include('Axioms/HL4001^2.ax').
thf(tp_c_2Emin_2E_40,type,(c_2Emin_2E_40:(del>$i))).
thf(mem_c_2Emin_2E_40,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_40@A_27a)@(arr@(arr@A_27a@bool)@A_27a)))).
thf(tp_c_2Ecombin_2EK,type,(c_2Ecombin_2EK:(del>(del>$i)))).
thf(mem_c_2Ecombin_2EK,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ecombin_2EK@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@A_27a)))))).
thf(tp_c_2Ecombin_2ES,type,(c_2Ecombin_2ES:(del>(del>(del>$i))))).
thf(mem_c_2Ecombin_2ES,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Ecombin_2ES@A_27a@A_27b@A_27c)@(arr@(arr@A_27a@(arr@A_27b@A_27c))@(arr@(arr@A_27a@A_27b)@(arr@A_27a@A_27c)))))))).
thf(tp_c_2Ecombin_2EC,type,(c_2Ecombin_2EC:(del>(del>(del>$i))))).
thf(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)))))))).
thf(tp_c_2Ecombin_2EI,type,(c_2Ecombin_2EI:(del>$i))).
thf(mem_c_2Ecombin_2EI,axiom,( ! [A_27a:del] : (mem@(c_2Ecombin_2EI@A_27a)@(arr@A_27a@A_27a)))).
thf(tp_c_2Ecombin_2Eo,type,(c_2Ecombin_2Eo:(del>(del>(del>$i))))).
thf(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)))))))).
thf(tp_ty_2Eextreal_2Eextreal,type,( ty_2Eextreal_2Eextreal:del )).
thf(stp_ty_2Eextreal_2Eextreal,type,(tp__ty_2Eextreal_2Eextreal : $tType)).
thf(stp_inj_ty_2Eextreal_2Eextreal,type,(inj__ty_2Eextreal_2Eextreal : (tp__ty_2Eextreal_2Eextreal > $i))).
thf(stp_surj_ty_2Eextreal_2Eextreal,type,(surj__ty_2Eextreal_2Eextreal : ($i > tp__ty_2Eextreal_2Eextreal))).
thf(stp_inj_surj_ty_2Eextreal_2Eextreal,axiom,( ! [X:tp__ty_2Eextreal_2Eextreal] : ((surj__ty_2Eextreal_2Eextreal @ (inj__ty_2Eextreal_2Eextreal @ X)) = X))).
thf(stp_inj_mem_ty_2Eextreal_2Eextreal,axiom,( ! [X:tp__ty_2Eextreal_2Eextreal] : (mem @ (inj__ty_2Eextreal_2Eextreal @ X) @ ty_2Eextreal_2Eextreal))).
thf(stp_iso_mem_ty_2Eextreal_2Eextreal,axiom,( ! [X:$i] : ((mem @ X @ ty_2Eextreal_2Eextreal) => (X = (inj__ty_2Eextreal_2Eextreal @ (surj__ty_2Eextreal_2Eextreal @ X)))))).
thf(tp_ty_2Erealax_2Ereal,type,( ty_2Erealax_2Ereal:del )).
thf(stp_ty_2Erealax_2Ereal,type,(tp__ty_2Erealax_2Ereal : $tType)).
thf(stp_inj_ty_2Erealax_2Ereal,type,(inj__ty_2Erealax_2Ereal : (tp__ty_2Erealax_2Ereal > $i))).
thf(stp_surj_ty_2Erealax_2Ereal,type,(surj__ty_2Erealax_2Ereal : ($i > tp__ty_2Erealax_2Ereal))).
thf(stp_inj_surj_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (inj__ty_2Erealax_2Ereal @ X)) = X))).
thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : (mem @ (inj__ty_2Erealax_2Ereal @ X) @ ty_2Erealax_2Ereal))).
thf(stp_iso_mem_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : ((mem @ X @ ty_2Erealax_2Ereal) => (X = (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X)))))).
thf(tp_c_2Eextreal_2ENormal,type,(c_2Eextreal_2ENormal:$i)).
thf(mem_c_2Eextreal_2ENormal,axiom,(mem@c_2Eextreal_2ENormal@(arr@ty_2Erealax_2Ereal@ty_2Eextreal_2Eextreal))).
thf(stp_fo_c_2Eextreal_2ENormal,type,(fo__c_2Eextreal_2ENormal:(tp__ty_2Erealax_2Ereal > tp__ty_2Eextreal_2Eextreal))).
thf(stp_eq_fo_c_2Eextreal_2ENormal,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2ENormal @ X0)) = (ap @ c_2Eextreal_2ENormal @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Eextreal_2Eextreal__add,type,(c_2Eextreal_2Eextreal__add:$i)).
thf(mem_c_2Eextreal_2Eextreal__add,axiom,(mem@c_2Eextreal_2Eextreal__add@(arr@ty_2Eextreal_2Eextreal@(arr@ty_2Eextreal_2Eextreal@ty_2Eextreal_2Eextreal)))).
thf(stp_fo_c_2Eextreal_2Eextreal__add,type,(fo__c_2Eextreal_2Eextreal__add:(tp__ty_2Eextreal_2Eextreal > (tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal)))).
thf(stp_eq_fo_c_2Eextreal_2Eextreal__add,axiom,( ! [X0:tp__ty_2Eextreal_2Eextreal] : ( ! [X1:tp__ty_2Eextreal_2Eextreal] : ((inj__ty_2Eextreal_2Eextreal @ ((fo__c_2Eextreal_2Eextreal__add @ X0) @ X1)) = (ap @ (ap @ c_2Eextreal_2Eextreal__add @ (inj__ty_2Eextreal_2Eextreal @ X0)) @ (inj__ty_2Eextreal_2Eextreal @ X1)))))).
thf(tp_ty_2Enum_2Enum,type,( ty_2Enum_2Enum:del )).
thf(stp_ty_2Enum_2Enum,type,(tp__ty_2Enum_2Enum : $tType)).
thf(stp_inj_ty_2Enum_2Enum,type,(inj__ty_2Enum_2Enum : (tp__ty_2Enum_2Enum > $i))).
thf(stp_surj_ty_2Enum_2Enum,type,(surj__ty_2Enum_2Enum : ($i > tp__ty_2Enum_2Enum))).
thf(stp_inj_surj_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (mem @ (inj__ty_2Enum_2Enum @ X) @ ty_2Enum_2Enum))).
thf(stp_iso_mem_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Eextreal_2Eextreal__of__num,type,(c_2Eextreal_2Eextreal__of__num:$i)).
thf(mem_c_2Eextreal_2Eextreal__of__num,axiom,(mem@c_2Eextreal_2Eextreal__of__num@(arr@ty_2Enum_2Enum@ty_2Eextreal_2Eextreal))).
