,A_27a,V0t) = V0t)))))).
tff(ax_thm_2Ebool_2ESELECT__AX,axiom,( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ( ! [V1x:$i] : (mem(V1x,A_27a) => (p(ap(V0P,V1x)) => p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)))))))))).
tff(ax_thm_2Ebool_2EIN__DEF,axiom,( ! [A_27a:del]: (c_2Ebool_2EIN(A_27a) = f33(A_27a)))).
tff(conj_thm_2Ebool_2ETRUTH,lemma,($true)).
tff(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,(( ! [V0t1:tp__o] : ( ! [V1t2:tp__o] : ((p(inj__o(V0t1)) => p(inj__o(V1t2))) => ((p(inj__o(V1t2)) => p(inj__o(V0t1))) => (p(inj__o(V0t1)) <=> p(inj__o(V1t2))))))))).
tff(conj_thm_2Ebool_2EFALSITY,lemma,(( ! [V0t:tp__o] : ($false => p(inj__o(V0t)))))).
tff(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,(( ! [V0t:tp__o] : (p(inj__o(V0t)) | (~~ p(inj__o(V0t))))))).
tff(conj_thm_2Ebool_2EFORALL__SIMP,lemma,(( ! [A_27a:del]: ( ! [V0t:tp__o] : (( ! [V1x:$i] : (mem(V1x,A_27a) => p(inj__o(V0t)))) <=> p(inj__o(V0t))))))).
tff(conj_thm_2Ebool_2EEXISTS__SIMP,lemma,(( ! [A_27a:del]: ( ! [V0t:tp__o] : ((? [V1x:$i] : (mem(V1x,A_27a) & p(inj__o(V0t)))) <=> p(inj__o(V0t))))))).
tff(conj_thm_2Ebool_2ECONJ__ASSOC,lemma,(( ! [V0t1:tp__o] : ( ! [V1t2:tp__o] : ( ! [V2t3:tp__o] : ((p(inj__o(V0t1)) & (p(inj__o(V1t2)) & p(inj__o(V2t3)))) <=> ((p(inj__o(V0t1)) & p(inj__o(V1t2))) & p(inj__o(V2t3))))))))).
tff(conj_thm_2Ebool_2EIMP__F,lemma,(( ! [V0t:tp__o] : ((p(inj__o(V0t)) => $false) => (~~ p(inj__o(V0t))))))).
tff(conj_thm_2Ebool_2EF__IMP,lemma,(( ! [V0t:tp__o] : ((~~ p(inj__o(V0t))) => (p(inj__o(V0t)) => $false))))).
tff(conj_thm_2Ebool_2EAND__CLAUSES,lemma,(( ! [V0t:tp__o] : ((($true & p(inj__o(V0t))) <=> p(inj__o(V0t))) & (((p(inj__o(V0t)) & $true) <=> p(inj__o(V0t))) & ((($false & p(inj__o(V0t))) <=> $false) & (((p(inj__o(V0t)) & $false) <=> $false) & ((p(inj__o(V0t)) & p(inj__o(V0t))) <=> p(inj__o(V0t)))))))))).
tff(conj_thm_2Ebool_2EOR__CLAUSES,lemma,(( ! [V0t:tp__o] : ((($true | p(inj__o(V0t))) <=> $true) & (((p(inj__o(V0t)) | $true) <=> $true) & ((($false | p(inj__o(V0t))) <=> p(inj__o(V0t))) & (((p(inj__o(V0t)) | $false) <=> p(inj__o(V0t))) & ((p(inj__o(V0t)) | p(inj__o(V0t))) <=> p(inj__o(V0t)))))))))).
tff(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,(( ! [V0t:tp__o] : ((($true => p(inj__o(V0t))) <=> p(inj__o(V0t))) & (((p(inj__o(V0t)) => $true) <=> $true) & ((($false => p(inj__o(V0t))) <=> $true) & (((p(inj__o(V0t)) => p(inj__o(V0t))) <=> $true) & ((p(inj__o(V0t)) => $false) <=> (~~ p(inj__o(V0t))))))))))).
tff(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,((( ! [V0t:tp__o] : ((~~ (~~ p(inj__o(V0t)))) <=> p(inj__o(V0t)))) & (((~~ ($true)) <=> $false) & ((~~ ($false)) <=> $true))))).
tff(conj_thm_2Ebool_2EEQ__REFL,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => (V0x = V0x)))))).
tff(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ((V0x = V0x) <=> $true)))))).
tff(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ( ! [V1y:$i] : (mem(V1y,A_27a) => ((V0x = V1y) <=> (V1y = V0x))))))))).
tff(conj_thm_2Ebool_2EFUN__EQ__THM,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27a,A_27b)) => ( ! [V1g:$i] : (mem(V1g,arr(A_27a,A_27b)) => ((V0f = V1g) <=> ( ! [V2x:$i] : (mem(V2x,A_27a) => (ap(V0f,V2x) = ap(V1g,V2x))))))))))))).
tff(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,(( ! [V0t:tp__o] : ((($true <=> p(inj__o(V0t))) <=> p(inj__o(V0t))) & (((p(inj__o(V0t)) <=> $true) <=> p(inj__o(V0t))) & ((($false <=> p(inj__o(V0t))) <=> (~~ p(inj__o(V0t)))) & ((p(inj__o(V0t)) <=> $false) <=> (~~ p(inj__o(V0t)))))))))).
tff(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,(( ! [A_27a:del]: ( ! [V0t1:$i] : (mem(V0t1,A_27a) => ( ! [V1t2:$i] : (mem(V1t2,A_27a) => ((ap(ap(ap(c_2Ebool_2ECOND(A_27a),inj__o(fo__c_2Ebool_2ET)),V0t1),V1t2) = V0t1) & (ap(ap(ap(c_2Ebool_2ECOND(A_27a),inj__o(fo__c_2Ebool_2EF)),V0t1),V1t2) = V1t2))))))))).
tff(conj_thm_2Ebool_2ENOT__FORALL__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ((~~ ( ! [V1x:$i] : (mem(V1x,A_27a) => p(ap(V0P,V1x))))) <=> (? [V2x:$i] : (mem(V2x,A_27a) & (~~ p(ap(V0P,V2x))))))))))).
tff(conj_thm_2Ebool_2ENOT__EXISTS__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ((~~ (? [V1x:$i] : (mem(V1x,A_27a) & p(ap(V0P,V1x))))) <=> ( ! [V2x:$i] : (mem(V2x,A_27a) => (~~ p(ap(V0P,V2x))))))))))).
