include('Axioms/HL4001^2.ax').
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_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: del > del >del )).
thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum : $tType)).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum : (tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i))).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,(surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum : ($i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum))).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : (mem @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X) @ (ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)) => (X = (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ (surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Eieee_2Eexpwidth,type,(c_2Eieee_2Eexpwidth:$i)).
thf(mem_c_2Eieee_2Eexpwidth,axiom,(mem@c_2Eieee_2Eexpwidth@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eieee_2Eexpwidth,type,(fo__c_2Eieee_2Eexpwidth:(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eieee_2Eexpwidth,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eieee_2Eexpwidth @ X0)) = (ap @ c_2Eieee_2Eexpwidth @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Eieee_2Efracwidth,type,(c_2Eieee_2Efracwidth:$i)).
thf(mem_c_2Eieee_2Efracwidth,axiom,(mem@c_2Eieee_2Efracwidth@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eieee_2Efracwidth,type,(fo__c_2Eieee_2Efracwidth:(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eieee_2Efracwidth,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eieee_2Efracwidth @ X0)) = (ap @ c_2Eieee_2Efracwidth @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Eieee_2Ebias,type,(c_2Eieee_2Ebias:$i)).
thf(mem_c_2Eieee_2Ebias,axiom,(mem@c_2Eieee_2Ebias@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eieee_2Ebias,type,(fo__c_2Eieee_2Ebias:(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eieee_2Ebias,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eieee_2Ebias @ X0)) = (ap @ c_2Eieee_2Ebias @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Eieee_2Eemax,type,(c_2Eieee_2Eemax:$i)).
thf(mem_c_2Eieee_2Eemax,axiom,(mem@c_2Eieee_2Eemax@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eieee_2Eemax,type,(fo__c_2Eieee_2Eemax:(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eieee_2Eemax,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eieee_2Eemax @ X0)) = (ap @ c_2Eieee_2Eemax @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0))))).
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:$i] : ((mem @ X @ ty_2Erealax_2Ereal) => (X = (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X)))))).
thf(tp_c_2Eieee_2Elargest,type,(c_2Eieee_2Elargest:$i)).
thf(mem_c_2Eieee_2Elargest,axiom,(mem@c_2Eieee_2Elargest@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Eieee_2Elargest,type,(fo__c_2Eieee_2Elargest:(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Eieee_2Elargest,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Eieee_2Elargest @ X0)) = (ap @ c_2Eieee_2Elargest @ (inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del>(del>$i)))).
thf(mem_c_2Epair_2E_2C,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epair_2E_2C@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@A_27b))))))).
thf(tp_c_2Eieee_2Efloat__format,type,(c_2Eieee_2Efloat__format:$i)).
thf(mem_c_2Eieee_2Efloat__format,axiom,(mem@c_2Eieee_2Efloat__format@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
thf(mem_c_2Earithmetic_2E_3E_3D,axiom,(mem@c_2Earithmetic_2E_3E_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$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_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
thf(mem_c_2Enumeral_2EiZ,axiom,(mem@c_2Enumeral_2EiZ@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiZ @ X0)) = (ap @ c_2Enumeral_2EiZ @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$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_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Enumeral_2EiSUB,type,(c_2Enumeral_2EiSUB:$i)).
thf(mem_c_2Enumeral_2EiSUB,axiom,(mem@c_2Enumeral_2EiSUB@(arr@bool@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(tp_c_2Enumeral_2EiDUB,type,(c_2Enumeral_2EiDUB:$i)).
thf(mem_c_2Enumeral_2EiDUB,axiom,(mem@c_2Enumeral_2EiDUB@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiDUB,type,(fo__c_2Enumeral_2EiDUB:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiDUB @ X0)) = (ap @ c_2Enumeral_2EiDUB @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
thf(mem_c_2Earithmetic_2EEVEN,axiom,(mem@c_2Earithmetic_2EEVEN@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X0)) = (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2Eonecount,type,(c_2Enumeral_2Eonecount:$i)).
thf(mem_c_2Enumeral_2Eonecount,axiom,(mem@c_2Enumeral_2Eonecount@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Enumeral_2Eonecount,type,(fo__c_2Enumeral_2Eonecount:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Enumeral_2Eonecount,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Enumeral_2Eonecount @ X0) @ X1)) = (ap @ (ap @ c_2Enumeral_2Eonecount @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2Eexactlog,type,(c_2Enumeral_2Eexactlog:$i)).
thf(mem_c_2Enumeral_2Eexactlog,axiom,(mem@c_2Enumeral_2Eexactlog@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2Eexactlog,type,(fo__c_2Enumeral_2Eexactlog:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2Eexactlog,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2Eexactlog @ X0)) = (ap @ c_2Enumeral_2Eexactlog @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$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_2Earithmetic_2EDIV2,type,(c_2Earithmetic_2EDIV2:$i)).