thf(stp_fo_c_2Eextreal_2Eextreal__of__num,type,(fo__c_2Eextreal_2Eextreal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Eextreal_2Eextreal))).
thf(stp_eq_fo_c_2Eextreal_2Eextreal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Eextreal_2Eextreal @ (fo__c_2Eextreal_2Eextreal__of__num @ X0)) = (ap @ c_2Eextreal_2Eextreal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Eextreal_2Eextreal__le,type,(c_2Eextreal_2Eextreal__le:$i)).
thf(mem_c_2Eextreal_2Eextreal__le,axiom,(mem@c_2Eextreal_2Eextreal__le@(arr@ty_2Eextreal_2Eextreal@(arr@ty_2Eextreal_2Eextreal@bool)))).
thf(tp_c_2Eextreal_2EPosInf,type,(c_2Eextreal_2EPosInf:$i)).
thf(mem_c_2Eextreal_2EPosInf,axiom,(mem@c_2Eextreal_2EPosInf@ty_2Eextreal_2Eextreal)).
thf(stp_fo_c_2Eextreal_2EPosInf,type,(fo__c_2Eextreal_2EPosInf:tp__ty_2Eextreal_2Eextreal)).
thf(stp_eq_fo_c_2Eextreal_2EPosInf,axiom,((inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf) = c_2Eextreal_2EPosInf)).
thf(tp_c_2Epred__set_2EUNION,type,(c_2Epred__set_2EUNION:(del>$i))).
thf(mem_c_2Epred__set_2EUNION,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EUNION@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@(arr@A_27a@bool)))))).
thf(tp_c_2Epred__set_2ESUBSET,type,(c_2Epred__set_2ESUBSET:(del>$i))).
thf(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))))).
thf(tp_c_2Epred__set_2Ecountable,type,(c_2Epred__set_2Ecountable:(del>$i))).
thf(mem_c_2Epred__set_2Ecountable,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2Ecountable@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(tp_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: del > del >del )).
thf(tp_c_2Emeasure_2Ealgebra,type,(c_2Emeasure_2Ealgebra:(del>$i))).
thf(mem_c_2Emeasure_2Ealgebra,axiom,( ! [A_27a:del] : (mem@(c_2Emeasure_2Ealgebra@A_27a)@(arr@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))@bool)))).
thf(tp_c_2Emeasure_2Esubset__class,type,(c_2Emeasure_2Esubset__class:(del>$i))).
thf(mem_c_2Emeasure_2Esubset__class,axiom,( ! [A_27a:del] : (mem@(c_2Emeasure_2Esubset__class@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@(arr@A_27a@bool)@bool)@bool))))).
thf(tp_c_2Eextreal_2Eextreal__lt,type,(c_2Eextreal_2Eextreal__lt:$i)).
thf(mem_c_2Eextreal_2Eextreal__lt,axiom,(mem@c_2Eextreal_2Eextreal__lt@(arr@ty_2Eextreal_2Eextreal@(arr@ty_2Eextreal_2Eextreal@bool)))).
thf(tp_c_2Emeasure_2Esigma__algebra,type,(c_2Emeasure_2Esigma__algebra:(del>$i))).
thf(mem_c_2Emeasure_2Esigma__algebra,axiom,( ! [A_27a:del] : (mem@(c_2Emeasure_2Esigma__algebra@A_27a)@(arr@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))@bool)))).
thf(tp_c_2Emeasure_2Esubsets,type,(c_2Emeasure_2Esubsets:(del>$i))).
thf(mem_c_2Emeasure_2Esubsets,axiom,( ! [A_27a:del] : (mem@(c_2Emeasure_2Esubsets@A_27a)@(arr@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Emeasure_2Espace,type,(c_2Emeasure_2Espace:(del>$i))).
thf(mem_c_2Emeasure_2Espace,axiom,( ! [A_27a:del] : (mem@(c_2Emeasure_2Espace@A_27a)@(arr@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))@(arr@A_27a@bool))))).
thf(tp_c_2Eextreal_2ENegInf,type,(c_2Eextreal_2ENegInf:$i)).
thf(mem_c_2Eextreal_2ENegInf,axiom,(mem@c_2Eextreal_2ENegInf@ty_2Eextreal_2Eextreal)).
thf(stp_fo_c_2Eextreal_2ENegInf,type,(fo__c_2Eextreal_2ENegInf:tp__ty_2Eextreal_2Eextreal)).
thf(stp_eq_fo_c_2Eextreal_2ENegInf,axiom,((inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf) = c_2Eextreal_2ENegInf)).
thf(tp_c_2Emeasure_2EBorel,type,(c_2Emeasure_2EBorel:$i)).
thf(mem_c_2Emeasure_2EBorel,axiom,(mem@c_2Emeasure_2EBorel@(ty_2Epair_2Eprod@(arr@ty_2Eextreal_2Eextreal@bool)@(arr@(arr@ty_2Eextreal_2Eextreal@bool)@bool)))).
thf(tp_c_2Emeasure_2Emeasurable,type,(c_2Emeasure_2Emeasurable:(del>(del>$i)))).
thf(mem_c_2Emeasure_2Emeasurable,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Emeasure_2Emeasurable@A_27a@A_27b)@(arr@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))@(arr@(ty_2Epair_2Eprod@(arr@A_27b@bool)@(arr@(arr@A_27b@bool)@bool))@(arr@(arr@A_27a@A_27b)@bool))))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
thf(mem_c_2Earithmetic_2EEVEN,axiom,(mem@c_2Earithmetic_2EEVEN@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$i)).
thf(mem_c_2Earithmetic_2E_3E,axiom,(mem@c_2Earithmetic_2E_3E@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(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))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
thf(mem_c_2Earithmetic_2E_2D,axiom,(mem@c_2Earithmetic_2E_2D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2D @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(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)))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
thf(mem_c_2Enumeral_2EiZ,axiom,(mem@c_2Enumeral_2EiZ@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiZ @ X0)) = (ap @ c_2Enumeral_2EiZ @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(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)))))).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Epred__set_2EINTER,type,(c_2Epred__set_2EINTER:(del>$i))).
thf(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)))))).
thf(tp_c_2Epred__set_2EDIFF,type,(c_2Epred__set_2EDIFF:(del>$i))).
thf(mem_c_2Epred__set_2EDIFF,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EDIFF@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@(arr@A_27a@bool)))))).
thf(tp_c_2Epred__set_2EFUNSET,type,(c_2Epred__set_2EFUNSET:(del>(del>$i)))).
thf(mem_c_2Epred__set_2EFUNSET,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epred__set_2EFUNSET@A_27a@A_27b)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27b@bool)@(arr@(arr@A_27a@A_27b)@bool))))))).