tff(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ( ! [V1Q:tp__o] : ((? [V2x:$i] : (mem(V2x,A_27a) & (p(ap(V0P,V2x)) & p(inj__o(V1Q))))) <=> ((? [V3x:$i] : (mem(V3x,A_27a) & p(ap(V0P,V3x)))) & p(inj__o(V1Q)))))))))).
tff(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:tp__o] : ( ! [V1Q:$i] : (mem(V1Q,arr(A_27a,bool)) => ((? [V2x:$i] : (mem(V2x,A_27a) & (p(inj__o(V0P)) & p(ap(V1Q,V2x))))) <=> (p(inj__o(V0P)) & (? [V3x:$i] : (mem(V3x,A_27a) & p(ap(V1Q,V3x)))))))))))).
tff(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,lemma,(( ! [A_27a:del]: ( ! [V0Q:tp__o] : ( ! [V1P:$i] : (mem(V1P,arr(A_27a,bool)) => (( ! [V2x:$i] : (mem(V2x,A_27a) => (p(ap(V1P,V2x)) | p(inj__o(V0Q))))) <=> (( ! [V3x:$i] : (mem(V3x,A_27a) => p(ap(V1P,V3x)))) | p(inj__o(V0Q)))))))))).
tff(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:tp__o] : ( ! [V1Q:$i] : (mem(V1Q,arr(A_27a,bool)) => (( ! [V2x:$i] : (mem(V2x,A_27a) => (p(inj__o(V0P)) | p(ap(V1Q,V2x))))) <=> (p(inj__o(V0P)) | ( ! [V3x:$i] : (mem(V3x,A_27a) => p(ap(V1Q,V3x)))))))))))).
tff(conj_thm_2Ebool_2EDISJ__ASSOC,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : ( ! [V2C:tp__o] : ((p(inj__o(V0A)) | (p(inj__o(V1B)) | p(inj__o(V2C)))) <=> ((p(inj__o(V0A)) | p(inj__o(V1B))) | p(inj__o(V2C))))))))).
tff(conj_thm_2Ebool_2EDISJ__SYM,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : ((p(inj__o(V0A)) | p(inj__o(V1B))) <=> (p(inj__o(V1B)) | p(inj__o(V0A)))))))).
tff(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : (((~~ (p(inj__o(V0A)) & p(inj__o(V1B)))) <=> ((~~ p(inj__o(V0A))) | (~~ p(inj__o(V1B))))) & ((~~ (p(inj__o(V0A)) | p(inj__o(V1B)))) <=> ((~~ p(inj__o(V0A))) & (~~ p(inj__o(V1B)))))))))).
tff(conj_thm_2Ebool_2ELEFT__OR__OVER__AND,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : ( ! [V2C:tp__o] : ((p(inj__o(V0A)) | (p(inj__o(V1B)) & p(inj__o(V2C)))) <=> ((p(inj__o(V0A)) | p(inj__o(V1B))) & (p(inj__o(V0A)) | p(inj__o(V2C)))))))))).
tff(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : ( ! [V2C:tp__o] : (((p(inj__o(V1B)) & p(inj__o(V2C))) | p(inj__o(V0A))) <=> ((p(inj__o(V1B)) | p(inj__o(V0A))) & (p(inj__o(V2C)) | p(inj__o(V0A)))))))))).
tff(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : ((p(inj__o(V0A)) => p(inj__o(V1B))) <=> ((~~ p(inj__o(V0A))) | p(inj__o(V1B)))))))).
tff(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,(( ! [V0t:tp__o] : ((p(inj__o(V0t)) => $false) <=> (p(inj__o(V0t)) <=> $false))))).
tff(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,(( ! [V0t1:tp__o] : ( ! [V1t2:tp__o] : ( ! [V2t3:tp__o] : ((p(inj__o(V0t1)) => (p(inj__o(V1t2)) => p(inj__o(V2t3)))) <=> ((p(inj__o(V0t1)) & p(inj__o(V1t2))) => p(inj__o(V2t3))))))))).
tff(conj_thm_2Ebool_2EIMP__CONG,lemma,(( ! [V0x:tp__o] : ( ! [V1x_27:tp__o] : ( ! [V2y:tp__o] : ( ! [V3y_27:tp__o] : (((p(inj__o(V0x)) <=> p(inj__o(V1x_27))) & (p(inj__o(V1x_27)) => (p(inj__o(V2y)) <=> p(inj__o(V3y_27))))) => ((p(inj__o(V0x)) => p(inj__o(V2y))) <=> (p(inj__o(V1x_27)) => p(inj__o(V3y_27))))))))))).
tff(conj_thm_2Ebool_2ECOND__CONG,lemma,(( ! [A_27a:del]: ( ! [V0P:tp__o] : ( ! [V1Q:tp__o] : ( ! [V2x:$i] : (mem(V2x,A_27a) => ( ! [V3x_27:$i] : (mem(V3x_27,A_27a) => ( ! [V4y:$i] : (mem(V4y,A_27a) => ( ! [V5y_27:$i] : (mem(V5y_27,A_27a) => (((p(inj__o(V0P)) <=> p(inj__o(V1Q))) & ((p(inj__o(V1Q)) => (V2x = V3x_27)) & ((~~ p(inj__o(V1Q))) => (V4y = V5y_27)))) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a),inj__o(V0P)),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),inj__o(V1Q)),V3x_27),V5y_27)))))))))))))))).
tff(conj_thm_2Ebool_2EMONO__NOT__EQ,lemma,(( ! [V0y:tp__o] : ( ! [V1x:tp__o] : ((p(inj__o(V0y)) => p(inj__o(V1x))) <=> ((~~ p(inj__o(V1x))) => (~~ p(inj__o(V0y))))))))).
tff(conj_thm_2Ebool_2EUNWIND__THM2,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ( ! [V1a:$i] : (mem(V1a,A_27a) => ((? [V2x:$i] : (mem(V2x,A_27a) & ((V2x = V1a) & p(ap(V0P,V2x))))) <=> p(ap(V0P,V1a)))))))))).
tff(conj_thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ( ! [V1Q:tp__o] : (((? [V2x:$i] : (mem(V2x,A_27a) & p(ap(V0P,V2x)))) => p(inj__o(V1Q))) <=> ( ! [V3x:$i] : (mem(V3x,A_27a) => (p(ap(V0P,V3x)) => p(inj__o(V1Q)))))))))))).
tff(conj_thm_2Ecardinal_2Enum__INFINITE,lemma,((~~ p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))))).
tff(conj_thm_2Ecardinal_2ELT,lemma,((( ! [V0m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> $false)) & ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1m)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) <=> ((V1m = V2n) | p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))))))))).