thf(mem_c_2Earithmetic_2EDIV2,axiom,(mem@c_2Earithmetic_2EDIV2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EDIV2,type,(fo__c_2Earithmetic_2EDIV2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EDIV2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EDIV2 @ X0)) = (ap @ c_2Earithmetic_2EDIV2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2Etexp__help,type,(c_2Enumeral_2Etexp__help:$i)).
thf(mem_c_2Enumeral_2Etexp__help,axiom,(mem@c_2Enumeral_2Etexp__help@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Enumeral_2Etexp__help,type,(fo__c_2Enumeral_2Etexp__help:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Enumeral_2Etexp__help,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Enumeral_2Etexp__help @ X0) @ X1)) = (ap @ (ap @ c_2Enumeral_2Etexp__help @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ebool_2ELET,type,(c_2Ebool_2ELET:(del>(del>$i)))).
thf(mem_c_2Ebool_2ELET,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebool_2ELET@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@A_27a@A_27b)))))).
thf(tp_c_2Enumeral_2Einternal__mult,type,(c_2Enumeral_2Einternal__mult:$i)).
thf(mem_c_2Enumeral_2Einternal__mult,axiom,(mem@c_2Enumeral_2Einternal__mult@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Enumeral_2Einternal__mult,type,(fo__c_2Enumeral_2Einternal__mult:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Enumeral_2Einternal__mult,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Enumeral_2Einternal__mult @ X0) @ X1)) = (ap @ (ap @ c_2Enumeral_2Einternal__mult @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$i)).
thf(mem_c_2Ereal_2Ereal__sub,axiom,(mem@c_2Ereal_2Ereal__sub@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Ereal__sub,type,(fo__c_2Ereal_2Ereal__sub:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Ereal__sub @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Ereal__sub @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Erealax_2Einv,type,(c_2Erealax_2Einv:$i)).
thf(mem_c_2Erealax_2Einv,axiom,(mem@c_2Erealax_2Einv@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Erealax_2Einv,type,(fo__c_2Erealax_2Einv:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Erealax_2Einv,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Erealax_2Einv @ X0)) = (ap @ c_2Erealax_2Einv @ (inj__ty_2Erealax_2Ereal @ X0))))).
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_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:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$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_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
thf(mem_c_2Earithmetic_2E_2D,axiom,(mem@c_2Earithmetic_2E_2D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2D @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$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_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2B @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Erealax_2Ereal__add,type,(c_2Erealax_2Ereal__add:$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_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2A @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Erealax_2Ereal__mul,type,(c_2Erealax_2Ereal__mul:$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_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:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$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_2Epow,type,(c_2Ereal_2Epow:$i)).
thf(mem_c_2Ereal_2Epow,axiom,(mem@c_2Ereal_2Epow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Epow @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Epow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Emarker_2Eunint,type,(c_2Emarker_2Eunint:(del>$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_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Erealax_2Ereal__neg,type,(c_2Erealax_2Ereal__neg:$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_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
thf(mem_c_2Ereal_2Ereal__of__num,axiom,(mem@c_2Ereal_2Ereal__of__num@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Ereal__of__num @ X0)) = (ap @ c_2Ereal_2Ereal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:(del>$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_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:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_2F_5C@Q)@R)) <=> ((p@Q) & (p@R)))))))).
thf(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:(del>$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(ax_thm_2Ebool_2ELET__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ((c_2Ebool_2ELET@A_27a@A_27b) = (lam@(arr@A_27a@A_27b)@(^ [V0f:$i] : (lam@A_27a@(^ [V1x:$i] : (ap@V0f@V1x))))))))).
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(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) => ($false => (p@V0t))))).
thf(conj_thm_2Ebool_2EAND__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true & (p@V0t)) <=> (p@V0t)) & ((((p@V0t) & $true) <=> (p@V0t)) & ((($false & (p@V0t)) <=> $false) & ((((p@V0t) & $false) <=> $false) & (((p@V0t) & (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,( ! [V0t:$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)) <=> $true)))).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((V0x = V0x) <=> $true))))).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,( ! [V0t:$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:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2Ebool__case__thm,lemma,( ! [A_27a:del]: (( ! [V0t1:$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_2Eieee_2Eexpwidth,axiom,( ! [V0ew:tp__ty_2Enum_2Enum] : ( ! [V1fw:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eieee_2Eexpwidth@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0ew))@(inj__ty_2Enum_2Enum @ V1fw)))) = V0ew)))).
thf(ax_thm_2Eieee_2Efracwidth,axiom,( ! [V0ew:tp__ty_2Enum_2Enum] : ( ! [V1fw:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eieee_2Efracwidth@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0ew))@(inj__ty_2Enum_2Enum @ V1fw)))) = V1fw)))).