thf(tp_c_2Epred__set_2EBIGUNION,type,(c_2Epred__set_2EBIGUNION:(del>$i))).
thf(mem_c_2Epred__set_2EBIGUNION,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EBIGUNION@A_27a)@(arr@(arr@(arr@A_27a@bool)@bool)@(arr@A_27a@bool))))).
thf(tp_c_2Epred__set_2EIMAGE,type,(c_2Epred__set_2EIMAGE:(del>(del>$i)))).
thf(mem_c_2Epred__set_2EIMAGE,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epred__set_2EIMAGE@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@(arr@A_27a@bool)@(arr@A_27b@bool))))))).
thf(tp_c_2Epred__set_2EBIGINTER,type,(c_2Epred__set_2EBIGINTER:(del>$i))).
thf(mem_c_2Epred__set_2EBIGINTER,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EBIGINTER@A_27a)@(arr@(arr@(arr@A_27a@bool)@bool)@(arr@A_27a@bool))))).
thf(tp_c_2Ebool_2EIN,type,(c_2Ebool_2EIN:(del>$i))).
thf(mem_c_2Ebool_2EIN,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2EIN@A_27a)@(arr@A_27a@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Epred__set_2EEMPTY,type,(c_2Epred__set_2EEMPTY:(del>$i))).
thf(mem_c_2Epred__set_2EEMPTY,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EEMPTY@A_27a)@(arr@A_27a@bool)))).
thf(tp_c_2Epred__set_2EUNIV,type,(c_2Epred__set_2EUNIV:(del>$i))).
thf(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EUNIV@A_27a)@(arr@A_27a@bool)))).
thf(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del>(del>$i)))).
thf(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))))))).
thf(tp_c_2Epred__set_2EGSPEC,type,(c_2Epred__set_2EGSPEC:(del>(del>$i)))).
thf(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epred__set_2EGSPEC@A_27a@A_27b)@(arr@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@bool))@(arr@A_27a@bool)))))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$i)).
thf(mem_c_2Eprim__rec_2E_3C,axiom,(mem@c_2Eprim__rec_2E_3C@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2EODD,type,(c_2Earithmetic_2EODD:$i)).
thf(mem_c_2Earithmetic_2EODD,axiom,(mem@c_2Earithmetic_2EODD@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(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)))))).
thf(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Erealax_2Ereal__neg,type,(c_2Erealax_2Ereal__neg:$i)).
thf(mem_c_2Erealax_2Ereal__neg,axiom,(mem@c_2Erealax_2Ereal__neg@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Erealax_2Ereal__neg,type,(fo__c_2Erealax_2Ereal__neg:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(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))))).
thf(tp_c_2Erealax_2Ereal__mul,type,(c_2Erealax_2Ereal__mul:$i)).
thf(mem_c_2Erealax_2Ereal__mul,axiom,(mem@c_2Erealax_2Ereal__mul@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Erealax_2Ereal__mul,type,(fo__c_2Erealax_2Ereal__mul:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Erealax_2Ereal__mul,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Erealax_2Ereal__mul @ X0) @ X1)) = (ap @ (ap @ c_2Erealax_2Ereal__mul @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Emarker_2Eunint,type,(c_2Emarker_2Eunint:(del>$i))).
thf(mem_c_2Emarker_2Eunint,axiom,( ! [A_27a:del] : (mem@(c_2Emarker_2Eunint@A_27a)@(arr@A_27a@A_27a)))).
thf(tp_c_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:(del>$i))).
thf(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2ECOND@A_27a)@(arr@bool@(arr@A_27a@(arr@A_27a@A_27a)))))).
thf(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
thf(mem_c_2Ereal_2E_2F,axiom,(mem@c_2Ereal_2E_2F@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(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)))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
thf(mem_c_2Ebool_2EF,axiom,(mem@c_2Ebool_2EF@bool)).
thf(ax_false_p,axiom,(~ (p@c_2Ebool_2EF))).
thf(tp_c_2Ebool_2E_5C_2F,type,(c_2Ebool_2E_5C_2F:$i)).
thf(mem_c_2Ebool_2E_5C_2F,axiom,(mem@c_2Ebool_2E_5C_2F@(arr@bool@(arr@bool@bool)))).
thf(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)))))))).
thf(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
thf(mem_c_2Ebool_2E_7E,axiom,(mem@c_2Ebool_2E_7E@(arr@bool@bool))).
thf(ax_neg_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ((p@(ap@c_2Ebool_2E_7E@Q)) <=> (~ (p@Q)))))).
thf(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
thf(mem_c_2Earithmetic_2E_3E_3D,axiom,(mem@c_2Earithmetic_2E_3E_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Ebool_2E_3F,type,(c_2Ebool_2E_3F:(del>$i))).
thf(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_3F@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(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))))))))).
thf(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:(del>$i))).
thf(mem_c_2Emin_2E_3D,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_3D@A_27a)@(arr@A_27a@(arr@A_27a@bool))))).
thf(ax_eq_p,axiom,( ! [A:del] : ( ! [X:$i] : ((mem@X@A) => ( ! [Y:$i] : ((mem@Y@A) => ((p@(ap@(ap@(c_2Emin_2E_3D@A)@X)@Y)) <=> (X = Y)))))))).
thf(tp_c_2Erealax_2Ereal__add,type,(c_2Erealax_2Ereal__add:$i)).
thf(mem_c_2Erealax_2Ereal__add,axiom,(mem@c_2Erealax_2Ereal__add@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Erealax_2Ereal__add,type,(fo__c_2Erealax_2Ereal__add:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(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)))))).
thf(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$i)).
thf(mem_c_2Ereal_2Ereal__sub,axiom,(mem@c_2Ereal_2Ereal__sub@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Ereal__sub,type,(fo__c_2Ereal_2Ereal__sub:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Ereal__sub @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Ereal__sub @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
thf(mem_c_2Ereal_2Epow,axiom,(mem@c_2Ereal_2Epow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Epow @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Epow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
thf(mem_c_2Earithmetic_2EBIT1,axiom,(mem@c_2Earithmetic_2EBIT1@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X0)) = (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(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))))).
thf(tp_c_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
thf(mem_c_2Ereal_2Ereal__of__num,axiom,(mem@c_2Ereal_2Ereal__of__num@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Ereal__of__num @ X0)) = (ap @ c_2Ereal_2Ereal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ereal_2Eabs,type,(c_2Ereal_2Eabs:$i)).
thf(mem_c_2Ereal_2Eabs,axiom,(mem@c_2Ereal_2Eabs@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Eabs,type,(fo__c_2Ereal_2Eabs:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(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))))).
thf(tp_c_2Erealax_2Ereal__lt,type,(c_2Erealax_2Ereal__lt:$i)).