tff(conj_thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27a,A_27b)) => (( ! [V1x:$i] : (mem(V1x,A_27a) => ( ! [V2y:$i] : (mem(V2y,A_27a) => ((ap(V0f,V1x) = ap(V0f,V2y)) => (V1x = V2y)))))) <=> (? [V3g:$i] : (mem(V3g,arr(A_27b,A_27a)) & ( ! [V4x:$i] : (mem(V4x,A_27a) => (ap(V3g,ap(V0f,V4x)) = V4x)))))))))))).
tff(conj_thm_2Ecardinal_2ECONJ__ACI,lemma,(( ! [V0r:tp__o] : ( ! [V1p:tp__o] : ( ! [V2q:tp__o] : (((p(inj__o(V1p)) & p(inj__o(V2q))) <=> (p(inj__o(V2q)) & p(inj__o(V1p)))) & ((((p(inj__o(V1p)) & p(inj__o(V2q))) & p(inj__o(V0r))) <=> (p(inj__o(V1p)) & (p(inj__o(V2q)) & p(inj__o(V0r))))) & (((p(inj__o(V1p)) & (p(inj__o(V2q)) & p(inj__o(V0r)))) <=> (p(inj__o(V2q)) & (p(inj__o(V1p)) & p(inj__o(V0r))))) & (((p(inj__o(V1p)) & p(inj__o(V1p))) <=> p(inj__o(V1p))) & ((p(inj__o(V1p)) & (p(inj__o(V1p)) & p(inj__o(V2q)))) <=> (p(inj__o(V1p)) & p(inj__o(V2q))))))))))))).
tff(conj_thm_2Ecardinal_2Ele__c,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => (p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) <=> (? [V2f:$i] : (mem(V2f,arr(A_27a,A_27b)) & (( ! [V3x:$i] : (mem(V3x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V3x)),V1t))))) & ( ! [V4x:$i] : (mem(V4x,A_27a) => ( ! [V5y:$i] : (mem(V5y,A_27a) => ((p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V0s)) & (p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V0s)) & (ap(V2f,V4x) = ap(V2f,V5y)))) => (V4x = V5y)))))))))))))))))).
tff(conj_thm_2Ecardinal_2ELE__C,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => (p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) <=> (? [V2g:$i] : (mem(V2g,arr(A_27b,A_27a)) & ( ! [V3x:$i] : (mem(V3x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) => (? [V4y:$i] : (mem(V4y,A_27b) & (p(ap(ap(c_2Ebool_2EIN(A_27b),V4y),V1t)) & (ap(V2g,V4y) = V3x)))))))))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__LE__REFL,lemma,(( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27a),V0s),V0s))))))).
tff(conj_thm_2Ecardinal_2ECARD__LE__TRANS,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => ( ! [V2u:$i] : (mem(V2u,arr(A_27c,bool)) => ((p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27c),V1t),V2u))) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27c),V0s),V2u)))))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__LT__IMP__LE,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => ((~~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27a),V1t),V0s))) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__LE__ANTISYM,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => ((p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27a),V1t),V0s))) <=> p(ap(ap(c_2Ecardinal_2Ecardeq(A_27a,A_27b),V0s),V1t))))))))))).
tff(conj_thm_2Ecardinal_2EINFINITE__CARD__LE,lemma,(( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ((~~ p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))) <=> p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Enum_2Enum,A_27a),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),V0s)))))))).
tff(conj_thm_2Ecardinal_2Emul__c,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => (ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t) = 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)),f1869(A_27a,A_27b,V1t,V0s)))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__LE__MUL,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1s_27:$i] : (mem(V1s_27,arr(A_27b,bool)) => ( ! [V2t:$i] : (mem(V2t,arr(A_27c,bool)) => ( ! [V3t_27:$i] : (mem(V3t_27,arr(A_27d,bool)) => ((p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1s_27)) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27c,A_27d),V2t),V3t_27))) => p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Epair_2Eprod(A_27a,A_27c),ty_2Epair_2Eprod(A_27b,A_27d)),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27c),V0s),V2t)),ap(ap(c_2Epred__set_2ECROSS(A_27b,A_27d),V1s_27),V3t_27)))))))))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__MUL__ABSORB__LE,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => (((~~ p(ap(c_2Epred__set_2EFINITE(A_27b),V1t))) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))) => p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t)),V1t))))))))))).
tff(conj_thm_2Ecardinal_2ECARD__MUL2__ABSORB__LE,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27b,bool)) => ( ! [V2u:$i] : (mem(V2u,arr(A_27c,bool)) => (((~~ p(ap(c_2Epred__set_2EFINITE(A_27c),V2u))) & (p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27c),V0s),V2u)) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27c),V1t),V2u)))) => p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0s),V1t)),V2u)))))))))))))).
tff(conj_thm_2Ecardinal_2ECANTOR__THM__UNIV,lemma,(( ! [A_27a:del]: (~~ p(ap(ap(c_2Ecardinal_2Ecardleq(arr(A_27a,bool),A_27a),c_2Epred__set_2EUNIV(arr(A_27a,bool))),c_2Epred__set_2EUNIV(A_27a))))))).
tff(conj_thm_2Ecardinal_2EIN__ELIM__PAIR__THM,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,arr(A_27b,bool))) => ( ! [V1a:$i] : (mem(V1a,A_27a) => ( ! [V2b:$i] : (mem(V2b,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),V1a),V2b)),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)),f1886(A_27a,A_27b,V0P))))) <=> p(ap(ap(V0P,V1a),V2b))))))))))))).
tff(ax_thm_2Ecombin_2ES__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: (c_2Ecombin_2ES(A_27a,A_27b,A_27c) = f71(A_27c,A_27b,A_27a)))))).
tff(ax_thm_2Ecombin_2EC__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: (c_2Ecombin_2EC(A_27a,A_27b,A_27c) = f74(A_27a,A_27c,A_27b)))))).
tff(ax_thm_2Ecombin_2Eo__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27c,A_27b)) => ( ! [V1g:$i] : (mem(V1g,arr(A_27a,A_27c)) => (ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g) = f77(A_27b,A_27c,A_27a,V1g,V0f)))))))))).
tff(conj_thm_2Ecombin_2EI__THM,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => (ap(c_2Ecombin_2EI(A_27a),V0x) = V0x)))))).
tff(conj_thm_2Ecombin_2EI__o__ID,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27a,A_27b)) => ((ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)),V0f) = V0f) & (ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27a),V0f),c_2Ecombin_2EI(A_27a)) = V0f)))))))).