thf(ax_thm_2Eieee_2Eemax,axiom,( ! [V0X:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eieee_2Eemax@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@c_2Eieee_2Eexpwidth@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(ax_thm_2Eieee_2Ebias,axiom,( ! [V0X:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eieee_2Ebias@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Eieee_2Eexpwidth@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(ax_thm_2Eieee_2Elargest,axiom,( ! [V0X:tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Eieee_2Elargest@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Eieee_2Eemax@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Eieee_2Ebias@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X)))))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Eieee_2Efracwidth@(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ V0X)))))))))).
thf(ax_thm_2Eieee_2Efloat__format,axiom,((surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ c_2Eieee_2Efloat__format) = (surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ (ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))).
thf(conj_thm_2Enumeral_2Enumeral__suc,lemma,(((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
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__pre,lemma,(((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = fo__c_2Earithmetic_2EZERO) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))))) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1n)))))) & ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))))))))).
thf(conj_thm_2Enumeral_2EiSUB__THM,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@V1b)@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0x))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = V2n) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__sub,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Enumeral_2EiDUB__removal,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0n))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) & ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO))))).
thf(conj_thm_2Enumeral_2Enumeral__evenodd,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) & ((p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) & ((~ (p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & (p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__texp__help,lemma,( ! [V0acc:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Etexp__help@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0acc))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0acc)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V0acc))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1n))))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0acc))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V0acc))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0acc)))))))))).
thf(conj_thm_2Enumeral_2ETWO__EXP__THM,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(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))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(ax_thm_2Enumeral_2Eonecount__def,axiom,(( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Eonecount@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0x))) = V0x)) & (( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Eonecount@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V2x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Eonecount@(inj__ty_2Enum_2Enum @ V1n))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2x))))))) & ( ! [V3n:tp__ty_2Enum_2Enum] : ( ! [V4x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Eonecount@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3n)))@(inj__ty_2Enum_2Enum @ V4x))) = fo__c_2Earithmetic_2EZERO)))))).
thf(ax_thm_2Enumeral_2Eexactlog__def,axiom,(((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2Eexactlog@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = fo__c_2Earithmetic_2EZERO)) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(c_2Ebool_2ELET@ty_2Enum_2Enum@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V2x:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@V2x)@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT1@V2x)))))@(ap@(ap@c_2Enumeral_2Eonecount@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Enumeral_2EDIV2__BIT1,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EDIV2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0x)))) = V0x))).
thf(conj_thm_2Enumeral_2Eenumeral__mult,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Enum_2Enum] : ( ! [V2y:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2y)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral_2Einternal__mult@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2y))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(c_2Ebool_2ELET@ty_2Enum_2Enum@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@c_2Earithmetic_2EODD@V3n))@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EDIV2@V3n))@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1x)))))@(ap@(ap@c_2Enumeral_2Einternal__mult@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))))))@(ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2y)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(c_2Ebool_2ELET@ty_2Enum_2Enum@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V4m:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@c_2Earithmetic_2EODD@V4m))@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EDIV2@V4m))@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2y)))))@(ap@(ap@c_2Enumeral_2Einternal__mult@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2y)))))))@(ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(c_2Ebool_2ELET@ty_2Enum_2Enum@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V5m:$i] : (ap@(ap@(c_2Ebool_2ELET@ty_2Enum_2Enum@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V6n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@c_2Earithmetic_2EODD@V5m))@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EDIV2@V5m))@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))))@(ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@c_2Earithmetic_2EODD@V6n))@(ap@(ap@c_2Enumeral_2Etexp__help@(ap@c_2Earithmetic_2EDIV2@V6n))@(ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))))@(ap@(ap@c_2Enumeral_2Einternal__mult@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y))))))))@(ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2y)))))))@(ap@c_2Enumeral_2Eexactlog@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1x))))))))))))))).
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__MUL__RID,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__INV__1OVER,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
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__OVER1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__DIV__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Ereal_2Eadd__ratr,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2z))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(c_2Emarker_2Eunint@ty_2Erealax_2Ereal)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2Eadd__ints,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))))@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))))))))).
thf(conj_thm_2Ereal_2Emult__rat,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2u:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3v)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(c_2Emarker_2Eunint@ty_2Erealax_2Ereal)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3v))))@(ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V3v))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(c_2Emarker_2Eunint@ty_2Erealax_2Ereal)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3v)))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2u)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V3v)))))))))))).
thf(conj_thm_2Ereal_2Emult__ratr,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2z))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(c_2Emarker_2Eunint@ty_2Erealax_2Ereal)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2Emult__ints,lemma,( ! [V0a:tp__ty_2Enum_2Enum] : ( ! [V1b:tp__ty_2Enum_2Enum] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0a)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1b)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1b))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0a))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1b)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1b)))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0a)))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1b))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1b)))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0a))))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1b))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1b))))))))))).
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_2Efloat_2EFLOAT__LARGEST__EXPLICIT,conjecture,((surj__ty_2Erealax_2Ereal @ (ap@c_2Eieee_2Elargest@c_2Eieee_2Efloat__format)) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