thf(mem_c_2Erealax_2Ereal__lt,axiom,(mem@c_2Erealax_2Ereal__lt@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Eseq_2E_2D_2D_3E,type,(c_2Eseq_2E_2D_2D_3E:$i)).
thf(mem_c_2Eseq_2E_2D_2D_3E,axiom,(mem@c_2Eseq_2E_2D_2D_3E@(arr@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Ereal_2Ereal__lte,type,(c_2Ereal_2Ereal__lte:$i)).
thf(mem_c_2Ereal_2Ereal__lte,axiom,(mem@c_2Ereal_2Ereal__lte@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$i)).
thf(mem_c_2Ebool_2E_2F_5C,axiom,(mem@c_2Ebool_2E_2F_5C@(arr@bool@(arr@bool@bool)))).
thf(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)))))))).
thf(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$i)).
thf(mem_c_2Emin_2E_3D_3D_3E,axiom,(mem@c_2Emin_2E_3D_3D_3E@(arr@bool@(arr@bool@bool)))).
thf(ax_imp_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:(del>$i))).
thf(mem_c_2Ebool_2E_21,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_21@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(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))))))))).
thf(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))))))))))).
thf(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))))))).
thf(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))))))))))))).
thf(conj_thm_2Earithmetic_2EGREATER__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(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)))))))).
thf(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))))))).
thf(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)))))).
thf(ax_thm_2Ebool_2EEXISTS__DEF,axiom,( ! [A_27a:del]: ((c_2Ebool_2E_3F@A_27a) = (lam@(arr@A_27a@bool)@(^ [V0P:$i] : (ap@V0P@(ap@(c_2Emin_2E_40@A_27a)@V0P))))))).
thf(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0t:$i] : ((mem@V0t@(arr@A_27a@A_27b)) => ((lam@A_27a@(^ [V1x:$i] : (ap@V0t@V1x))) = V0t)))))).
thf(ax_thm_2Ebool_2ESELECT__AX,axiom,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ((p@(ap@V0P@V1x)) => (p@(ap@V0P@(ap@(c_2Emin_2E_40@A_27a)@V0P)))))))))).
thf(conj_thm_2Ebool_2ETRUTH,lemma,$true).
thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => (((p@V0t1) => (p@V1t2)) => (((p@V1t2) => (p@V0t1)) => ((p@V0t1) <=> (p@V1t2))))))))).
thf(conj_thm_2Ebool_2EFALSITY,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ($false => (p@V0t))))).
thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((p@V0t) | (~ (p@V0t)))))).
thf(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a:del]: ( ! [V0t:$i] : ((mem@V0t@bool) => (( ! [V1x:$i] : ((mem@V1x@A_27a) => (p@V0t))) <=> (p@V0t)))))).
thf(conj_thm_2Ebool_2EF__IMP,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (p@V0t)) => ((p@V0t) => $false))))).
thf(conj_thm_2Ebool_2EAND__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true & (p@V0t)) <=> (p@V0t)) & ((((p@V0t) & $true) <=> (p@V0t)) & ((($false & (p@V0t)) <=> $false) & ((((p@V0t) & $false) <=> $false) & (((p@V0t) & (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EOR__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true | (p@V0t)) <=> $true) & ((((p@V0t) | $true) <=> $true) & ((($false | (p@V0t)) <=> (p@V0t)) & ((((p@V0t) | $false) <=> (p@V0t)) & (((p@V0t) | (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true => (p@V0t)) <=> (p@V0t)) & ((((p@V0t) => $true) <=> $true) & ((($false => (p@V0t)) <=> $true) & ((((p@V0t) => (p@V0t)) <=> $true) & (((p@V0t) => $false) <=> (~ (p@V0t)))))))))).
thf(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t)))) & (((~ ($true)) <=> $false) & ((~ ($false)) <=> $true)))).
thf(conj_thm_2Ebool_2EEQ__REFL,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (V0x = V0x))))).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((V0x = V0x) <=> $true))))).
thf(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2Ebool_2EFUN__EQ__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$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)))))))))))).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true <=> (p@V0t)) <=> (p@V0t)) & ((((p@V0t) <=> $true) <=> (p@V0t)) & ((($false <=> (p@V0t)) <=> (~ (p@V0t))) & (((p@V0t) <=> $false) <=> (~ (p@V0t))))))))).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a:del]: ( ! [V0t1:$i] : ((mem@V0t1@A_27a) => ( ! [V1t2:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2EFORALL__AND__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@V0P@V2x)) & (p@(ap@V1Q@V2x))))) <=> (( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V0P@V3x)))) & ( ! [V4x:$i] : ((mem@V4x@A_27a) => (p@(ap@V1Q@V4x)))))))))))).
thf(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (((p@V0P) & ( ! [V2x:$i] : ((mem@V2x@A_27a) => (p@(ap@V1Q@V2x))))) <=> ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@V0P) & (p@(ap@V1Q@V3x)))))))))))).
thf(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,lemma,( ! [A_27a:del]: ( ! [V0Q:$i] : ((mem@V0Q@bool) => ( ! [V1P:$i] : ((mem@V1P@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@V1P@V2x)) | (p@V0Q)))) <=> (( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V1P@V3x)))) | (p@V0Q))))))))).
thf(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@V0P) | (p@(ap@V1Q@V2x))))) <=> ((p@V0P) | ( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V1Q@V3x)))))))))))).
thf(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) & (p@V1B))) <=> ((~ (p@V0A)) | (~ (p@V1B)))) & ((~ ((p@V0A) | (p@V1B))) <=> ((~ (p@V0A)) & (~ (p@V1B)))))))))).
thf(conj_thm_2Ebool_2ELEFT__OR__OVER__AND,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => (((p@V0A) | ((p@V1B) & (p@V2C))) <=> (((p@V0A) | (p@V1B)) & ((p@V0A) | (p@V2C))))))))))).
thf(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => ((((p@V1B) & (p@V2C)) | (p@V0A)) <=> (((p@V1B) | (p@V0A)) & ((p@V2C) | (p@V0A))))))))))).
thf(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => (((p@V0t) => $false) <=> ((p@V0t) <=> $false))))).
thf(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => ( ! [V2t3:$i] : ((mem@V2t3@bool) => (((p@V0t1) => ((p@V1t2) => (p@V2t3))) <=> (((p@V0t1) & (p@V1t2)) => (p@V2t3)))))))))).
thf(conj_thm_2Ebool_2EIMP__CONG,lemma,( ! [V0x:$i] : ((mem@V0x@bool) => ( ! [V1x_27:$i] : ((mem@V1x_27@bool) => ( ! [V2y:$i] : ((mem@V2y@bool) => ( ! [V3y_27:$i] : ((mem@V3y_27@bool) => ((((p@V0x) <=> (p@V1x_27)) & ((p@V1x_27) => ((p@V2y) <=> (p@V3y_27)))) => (((p@V0x) => (p@V2y)) <=> ((p@V1x_27) => (p@V3y_27))))))))))))).