tff(conj_thm_2Eiterate_2ESUP,lemma,(( ! [V0s:$i] : (mem(V0s,arr(ty_2Erealax_2Ereal,bool)) => (((~~ (V0s = c_2Epred__set_2EEMPTY(ty_2Erealax_2Ereal))) & (? [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ebool_2EIN(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2x)),V0s)) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V1b))))))) => (( ! [V3x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ebool_2EIN(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V3x)),V0s)) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V3x)),ap(c_2Ereal_2Esup,V0s))))) & ( ! [V4b:tp__ty_2Erealax_2Ereal] : (( ! [V5x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ebool_2EIN(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V5x)),V0s)) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V5x)),inj__ty_2Erealax_2Ereal(V4b))))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Esup,V0s)),inj__ty_2Erealax_2Ereal(V4b))))))))))).
tff(conj_thm_2Eiterate_2EREAL__SUP__LE__S,lemma,(( ! [V0s:$i] : (mem(V0s,arr(ty_2Erealax_2Ereal,bool)) => ( ! [V1b:tp__ty_2Erealax_2Ereal] : (((~~ (V0s = c_2Epred__set_2EEMPTY(ty_2Erealax_2Ereal))) & ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ebool_2EIN(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2x)),V0s)) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V1b)))))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Esup,V0s)),inj__ty_2Erealax_2Ereal(V1b))))))))).
tff(conj_thm_2Eiterate_2EFINITE__NUMSEG,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : p(ap(c_2Epred__set_2EFINITE(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Eiterate_2ENUMSEG__SING,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V0n)) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V0n)),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)))))).
tff(conj_thm_2Eiterate_2ENUMSEG__EMPTY,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)) = c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m)))))))).
tff(conj_thm_2Eiterate_2ESUBSET__NUMSEG,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ( ! [V3q:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V2p)),inj__ty_2Enum_2Enum(V3q)))) <=> (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V0m))) | (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2p)),inj__ty_2Enum_2Enum(V0m))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(V3q)))))))))))).
tff(conj_thm_2Eiterate_2ESUM__CLAUSES,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: (( ! [V0f:$i] : (mem(V0f,arr(A_27a,ty_2Erealax_2Ereal)) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0f)) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) & ( ! [V1x:$i] : (mem(V1x,A_27b) => ( ! [V2f:$i] : (mem(V2f,arr(A_27b,ty_2Erealax_2Ereal)) => ( ! [V3s:$i] : (mem(V3s,arr(A_27b,bool)) => (p(ap(c_2Epred__set_2EFINITE(A_27b),V3s)) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(A_27b),ap(ap(c_2Epred__set_2EINSERT(A_27b),V1x),V3s)),V2f)) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ebool_2EIN(A_27b),V1x),V3s)),ap(ap(c_2Eiterate_2ESum(A_27b),V3s),V2f)),ap(ap(c_2Erealax_2Ereal__add,ap(V2f,V1x)),ap(ap(c_2Eiterate_2ESum(A_27b),V3s),V2f))))))))))))))))).
tff(conj_thm_2Eiterate_2ESUM__SING,lemma,(( ! [A_27a:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27a,ty_2Erealax_2Ereal)) => ( ! [V1x:$i] : (mem(V1x,A_27a) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))),V0f)) = surj__ty_2Erealax_2Ereal(ap(V0f,V1x)))))))))).
tff(conj_thm_2Eiterate_2ESUM__RESTRICT__SET,lemma,(( ! [A_27a:del]: ( ! [V0P:$i] : (mem(V0P,arr(A_27a,bool)) => ( ! [V1s:$i] : (mem(V1s,arr(A_27a,bool)) => ( ! [V2f:$i] : (mem(V2f,arr(A_27a,ty_2Erealax_2Ereal)) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f3315(A_27a,V0P,V1s))),V2f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(A_27a),V1s),f3365(A_27a,V2f,V0P))))))))))))).
tff(conj_thm_2Eiterate_2ESUM__SUBSET__SIMPLE,lemma,(( ! [A_27a:del]: ( ! [V0u:$i] : (mem(V0u,arr(A_27a,bool)) => ( ! [V1v:$i] : (mem(V1v,arr(A_27a,bool)) => ( ! [V2f:$i] : (mem(V2f,arr(A_27a,ty_2Erealax_2Ereal)) => ((p(ap(c_2Epred__set_2EFINITE(A_27a),V1v)) & (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0u),V1v)) & ( ! [V3x:$i] : (mem(V3x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1v),V0u))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(V2f,V3x)))))))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Eiterate_2ESum(A_27a),V0u),V2f)),ap(ap(c_2Eiterate_2ESum(A_27a),V1v),V2f))))))))))))).
tff(conj_thm_2Eiterate_2ESUM__EQ__NUMSEG,lemma,(( ! [V0f:$i] : (mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : (mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : (( ! [V4i:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V4i))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V4i)),inj__ty_2Enum_2Enum(V3n)))) => (surj__ty_2Erealax_2Ereal(ap(V0f,inj__ty_2Enum_2Enum(V4i))) = surj__ty_2Erealax_2Ereal(ap(V1g,inj__ty_2Enum_2Enum(V4i)))))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(V3n))),V1g)))))))))))).
tff(conj_thm_2Eiterate_2ESUM__CLAUSES__LEFT,lemma,(( ! [V0f:$i] : (mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(V0f,inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V2n))),V0f))))))))))).
tff(conj_thm_2Eiterate_2ESUM__CLAUSES__RIGHT,lemma,(( ! [V0f:$i] : (mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V2n))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f)) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V1m)),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),V0f)),ap(V0f,inj__ty_2Enum_2Enum(V2n)))))))))))).
tff(conj_thm_2Eiterate_2ESUM__COMBINE__R,lemma,(( ! [V0f:$i] : (mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3p:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V3p)))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n))),V0f)),ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V3p))),V0f))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Eiterate_2ESum(ty_2Enum_2Enum),ap(ap(c_2Eiterate_2E_2E_2E,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V3p))),V0f))))))))))).
tff(conj_thm_2Enum_2EINDUCTION,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Enum_2Enum,bool)) => ((p(ap(V0P,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ( ! [V1n:tp__ty_2Enum_2Enum] : (p(ap(V0P,inj__ty_2Enum_2Enum(V1n))) => p(ap(V0P,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n))))))) => ( ! [V2n:tp__ty_2Enum_2Enum] : p(ap(V0P,inj__ty_2Enum_2Enum(V2n))))))))).
tff(conj_thm_2Enumeral_2Enumeral__suc,lemma,(((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) & (( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))))) & ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V1n)))))))))).
tff(conj_thm_2Enumeral_2Enumeral__distrib,lemma,((( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))) = V0n)) & (( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V1n)) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V3m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2n)),inj__ty_2Enum_2Enum(V3m)))))))) & (( ! [V4n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V4n))) = fo__c_2Enum_2E0)) & (( ! [V5n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V5n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V6n:tp__ty_2Enum_2Enum] : ( ! [V7m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V6n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V7m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V6n)),inj__ty_2Enum_2Enum(V7m))))))) & (( ! [V8n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V8n))) = fo__c_2Enum_2E0)) & (( ! [V9n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V9n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = V9n)) & (( ! [V10n:tp__ty_2Enum_2Enum] : ( ! [V11m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V10n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V11m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V10n)),inj__ty_2Enum_2Enum(V11m))))))) & (( ! [V12n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V12n))))) = fo__c_2Enum_2E0)) & (( ! [V13n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V13n))))) = fo__c_2Enum_2E0)) & (( ! [V14n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V14n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & (( ! [V15n:tp__ty_2Enum_2Enum] : ( ! [V16m:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V15n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V16m)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,inj__ty_2Enum_2Enum(V15n)),inj__ty_2Enum_2Enum(V16m))))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & (( ! [V17n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V17n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V17n)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (( ! [V18n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V18n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,inj__ty_2Enum_2Enum(V18n)))))) & (( ! [V19n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V19n))) = fo__c_2Enum_2E0) <=> (V19n = fo__c_2Earithmetic_2EZERO))) & (( ! [V20n:tp__ty_2Enum_2Enum] : ((fo__c_2Enum_2E0 = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V20n)))) <=> (V20n = fo__c_2Earithmetic_2EZERO))) & (( ! [V21n:tp__ty_2Enum_2Enum] : ( ! [V22m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V21n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V22m)))) <=> (V21n = V22m)))) & (( ! [V23n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V23n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> $false)) & (( ! [V24n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V24n)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V24n))))) & (( ! [V25n:tp__ty_2Enum_2Enum] : ( ! [V26m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V25n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V26m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V25n)),inj__ty_2Enum_2Enum(V26m)))))) & (( ! [V27n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V27n))) <=> $false)) & (( ! [V28n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V28n))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V28n))))) & (( ! [V29n:tp__ty_2Enum_2Enum] : ( ! [V30m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V29n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V30m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V30m)),inj__ty_2Enum_2Enum(V29n)))))) & (( ! [V31n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V31n))) <=> $true)) & (( ! [V32n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V32n))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V32n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & (( ! [V33n:tp__ty_2Enum_2Enum] : ( ! [V34m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V33n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V34m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V33n)),inj__ty_2Enum_2Enum(V34m)))))) & (( ! [V35n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(V35n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) <=> $true)) & (( ! [V36n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E_3D,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V36n))) <=> (V36n = fo__c_2Enum_2E0))) & (( ! [V37n:tp__ty_2Enum_2Enum] : ( ! [V38m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V37n))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V38m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V38m)),inj__ty_2Enum_2Enum(V37n)))))) & (( ! [V39n:tp__ty_2Enum_2Enum] : (p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V39n)))) <=> p(ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(V39n))))) & (( ! [V40n:tp__ty_2Enum_2Enum] : (p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V40n)))) <=> p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(V40n))))) & ((~~ p(ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Enumeral_2Enumeral__add,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = V0n) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = V0n) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(V0n)))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,inj__ty_2Enum_2Enum(V0n)))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & (surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))))))))))))))))))))))))).
tff(conj_thm_2Enumeral_2Enumeral__eq,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((fo__c_2Earithmetic_2EZERO = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) <=> $false) & (((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO) <=> $false) & (((fo__c_2Earithmetic_2EZERO = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n)))) <=> $false) & (((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO) <=> $false) & (((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> $false) & (((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> $false) & (((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> (V0n = V1m)) & ((surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> (V0n = V1m))))))))))))).
tff(conj_thm_2Enumeral_2Enumeral__lt,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) <=> $true) & ((p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n)))) <=> $true) & ((p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) <=> $false) & ((p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> (~~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n))))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))))))))))).
tff(conj_thm_2Enumeral_2Enumeral__lte,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n))) <=> $true) & ((p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) <=> $false) & ((p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) <=> $false) & ((p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1m)))) <=> (~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n))))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))))))))))).
tff(conj_thm_2Enumeral_2EiDUB__removal,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(V0n))))) & ((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))))) & (surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO)))))).
tff(conj_thm_2Enumeral_2Enumeral__mult,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))),inj__ty_2Enum_2Enum(V1m))))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))),inj__ty_2Enum_2Enum(V1m))))))))))))).
tff(conj_thm_2Enumeral_2Enumeral__evenodd,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (p(ap(c_2Earithmetic_2EEVEN,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) & (p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n)))) & ((~~ p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))))) & ((~~ p(ap(c_2Earithmetic_2EODD,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))) & ((~~ p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))))) & p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))))))))))).
tff(ax_thm_2Enumeral_2Eonecount__def,axiom,(( ! [V0x:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Eonecount,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0x))) = V0x)) & (( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2x:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1n))),inj__ty_2Enum_2Enum(V2x))) = surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Eonecount,inj__ty_2Enum_2Enum(V1n)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2x))))))) & ( ! [V3n:tp__ty_2Enum_2Enum] : ( ! [V4x:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V3n))),inj__ty_2Enum_2Enum(V4x))) = fo__c_2Earithmetic_2EZERO)))))).
tff(ax_thm_2Enumeral_2Eexactlog__def,axiom,((surj__ty_2Enum_2Enum(ap(c_2Enumeral_2Eexactlog,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & (( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n)))) = fo__c_2Earithmetic_2EZERO)) & ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Enum_2Enum(ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f202),ap(ap(c_2Enumeral_2Eonecount,inj__ty_2Enum_2Enum(V1n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))).
tff(conj_thm_2Enumeral_2Eenumeral__mult,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Enum_2Enum] : ( ! [V2y:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V2y)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V2y))))) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V2y)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f203(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V2y)))))) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1x))),ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V2y)))) = surj__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,inj__ty_2Enum_2Enum(V1x)))))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1x))),ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V2y)))) = surj__ty_2Enum_2Enum(ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f206(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1x)))))))))))))))).
tff(conj_thm_2Enumeral_2Einternal__mult__characterisation,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Einternal__mult,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)),inj__ty_2Enum_2Enum(V0n))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Einternal__mult,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & ((surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral_2Einternal__mult,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))),inj__ty_2Enum_2Enum(V1m))))) & (surj__ty_2Enum_2Enum(ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V0n))),inj__ty_2Enum_2Enum(V1m))) = surj__ty_2Enum_2Enum(ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumeral_2Einternal__mult,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))),inj__ty_2Enum_2Enum(V1m))))))))))))).