thf(conj_thm_2Ebool_2ECOND__CONG,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => ( ! [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@V0P) <=> (p@V1Q)) & (((p@V1Q) => (V2x = V3x_27)) & ((~ (p@V1Q)) => (V4y = V5y_27)))) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0P)@V2x)@V4y) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V1Q)@V3x_27)@V5y_27))))))))))))))))).
thf(conj_thm_2Ebool_2EUNWIND__THM2,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1a:$i] : ((mem@V1a@A_27a) => ((? [V2x:$i] : ((mem@V2x@A_27a) & ((V2x = V1a) & (p@(ap@V0P@V2x))))) <=> (p@(ap@V0P@V1a))))))))).
thf(conj_thm_2Ebool_2Ebool__case__thm,lemma,( ! [A_27a:del]: (( ! [V0t1:$i] : ((mem@V0t1@A_27a) => ( ! [V1t2:$i] : ((mem@V1t2@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1))))) & ( ! [V2t1:$i] : ((mem@V2t1@A_27a) => ( ! [V3t2:$i] : ((mem@V3t2@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V2t1)@V3t2) = V3t2)))))))).
thf(ax_thm_2Ecombin_2EK__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ((c_2Ecombin_2EK@A_27a@A_27b) = (lam@A_27a@(^ [V0x:$i] : (lam@A_27b@(^ [V1y:$i] : V0x)))))))).
thf(ax_thm_2Ecombin_2ES__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ((c_2Ecombin_2ES@A_27a@A_27b@A_27c) = (lam@(arr@A_27a@(arr@A_27b@A_27c))@(^ [V0f:$i] : (lam@(arr@A_27a@A_27b)@(^ [V1g:$i] : (lam@A_27a@(^ [V2x:$i] : (ap@(ap@V0f@V2x)@(ap@V1g@V2x))))))))))))).
thf(ax_thm_2Ecombin_2EC__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ((c_2Ecombin_2EC@A_27a@A_27b@A_27c) = (lam@(arr@A_27a@(arr@A_27b@A_27c))@(^ [V0f:$i] : (lam@A_27b@(^ [V1x:$i] : (lam@A_27a@(^ [V2y:$i] : (ap@(ap@V0f@V2y)@V1x)))))))))))).
thf(ax_thm_2Ecombin_2Eo__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27c@A_27b)) => ( ! [V1g:$i] : ((mem@V1g@(arr@A_27a@A_27c)) => ((ap@(ap@(c_2Ecombin_2Eo@A_27a@A_27b@A_27c)@V0f)@V1g) = (lam@A_27a@(^ [V2x:$i] : (ap@V0f@(ap@V1g@V2x))))))))))))).
thf(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((ap@(c_2Ecombin_2EI@A_27a)@V0x) = V0x))))).
thf(conj_thm_2Ecombin_2EI__o__ID,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$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))))))).
thf(ax_thm_2Eextreal_2Eextreal__of__num__def,axiom,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2Eextreal__of__num@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2ENormal@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(conj_thm_2Eextreal_2Eextreal__add__def,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Eextreal_2Eextreal] : ( ! [V3v2:tp__ty_2Erealax_2Ereal] : ( ! [V4v5:tp__ty_2Erealax_2Ereal] : ( ! [V5v3:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2ENormal@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))) & (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(inj__ty_2Eextreal_2Eextreal @ V2a))) = fo__c_2Eextreal_2EPosInf) & (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) = fo__c_2Eextreal_2EPosInf) & (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V3v2)))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) = fo__c_2Eextreal_2EPosInf) & (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))) = fo__c_2Eextreal_2ENegInf) & (((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V4v5)))) = fo__c_2Eextreal_2ENegInf) & ((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V5v3)))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))) = fo__c_2Eextreal_2ENegInf)))))))))))))).
thf(conj_thm_2Eextreal_2Eextreal__le__def,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Eextreal_2Eextreal] : ( ! [V3v2:tp__ty_2Erealax_2Ereal] : ( ! [V4v3:tp__ty_2Erealax_2Ereal] : ( ! [V5v5:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) & (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ V2a))) <=> $true) & (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) <=> $true) & (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V3v2)))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) <=> $true) & (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))) <=> $false) & (((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V4v3)))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))) <=> $false) & ((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V5v5)))) <=> $false)))))))))))))).
thf(ax_thm_2Eextreal_2Eextreal__lt__def,axiom,( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ( ! [V1y:tp__ty_2Eextreal_2Eextreal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ V0x))@(inj__ty_2Eextreal_2Eextreal @ V1y))) <=> (~ (p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ V1y))@(inj__ty_2Eextreal_2Eextreal @ V0x)))))))).
thf(conj_thm_2Eextreal_2Eextreal__cases,lemma,( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ((V0x = fo__c_2Eextreal_2ENegInf) | ((V0x = fo__c_2Eextreal_2EPosInf) | (? [V1r:tp__ty_2Erealax_2Ereal] : (V0x = (surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1r))))))))).
thf(conj_thm_2Eextreal_2Eextreal__not__infty,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~ ((surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V0x))) = fo__c_2Eextreal_2ENegInf)) & (~ ((surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V0x))) = fo__c_2Eextreal_2EPosInf))))).
thf(conj_thm_2Eextreal_2Enum__not__infty,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((~ ((surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2Eextreal__of__num@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Eextreal_2ENegInf)) & (~ ((surj__ty_2Eextreal_2Eextreal @ (ap@c_2Eextreal_2Eextreal__of__num@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Eextreal_2EPosInf))))).
thf(conj_thm_2Eextreal_2Eextreal__lt__eq,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Eextreal_2Ele__infty,lemma,(( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ V0x))) & (p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ V0x))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))))) & (( ! [V1x:tp__ty_2Eextreal_2Eextreal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ V1x))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))) <=> (V1x = fo__c_2Eextreal_2ENegInf))) & ( ! [V2x:tp__ty_2Eextreal_2Eextreal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(inj__ty_2Eextreal_2Eextreal @ V2x))) <=> (V2x = fo__c_2Eextreal_2EPosInf)))))).
thf(conj_thm_2Eextreal_2Elt__infty,lemma,( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1y)))) & ((p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(ap@c_2Eextreal_2ENormal@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) & ((p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))) & ((~ (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ V0x))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf)))) & ((~ (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf))@(inj__ty_2Eextreal_2Eextreal @ V0x)))) & (((~ (V0x = fo__c_2Eextreal_2EPosInf)) <=> (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ V0x))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf)))) & ((~ (V0x = fo__c_2Eextreal_2ENegInf)) <=> (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf))@(inj__ty_2Eextreal_2Eextreal @ V0x))))))))))))).