tff(conj_thm_2Epair_2EPAIR__EQ,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ( ! [V1y:$i] : (mem(V1y,A_27b) => ( ! [V2a:$i] : (mem(V2a,A_27a) => ( ! [V3b:$i] : (mem(V3b,A_27b) => ((ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b)) <=> ((V0x = V2a) & (V1y = V3b))))))))))))))).
tff(conj_thm_2Epair_2ECLOSED__PAIR__EQ,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ( ! [V1y:$i] : (mem(V1y,A_27b) => ( ! [V2a:$i] : (mem(V2a,A_27a) => ( ! [V3b:$i] : (mem(V3b,A_27b) => ((ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b)) <=> ((V0x = V2a) & (V1y = V3b))))))))))))))).
tff(conj_thm_2Epair_2EFST,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ( ! [V1y:$i] : (mem(V1y,A_27b) => (ap(c_2Epair_2EFST(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V0x))))))))).
tff(conj_thm_2Epair_2ESND,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => ( ! [V1y:$i] : (mem(V1y,A_27b) => (ap(c_2Epair_2ESND(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V1y))))))))).
tff(conj_thm_2Epair_2EUNCURRY__DEF,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) => ( ! [V1x:$i] : (mem(V1x,A_27a) => ( ! [V2y:$i] : (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))))))))))))).
tff(conj_thm_2Epair_2EEXISTS__PROD,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) => ((? [V1p:$i] : (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) & p(ap(V0P,V1p)))) <=> (? [V2p__1:$i] : (mem(V2p__1,A_27a) & (? [V3p__2:$i] : (mem(V3p__2,A_27b) & p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2)))))))))))))).
tff(conj_thm_2Epair_2EFORALL__PROD,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) => (( ! [V1p:$i] : (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) => p(ap(V0P,V1p)))) <=> ( ! [V2p__1:$i] : (mem(V2p__1,A_27a) => ( ! [V3p__2:$i] : (mem(V3p__2,A_27b) => p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2)))))))))))))).
tff(conj_thm_2Epred__set_2EEXTENSION,lemma,(( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27a,bool)) => ((V0s = V1t) <=> ( ! [V2x:$i] : (mem(V2x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))))))))))))).
tff(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ( ! [V1v:$i] : (mem(V1v,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f))) <=> (? [V2x:$i] : (mem(V2x,A_27b) & (ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),inj__o(fo__c_2Ebool_2ET)) = ap(V0f,V2x)))))))))))).
tff(conj_thm_2Epred__set_2ENOT__IN__EMPTY,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => (~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))))).
tff(conj_thm_2Epred__set_2EIN__UNIV,lemma,(( ! [A_27a:del]: ( ! [V0x:$i] : (mem(V0x,A_27a) => p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a)))))))).
tff(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27a,bool)) => (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ( ! [V2x:$i] : (mem(V2x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))).
tff(ax_thm_2Epred__set_2EINTER__DEF,axiom,( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27a,bool)) => (ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f264(A_27a,V1t,V0s))))))))).
tff(conj_thm_2Epred__set_2EIN__INTER,lemma,(( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (mem(V1t,arr(A_27a,bool)) => ( ! [V2x:$i] : (mem(V2x,A_27a) => (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))) <=> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))))))))))))).
tff(conj_thm_2Epred__set_2EINTER__COMM,lemma,(( ! [A_27a:del]: ( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (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))))))))).
tff(conj_thm_2Epred__set_2EINTER__SUBSET,lemma,(( ! [A_27a:del]: (( ! [V0s:$i] : (mem(V0s,arr(A_27a,bool)) => ( ! [V1t:$i] : (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)))))) & ( ! [V2s:$i] : (mem(V2s,arr(A_27a,bool)) => ( ! [V3t:$i] : (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)))))))))).
tff(conj_thm_2Epred__set_2EFINITE__INTER,lemma,(( ! [A_27a:del]: ( ! [V0s1:$i] : (mem(V0s1,arr(A_27a,bool)) => ( ! [V1s2:$i] : (mem(V1s2,arr(A_27a,bool)) => ((p(ap(c_2Epred__set_2EFINITE(A_27a),V0s1)) | p(ap(c_2Epred__set_2EFINITE(A_27a),V1s2))) => p(ap(c_2Epred__set_2EFINITE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s1),V1s2))))))))))).
tff(conj_thm_2Eprim__rec_2ELESS__REFL,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (~~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Eprim__rec_2ENOT__LESS__0,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (~~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__ASSOC,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__MUL__LINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(ax_thm_2Ereal_2Ereal__sub,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(ax_thm_2Ereal_2Ereal__div,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__RID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__ADD__RINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__RID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__RZERO,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) | p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x)))))).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__LE,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(conj_thm_2Ereal_2EREAL__LTE__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LET__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))) <=> (V0x = V1y)))))).
tff(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__SUB__LT,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__NE,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) => (~~ (V0x = V1y))))))).
tff(conj_thm_2Ereal_2EREAL__LT__RMUL__IMP,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__INV__1OVER,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__LT__INV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__LE__INV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__POS,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ereal_2EREAL__LE,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Ereal_2EREAL__INJ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> (V0m = V1n)))))).
tff(conj_thm_2Ereal_2EREAL__ADD,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__INV1,lemma,((surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))).
tff(conj_thm_2Ereal_2EREAL__DIV__REFL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ereal_2EREAL__INV__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V1y = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__DIV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__LMUL__IMP,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(ax_thm_2Ereal_2Eabs,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))))).
tff(ax_thm_2Ereal_2Epow,axiom,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1x)),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Enum_2Enum(V2n))))))))).
tff(conj_thm_2Ereal_2EPOW__NZ,lemma,(( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ (V0c = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (~~ (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0c)),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))))).
tff(conj_thm_2Ereal_2EPOW__1,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0x)))).
tff(conj_thm_2Ereal_2EPOW__POS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) => ( ! [V1n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__POW__LT,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__ARCH,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) => ( ! [V1y:tp__ty_2Erealax_2Ereal] : (? [V2n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2n))),inj__ty_2Erealax_2Ereal(V0x)))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__RNEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__LNEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2Ereal__lt,lemma,(( ! [V0y:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V0y))) <=> (~~ p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0y)),inj__ty_2Erealax_2Ereal(V1x))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__LADD__IMP,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__LNEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__NEG2,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__NEG__NEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__LE__RNEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))).
tff(conj_thm_2Ereal_2EREAL__POW__ADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V2n)))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__RDIV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2z))) => (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__RDIV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2z))) => (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__LDIV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2z))) => (p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__LDISTRIB,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__LE,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__OF__NUM__SUC,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))))))).
tff(conj_thm_2Ereal_2EREAL__BIGNUM,lemma,(( ! [V0r:tp__ty_2Erealax_2Ereal] : (? [V1n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0r)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Ereal_2EREAL__HALF__BETWEEN,lemma,(((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ereal_2Eadd__ratr,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2z)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2Eadd__ints,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n))))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))))) & (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m))))))))))))).
tff(conj_thm_2Ereal_2Emult__rat,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2u:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2u)),inj__ty_2Erealax_2Ereal(V3v)))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1y)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2u)),inj__ty_2Erealax_2Ereal(V3v)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V3v)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V2u)),inj__ty_2Erealax_2Ereal(V3v))))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2u))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V3v))))))))))))).
tff(conj_thm_2Ereal_2Emult__ints,lemma,(( ! [V0a:tp__ty_2Enum_2Enum] : ( ! [V1b:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0a))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1b)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0a)))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1b)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b)))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0a))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1b))))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b)))))) & (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0a)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1b))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0a)),inj__ty_2Enum_2Enum(V1b)))))))))))).
tff(conj_thm_2Ereal_2Epow__rat,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2a:tp__ty_2Enum_2Enum] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V1n))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V1n))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2a)))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2a))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n)))))) & ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2a))))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(ap(c_2Ebool_2ECOND(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n)))),c_2Erealax_2Ereal__neg),i(ty_2Erealax_2Ereal)),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V2a))),ap(c_2Earithmetic_2ENUMERAL,inj__ty_2Enum_2Enum(V1n))))))) & (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V3y))),inj__ty_2Enum_2Enum(V1n))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Enum_2Enum(V1n))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V3y)),inj__ty_2Enum_2Enum(V1n)))))))))))))))).
tff(conj_thm_2Ereal_2Eeq__ints,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> (V0n = V1m)) & (((surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> ((V0n = fo__c_2Enum_2E0) & (V1m = fo__c_2Enum_2E0))) & (((surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> ((V0n = fo__c_2Enum_2E0) & (V1m = fo__c_2Enum_2E0))) & ((surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> (V0n = V1m))))))))).
tff(conj_thm_2Ereal_2Ediv__ratl,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V1y)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V2z)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z)))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))))))))))).
tff(conj_thm_2Ereal_2Ele__ratr,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2m:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1u)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2m))))) <=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),inj__ty_2Enum_2Enum(V2m)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V1u)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))),ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V2m))),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V1u)))))))))).
tff(conj_thm_2Ereal_2Ele__int,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> $true) & ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> ((V0n = fo__c_2Enum_2E0) & (V1m = fo__c_2Enum_2E0))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n))))))))))).
tff(conj_thm_2Ereal_2Elt__int,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0n)),inj__ty_2Enum_2Enum(V1m)))) & ((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m)))) <=> ((~~ (V0n = fo__c_2Enum_2E0)) | (~~ (V1m = fo__c_2Enum_2E0)))) & ((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> $false) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1m))))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V0n))))))))))).
tff(conj_thm_2Ereal__topology_2EFORALL__IN__GSPEC,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [A_27e:del]: ( ! [A_27f:del]: ( ! [A_27g:del]: ( ! [V0Q:$i] : (mem(V0Q,arr(A_27b,bool)) => (( ! [V1P:$i] : (mem(V1P,arr(A_27a,bool)) => ( ! [V2f:$i] : (mem(V2f,arr(A_27a,A_27b)) => (( ! [V3z:$i] : (mem(V3z,A_27b) => (p(ap(ap(c_2Ebool_2EIN(A_27b),V3z),ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f3397(A_27b,A_27a,V2f,V1P)))) => p(ap(V0Q,V3z))))) <=> ( ! [V5x:$i] : (mem(V5x,A_27a) => (p(ap(V1P,V5x)) => p(ap(V0Q,ap(V2f,V5x))))))))))) & (( ! [V6P:$i] : (mem(V6P,arr(A_27c,arr(A_27d,bool))) => ( ! [V7f:$i] : (mem(V7f,arr(A_27c,arr(A_27d,A_27b))) => (( ! [V8z:$i] : (mem(V8z,A_27b) => (p(ap(ap(c_2Ebool_2EIN(A_27b),V8z),ap(c_2Epred__set_2EGSPEC(A_27b,ty_2Epair_2Eprod(A_27c,A_27d)),ap(c_2Epair_2EUNCURRY(A_27c,A_27d,ty_2Epair_2Eprod(A_27b,bool)),f3399(A_27b,A_27c,A_27d,V7f,V6P))))) => p(ap(V0Q,V8z))))) <=> ( ! [V11x:$i] : (mem(V11x,A_27c) => ( ! [V12y:$i] : (mem(V12y,A_27d) => (p(ap(ap(V6P,V11x),V12y)) => p(ap(V0Q,ap(ap(V7f,V11x),V12y))))))))))))) & ( ! [V13P:$i] : (mem(V13P,arr(A_27e,arr(A_27f,arr(A_27g,bool)))) => ( ! [V14f:$i] : (mem(V14f,arr(A_27e,arr(A_27f,arr(A_27g,A_27b)))) => (( ! [V15z:$i] : (mem(V15z,A_27b) => (p(ap(ap(c_2Ebool_2EIN(A_27b),V15z),ap(c_2Epred__set_2EGSPEC(A_27b,ty_2Epair_2Eprod(A_27e,ty_2Epair_2Eprod(A_27f,A_27g))),ap(c_2Epair_2EUNCURRY(A_27e,ty_2Epair_2Eprod(A_27f,A_27g),ty_2Epair_2Eprod(A_27b,bool)),f3402(A_27e,A_27g,A_27b,A_27f,V13P,V14f))))) => p(ap(V0Q,V15z))))) <=> ( ! [V19w:$i] : (mem(V19w,A_27e) => ( ! [V20x:$i] : (mem(V20x,A_27f) => ( ! [V21y:$i] : (mem(V21y,A_27g) => (p(ap(ap(ap(V13P,V19w),V20x),V21y)) => p(ap(V0Q,ap(ap(ap(V14f,V19w),V20x),V21y)))))))))))))))))))))))))))).