thf(conj_thm_2Eextreal_2Elet__add2,lemma,( ! [V0w:tp__ty_2Eextreal_2Eextreal] : ( ! [V1x:tp__ty_2Eextreal_2Eextreal] : ( ! [V2y:tp__ty_2Eextreal_2Eextreal] : ( ! [V3z:tp__ty_2Eextreal_2Eextreal] : (((~ (V0w = fo__c_2Eextreal_2ENegInf)) & ((~ (V0w = fo__c_2Eextreal_2EPosInf)) & ((p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ V0w))@(inj__ty_2Eextreal_2Eextreal @ V1x))) & (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(inj__ty_2Eextreal_2Eextreal @ V2y))@(inj__ty_2Eextreal_2Eextreal @ V3z)))))) => (p@(ap@(ap@c_2Eextreal_2Eextreal__lt@(ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ V0w))@(inj__ty_2Eextreal_2Eextreal @ V2y)))@(ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ V1x))@(inj__ty_2Eextreal_2Eextreal @ V3z)))))))))).
thf(conj_thm_2Eextreal_2Eadd__rzero,lemma,( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ((surj__ty_2Eextreal_2Eextreal @ (ap@(ap@c_2Eextreal_2Eextreal__add@(inj__ty_2Eextreal_2Eextreal @ V0x))@(ap@c_2Eextreal_2Eextreal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(conj_thm_2Eextreal_2ESIMP__EXTREAL__ARCH,lemma,( ! [V0x:tp__ty_2Eextreal_2Eextreal] : ((~ (V0x = fo__c_2Eextreal_2EPosInf)) => (? [V1n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Eextreal_2Eextreal__le@(inj__ty_2Eextreal_2Eextreal @ V0x))@(ap@c_2Eextreal_2Eextreal__of__num@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(ax_thm_2Emeasure_2Ealgebra__def,axiom,( ! [A_27a:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(c_2Emeasure_2Ealgebra@A_27a)@V0a)) <=> ((p@(ap@(ap@(c_2Emeasure_2Esubset__class@A_27a)@(ap@(c_2Emeasure_2Espace@A_27a)@V0a))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) & ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(c_2Epred__set_2EEMPTY@A_27a))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) & (( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V1s)@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EDIFF@A_27a)@(ap@(c_2Emeasure_2Espace@A_27a)@V0a))@V1s))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))) & ( ! [V2s:$i] : ((mem@V2s@(arr@A_27a@bool)) => ( ! [V3t:$i] : ((mem@V3t@(arr@A_27a@bool)) => (((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V2s)@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) & (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V3t)@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EUNION@A_27a)@V2s)@V3t))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))))))))))))).
thf(ax_thm_2Emeasure_2Esigma__algebra__def,axiom,( ! [A_27a:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(c_2Emeasure_2Esigma__algebra@A_27a)@V0a)) <=> ((p@(ap@(c_2Emeasure_2Ealgebra@A_27a)@V0a)) & ( ! [V1c:$i] : ((mem@V1c@(arr@(arr@A_27a@bool)@bool)) => (((p@(ap@(c_2Epred__set_2Ecountable@(arr@A_27a@bool))@V1c)) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@(arr@A_27a@bool))@V1c)@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(c_2Epred__set_2EBIGUNION@A_27a)@V1c))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))))))))).
thf(conj_thm_2Emeasure_2EALGEBRA__SPACE,lemma,( ! [A_27a:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(c_2Emeasure_2Ealgebra@A_27a)@V0a)) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(c_2Emeasure_2Espace@A_27a)@V0a))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))))).
thf(conj_thm_2Emeasure_2ESIGMA__ALGEBRA__ENUM,lemma,( ! [A_27a:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Enum_2Enum@(arr@A_27a@bool))) => (((p@(ap@(c_2Emeasure_2Esigma__algebra@A_27a)@V0a)) & (p@(ap@(ap@(c_2Ebool_2EIN@(arr@ty_2Enum_2Enum@(arr@A_27a@bool)))@V1f)@(ap@(ap@(c_2Epred__set_2EFUNSET@ty_2Enum_2Enum@(arr@A_27a@bool))@(c_2Epred__set_2EUNIV@ty_2Enum_2Enum))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(c_2Epred__set_2EBIGUNION@A_27a)@(ap@(ap@(c_2Epred__set_2EIMAGE@ty_2Enum_2Enum@(arr@A_27a@bool))@V1f)@(c_2Epred__set_2EUNIV@ty_2Enum_2Enum))))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))))))).
thf(conj_thm_2Emeasure_2ESIGMA__ALGEBRA__FN__BIGINTER,lemma,( ! [A_27a:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(c_2Emeasure_2Esigma__algebra@A_27a)@V0a)) => ((p@(ap@(ap@(c_2Emeasure_2Esubset__class@A_27a)@(ap@(c_2Emeasure_2Espace@A_27a)@V0a))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) & ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(c_2Epred__set_2EEMPTY@A_27a))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) & (( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V1s)@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EDIFF@A_27a)@(ap@(c_2Emeasure_2Espace@A_27a)@V0a))@V1s))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))) & ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Enum_2Enum@(arr@A_27a@bool))) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@ty_2Enum_2Enum@(arr@A_27a@bool)))@V2f)@(ap@(ap@(c_2Epred__set_2EFUNSET@ty_2Enum_2Enum@(arr@A_27a@bool))@(c_2Epred__set_2EUNIV@ty_2Enum_2Enum))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(c_2Epred__set_2EBIGINTER@A_27a)@(ap@(ap@(c_2Epred__set_2EIMAGE@ty_2Enum_2Enum@(arr@A_27a@bool))@V2f)@(c_2Epred__set_2EUNIV@ty_2Enum_2Enum))))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V0a)))))))))))))).
thf(conj_thm_2Emeasure_2EIN__MEASURABLE__BOREL,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@ty_2Eextreal_2Eextreal)) => ( ! [V1a:$i] : ((mem@V1a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@ty_2Eextreal_2Eextreal))@V0f)@(ap@(ap@(c_2Emeasure_2Emeasurable@A_27a@ty_2Eextreal_2Eextreal)@V1a)@c_2Emeasure_2EBorel))) <=> ((p@(ap@(c_2Emeasure_2Esigma__algebra@A_27a)@V1a)) & ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@ty_2Eextreal_2Eextreal))@V0f)@(ap@(ap@(c_2Epred__set_2EFUNSET@A_27a@ty_2Eextreal_2Eextreal)@(ap@(c_2Emeasure_2Espace@A_27a)@V1a))@(c_2Epred__set_2EUNIV@ty_2Eextreal_2Eextreal)))) & ( ! [V2c:tp__ty_2Eextreal_2Eextreal] : (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EINTER@A_27a)@(ap@(c_2Epred__set_2EGSPEC@A_27a@A_27a)@(lam@A_27a@(^ [V3x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V3x)@(ap@(ap@c_2Eextreal_2Eextreal__lt@(ap@V0f@V3x))@(inj__ty_2Eextreal_2Eextreal @ V2c)))))))@(ap@(c_2Emeasure_2Espace@A_27a)@V1a)))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V1a))))))))))))).
thf(conj_thm_2Emeasure_2EIN__MEASURABLE__BOREL__NEGINF,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@ty_2Eextreal_2Eextreal)) => ( ! [V1a:$i] : ((mem@V1a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@ty_2Eextreal_2Eextreal))@V0f)@(ap@(ap@(c_2Emeasure_2Emeasurable@A_27a@ty_2Eextreal_2Eextreal)@V1a)@c_2Emeasure_2EBorel))) => (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EINTER@A_27a)@(ap@(c_2Epred__set_2EGSPEC@A_27a@A_27a)@(lam@A_27a@(^ [V2x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V2x)@(ap@(ap@(c_2Emin_2E_3D@ty_2Eextreal_2Eextreal)@(ap@V0f@V2x))@(inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf)))))))@(ap@(c_2Emeasure_2Espace@A_27a)@V1a)))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V1a)))))))))).
thf(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))))))))))))))))))))))))))))))))))))))).
thf(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)))))))))))).
thf(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))))))))))))).
thf(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))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Epair_2ECLOSED__PAIR__EQ,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27b) => ( ! [V2a:$i] : ((mem@V2a@A_27a) => ( ! [V3b:$i] : ((mem@V3b@A_27b) => (((ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V0x)@V1y) = (ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V2a)@V3b)) <=> ((V0x = V2a) & (V1y = V3b)))))))))))))).
thf(conj_thm_2Epred__set_2EEXTENSION,lemma,( ! [A_27a:del]: ( ! [V0s:$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)))))))))))).
thf(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:$i] : ((mem@V2x@A_27b) & ((ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V1v)@c_2Ebool_2ET) = (ap@V0f@V2x)))))))))))).
thf(conj_thm_2Epred__set_2EIN__UNIV,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(c_2Epred__set_2EUNIV@A_27a))))))).
thf(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:$i] : ((mem@V2x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@(ap@(ap@(c_2Epred__set_2EINTER@A_27a)@V0s)@V1t))) <=> ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) & (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t)))))))))))).
thf(conj_thm_2Epred__set_2EINTER__EMPTY,lemma,( ! [A_27a:del]: (( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ((ap@(ap@(c_2Epred__set_2EINTER@A_27a)@(c_2Epred__set_2EEMPTY@A_27a))@V0s) = (c_2Epred__set_2EEMPTY@A_27a)))) & ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((ap@(ap@(c_2Epred__set_2EINTER@A_27a)@V1s)@(c_2Epred__set_2EEMPTY@A_27a)) = (c_2Epred__set_2EEMPTY@A_27a))))))).
thf(conj_thm_2Epred__set_2EINTER__UNIV,lemma,( ! [A_27a:del]: (( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ((ap@(ap@(c_2Epred__set_2EINTER@A_27a)@(c_2Epred__set_2EUNIV@A_27a))@V0s) = V0s))) & ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((ap@(ap@(c_2Epred__set_2EINTER@A_27a)@V1s)@(c_2Epred__set_2EUNIV@A_27a)) = V1s)))))).
thf(conj_thm_2Epred__set_2EIN__DIFF,lemma,( ! [A_27a:del]: ( ! [V0s:$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_2EDIFF@A_27a)@V0s)@V1t))) <=> ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) & (~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t))))))))))))).
thf(conj_thm_2Epred__set_2EIN__FUNSET,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1P:$i] : ((mem@V1P@(arr@A_27a@bool)) => ( ! [V2Q:$i] : ((mem@V2Q@(arr@A_27b@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@A_27b))@V0f)@(ap@(ap@(c_2Epred__set_2EFUNSET@A_27a@A_27b)@V1P)@V2Q))) <=> ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3x)@V1P)) => (p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@(ap@V0f@V3x))@V2Q))))))))))))))).
thf(conj_thm_2Epred__set_2EIN__BIGUNION__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@(arr@A_27b@bool))) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ( ! [V2y:$i] : ((mem@V2y@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V2y)@(ap@(c_2Epred__set_2EBIGUNION@A_27b)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27a@(arr@A_27b@bool))@V0f)@V1s)))) <=> (? [V3x:$i] : ((mem@V3x@A_27a) & ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3x)@V1s)) & (p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V2y)@(ap@V0f@V3x)))))))))))))))).
thf(conj_thm_2Epred__set_2EIN__BIGINTER__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27b@(arr@A_27a@bool))) => ( ! [V2s:$i] : ((mem@V2s@(arr@A_27b@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(c_2Epred__set_2EBIGINTER@A_27a)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27b@(arr@A_27a@bool))@V1f)@V2s)))) <=> ( ! [V3y:$i] : ((mem@V3y@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V3y)@V2s)) => (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@V1f@V3y)))))))))))))))).
thf(conj_thm_2Epred__set_2EGSPEC__F,lemma,( ! [A_27a:del]: ((ap@(c_2Epred__set_2EGSPEC@A_27a@A_27a)@(lam@A_27a@(^ [V0x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V0x)@c_2Ebool_2EF)))) = (c_2Epred__set_2EEMPTY@A_27a)))).
thf(conj_thm_2Epred__set_2EGSPEC__T,lemma,( ! [A_27a:del]: ((ap@(c_2Epred__set_2EGSPEC@A_27a@A_27a)@(lam@A_27a@(^ [V0x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V0x)@c_2Ebool_2ET)))) = (c_2Epred__set_2EUNIV@A_27a)))).
thf(conj_thm_2Ereal_2EREAL__ADD__COMM,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))))))).
thf(conj_thm_2Ereal_2EREAL__LT__IADD,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 @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))) => (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))))))))).
thf(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)))))))).
thf(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))).
thf(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)))))).
thf(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))))))).
thf(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)))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(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))))).
thf(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))))))).
thf(conj_thm_2Ereal_2EREAL__LT,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(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_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(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))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADD__SUB,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)))@(inj__ty_2Erealax_2Ereal @ V2z))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__RZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(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))))))).
thf(conj_thm_2Ereal_2EABS__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x))) = 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)))))).
thf(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)))))))).
thf(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)))))))).
thf(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))))))))).
thf(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)@(lam@ty_2Erealax_2Ereal@(^ [V4x:$i] : V4x)))@(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))))))))))))))).