tff(conj_thm_2Ereal__topology_2EREAL__WLOG__LT,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) => ((( ! [V1x:tp__ty_2Erealax_2Ereal] : p(ap(ap(V0P,inj__ty_2Erealax_2Ereal(V1x)),inj__ty_2Erealax_2Ereal(V1x)))) & (( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(V0P,inj__ty_2Erealax_2Ereal(V2x)),inj__ty_2Erealax_2Ereal(V3y))) <=> p(ap(ap(V0P,inj__ty_2Erealax_2Ereal(V3y)),inj__ty_2Erealax_2Ereal(V2x)))))) & ( ! [V4x:tp__ty_2Erealax_2Ereal] : ( ! [V5y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V5y))) => p(ap(ap(V0P,inj__ty_2Erealax_2Ereal(V4x)),inj__ty_2Erealax_2Ereal(V5y)))))))) => ( ! [V6x:tp__ty_2Erealax_2Ereal] : ( ! [V7y:tp__ty_2Erealax_2Ereal] : p(ap(ap(V0P,inj__ty_2Erealax_2Ereal(V6x)),inj__ty_2Erealax_2Ereal(V7y)))))))))).
tff(conj_thm_2Ereal__topology_2ELE__1,lemma,((( ! [V0n:tp__ty_2Enum_2Enum] : ((~~ (V0n = fo__c_2Enum_2E0)) => p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0n))))) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ (V1n = fo__c_2Enum_2E0)) => p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V1n))))) & (( ! [V2n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V2n))) => (~~ (V2n = fo__c_2Enum_2E0)))) & (( ! [V3n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V3n))) => p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V3n))))) & (( ! [V4n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V4n))) => p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V4n))))) & ( ! [V5n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V5n))) => (~~ (V5n = fo__c_2Enum_2E0))))))))))).
tff(conj_thm_2Esat_2ENOT__NOT,lemma,(( ! [V0t:tp__o] : ((~~ (~~ p(inj__o(V0t)))) <=> p(inj__o(V0t)))))).
tff(conj_thm_2Esat_2EAND__INV__IMP,lemma,(( ! [V0A:tp__o] : (p(inj__o(V0A)) => ((~~ p(inj__o(V0A))) => $false))))).
tff(conj_thm_2Esat_2EOR__DUAL2,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : (((~~ (p(inj__o(V0A)) | p(inj__o(V1B)))) => $false) <=> ((p(inj__o(V0A)) => $false) => ((~~ p(inj__o(V1B))) => $false))))))).
tff(conj_thm_2Esat_2EOR__DUAL3,lemma,(( ! [V0A:tp__o] : ( ! [V1B:tp__o] : (((~~ ((~~ p(inj__o(V0A))) | p(inj__o(V1B)))) => $false) <=> (p(inj__o(V0A)) => ((~~ p(inj__o(V1B))) => $false))))))).
tff(conj_thm_2Esat_2EAND__INV2,lemma,(( ! [V0A:tp__o] : (((~~ p(inj__o(V0A))) => $false) => ((p(inj__o(V0A)) => $false) => $false))))).
tff(conj_thm_2Esat_2Edc__eq,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ( ! [V2r:tp__o] : ((p(inj__o(V0p)) <=> (p(inj__o(V1q)) <=> p(inj__o(V2r)))) <=> ((p(inj__o(V0p)) | (p(inj__o(V1q)) | p(inj__o(V2r)))) & ((p(inj__o(V0p)) | ((~~ p(inj__o(V2r))) | (~~ p(inj__o(V1q))))) & ((p(inj__o(V1q)) | ((~~ p(inj__o(V2r))) | (~~ p(inj__o(V0p))))) & (p(inj__o(V2r)) | ((~~ p(inj__o(V1q))) | (~~ p(inj__o(V0p)))))))))))))).
tff(conj_thm_2Esat_2Edc__conj,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ( ! [V2r:tp__o] : ((p(inj__o(V0p)) <=> (p(inj__o(V1q)) & p(inj__o(V2r)))) <=> ((p(inj__o(V0p)) | ((~~ p(inj__o(V1q))) | (~~ p(inj__o(V2r))))) & ((p(inj__o(V1q)) | (~~ p(inj__o(V0p)))) & (p(inj__o(V2r)) | (~~ p(inj__o(V0p)))))))))))).
tff(conj_thm_2Esat_2Edc__disj,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ( ! [V2r:tp__o] : ((p(inj__o(V0p)) <=> (p(inj__o(V1q)) | p(inj__o(V2r)))) <=> ((p(inj__o(V0p)) | (~~ p(inj__o(V1q)))) & ((p(inj__o(V0p)) | (~~ p(inj__o(V2r)))) & (p(inj__o(V1q)) | (p(inj__o(V2r)) | (~~ p(inj__o(V0p))))))))))))).
tff(conj_thm_2Esat_2Edc__imp,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ( ! [V2r:tp__o] : ((p(inj__o(V0p)) <=> (p(inj__o(V1q)) => p(inj__o(V2r)))) <=> ((p(inj__o(V0p)) | p(inj__o(V1q))) & ((p(inj__o(V0p)) | (~~ p(inj__o(V2r)))) & ((~~ p(inj__o(V1q))) | (p(inj__o(V2r)) | (~~ p(inj__o(V0p))))))))))))).
tff(conj_thm_2Esat_2Edc__neg,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ((p(inj__o(V0p)) <=> (~~ p(inj__o(V1q)))) <=> ((p(inj__o(V0p)) | p(inj__o(V1q))) & ((~~ p(inj__o(V1q))) | (~~ p(inj__o(V0p)))))))))).
tff(conj_thm_2Esat_2Epth__ni1,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ((~~ (p(inj__o(V0p)) => p(inj__o(V1q)))) => p(inj__o(V0p))))))).
tff(conj_thm_2Esat_2Epth__ni2,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ((~~ (p(inj__o(V0p)) => p(inj__o(V1q)))) => (~~ p(inj__o(V1q)))))))).
tff(conj_thm_2Esat_2Epth__no1,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ((~~ (p(inj__o(V0p)) | p(inj__o(V1q)))) => (~~ p(inj__o(V0p)))))))).
tff(conj_thm_2Esat_2Epth__no2,lemma,(( ! [V0p:tp__o] : ( ! [V1q:tp__o] : ((~~ (p(inj__o(V0p)) | p(inj__o(V1q)))) => (~~ p(inj__o(V1q)))))))).
tff(conj_thm_2Esat_2Epth__nn,lemma,(( ! [V0p:tp__o] : ((~~ (~~ p(inj__o(V0p)))) => p(inj__o(V0p)))))).
tff(conj_thm_2Ereal__topology_2ECARD__EQ__REAL,conjecture,(p(ap(ap(c_2Ecardinal_2Ecardeq(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,bool)),c_2Epred__set_2EUNIV(ty_2Erealax_2Ereal)),c_2Epred__set_2EUNIV(arr(ty_2Enum_2Enum,bool)))))).