thf(conj_thm_2Ereal_2Eneg__rat,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (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@c_2Erealax_2Ereal__neg@(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@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) = (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@(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@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(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)))))))).
thf(conj_thm_2Ereal_2Elt__ratr,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(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_2Erealax_2Ereal__lt@(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_2Erealax_2Ereal__lt@(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))))))))).
thf(conj_thm_2Esat_2ENOT__NOT,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t))))).
thf(conj_thm_2Esat_2EAND__INV__IMP,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ((p@V0A) => ((~ (p@V0A)) => $false))))).
thf(conj_thm_2Esat_2EOR__DUAL2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) | (p@V1B))) => $false) <=> (((p@V0A) => $false) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EOR__DUAL3,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((~ (p@V0A)) | (p@V1B))) => $false) <=> ((p@V0A) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EAND__INV2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => (((~ (p@V0A)) => $false) => (((p@V0A) => $false) => $false))))).
thf(conj_thm_2Esat_2Edc__eq,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) <=> (p@V2r))) <=> (((p@V0p) | ((p@V1q) | (p@V2r))) & (((p@V0p) | ((~ (p@V2r)) | (~ (p@V1q)))) & (((p@V1q) | ((~ (p@V2r)) | (~ (p@V0p)))) & ((p@V2r) | ((~ (p@V1q)) | (~ (p@V0p))))))))))))))).
thf(conj_thm_2Esat_2Edc__conj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) & (p@V2r))) <=> (((p@V0p) | ((~ (p@V1q)) | (~ (p@V2r)))) & (((p@V1q) | (~ (p@V0p))) & ((p@V2r) | (~ (p@V0p))))))))))))).
thf(conj_thm_2Esat_2Edc__disj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) | (p@V2r))) <=> (((p@V0p) | (~ (p@V1q))) & (((p@V0p) | (~ (p@V2r))) & ((p@V1q) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__imp,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) => (p@V2r))) <=> (((p@V0p) | (p@V1q)) & (((p@V0p) | (~ (p@V2r))) & ((~ (p@V1q)) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__neg,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (~ (p@V1q))) <=> (((p@V0p) | (p@V1q)) & ((~ (p@V1q)) | (~ (p@V0p)))))))))).
thf(conj_thm_2Esat_2Epth__ni1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (p@V0p))))))).
thf(conj_thm_2Esat_2Epth__ni2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__no1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V0p)))))))).
thf(conj_thm_2Esat_2Epth__no2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__nn,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((~ (~ (p@V0p))) => (p@V0p))))).
thf(conj_thm_2Eseq_2ESEQ,lemma,( ! [V0x:$i] : ((mem@V0x@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1x0:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V0x)@(inj__ty_2Erealax_2Ereal @ V1x0))) <=> ( ! [V2e:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2e))) => (? [V3N:tp__ty_2Enum_2Enum] : ( ! [V4n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V4n))@(inj__ty_2Enum_2Enum @ V3N))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0x@(inj__ty_2Enum_2Enum @ V4n)))@(inj__ty_2Erealax_2Ereal @ V1x0))))@(inj__ty_2Erealax_2Ereal @ V2e))))))))))))).
thf(conj_thm_2Eseq_2ESEQ__CONST,lemma,( ! [V0k:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@(lam@ty_2Enum_2Enum@(^ [V1x:$i] : (inj__ty_2Erealax_2Ereal @ V0k))))@(inj__ty_2Erealax_2Ereal @ V0k))))).
thf(conj_thm_2Eseq_2ESEQ__ADD,lemma,( ! [V0x:$i] : ((mem@V0x@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1x0:tp__ty_2Erealax_2Ereal] : ( ! [V2y:$i] : ((mem@V2y@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V3y0:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V0x)@(inj__ty_2Erealax_2Ereal @ V1x0))) & (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V2y)@(inj__ty_2Erealax_2Ereal @ V3y0)))) => (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@(lam@ty_2Enum_2Enum@(^ [V4n:$i] : (ap@(ap@c_2Erealax_2Ereal__add@(ap@V0x@V4n))@(ap@V2y@V4n)))))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x0))@(inj__ty_2Erealax_2Ereal @ V3y0)))))))))))).
thf(conj_thm_2Eseq_2ESEQ__SUB,lemma,( ! [V0x:$i] : ((mem@V0x@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1x0:tp__ty_2Erealax_2Ereal] : ( ! [V2y:$i] : ((mem@V2y@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V3y0:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V0x)@(inj__ty_2Erealax_2Ereal @ V1x0))) & (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V2y)@(inj__ty_2Erealax_2Ereal @ V3y0)))) => (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@(lam@ty_2Enum_2Enum@(^ [V4n:$i] : (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0x@V4n))@(ap@V2y@V4n)))))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1x0))@(inj__ty_2Erealax_2Ereal @ V3y0)))))))))))).
thf(conj_thm_2Eseq_2ESEQ__POWER,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0c)))@(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_2Eseq_2E_2D_2D_3E@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@V1n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Eseq_2ELE__SEQ__IMP__LE__LIM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((( ! [V3n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@V2f@(inj__ty_2Enum_2Enum @ V3n))))) & (p@(ap@(ap@c_2Eseq_2E_2D_2D_3E@V2f)@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Emeasure_2EIN__MEASURABLE__BOREL__ALT2,conjecture,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@ty_2Eextreal_2Eextreal)) => ( ! [V1a:$i] : ((mem@V1a@(ty_2Epair_2Eprod@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@ty_2Eextreal_2Eextreal))@V0f)@(ap@(ap@(c_2Emeasure_2Emeasurable@A_27a@ty_2Eextreal_2Eextreal)@V1a)@c_2Emeasure_2EBorel))) <=> ((p@(ap@(c_2Emeasure_2Esigma__algebra@A_27a)@V1a)) & ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@ty_2Eextreal_2Eextreal))@V0f)@(ap@(ap@(c_2Epred__set_2EFUNSET@A_27a@ty_2Eextreal_2Eextreal)@(ap@(c_2Emeasure_2Espace@A_27a)@V1a))@(c_2Epred__set_2EUNIV@ty_2Eextreal_2Eextreal)))) & ( ! [V2c:tp__ty_2Eextreal_2Eextreal] : (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@(ap@(ap@(c_2Epred__set_2EINTER@A_27a)@(ap@(c_2Epred__set_2EGSPEC@A_27a@A_27a)@(lam@A_27a@(^ [V3x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V3x)@(ap@(ap@c_2Eextreal_2Eextreal__le@(ap@V0f@V3x))@(inj__ty_2Eextreal_2Eextreal @ V2c)))))))@(ap@(c_2Emeasure_2Espace@A_27a)@V1a)))@(ap@(c_2Emeasure_2Esubsets@A_27a)@V1a))))))))))))).
