include('Axioms/basis_emit^2.ax').
thf(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
thf(mem_c_2Ereal_2E_2F,axiom,(mem@c_2Ereal_2E_2F@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2E_2F,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2E_2F @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2E_2F @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Ereal_2ENUM__CEILING,type,(c_2Ereal_2ENUM__CEILING:$i)).
thf(mem_c_2Ereal_2ENUM__CEILING,axiom,(mem@c_2Ereal_2ENUM__CEILING@(arr@ty_2Erealax_2Ereal@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ereal_2ENUM__CEILING,type,(fo__c_2Ereal_2ENUM__CEILING:(tp__ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ereal_2ENUM__CEILING,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ereal_2ENUM__CEILING @ X0)) = (ap @ c_2Ereal_2ENUM__CEILING @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Ereal_2ENUM__FLOOR,type,(c_2Ereal_2ENUM__FLOOR:$i)).
thf(mem_c_2Ereal_2ENUM__FLOOR,axiom,(mem@c_2Ereal_2ENUM__FLOOR@(arr@ty_2Erealax_2Ereal@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ereal_2ENUM__FLOOR,type,(fo__c_2Ereal_2ENUM__FLOOR:(tp__ty_2Erealax_2Ereal > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ereal_2ENUM__FLOOR,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ereal_2ENUM__FLOOR @ X0)) = (ap @ c_2Ereal_2ENUM__FLOOR @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Ereal_2Eabs,type,(c_2Ereal_2Eabs:$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_2Ereal_2Einf,type,(c_2Ereal_2Einf:$i)).
thf(mem_c_2Ereal_2Einf,axiom,(mem@c_2Ereal_2Einf@(arr@(arr@ty_2Erealax_2Ereal@bool)@ty_2Erealax_2Ereal))).
thf(tp_c_2Ereal_2Emax,type,(c_2Ereal_2Emax:$i)).
thf(mem_c_2Ereal_2Emax,axiom,(mem@c_2Ereal_2Emax@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Emax,type,(fo__c_2Ereal_2Emax:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Emax,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Emax @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Emax @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Ereal_2Emin,type,(c_2Ereal_2Emin:$i)).
thf(mem_c_2Ereal_2Emin,axiom,(mem@c_2Ereal_2Emin@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Emin,type,(fo__c_2Ereal_2Emin:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Emin,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Emin @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Emin @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Ereal_2Epos,type,(c_2Ereal_2Epos:$i)).
thf(mem_c_2Ereal_2Epos,axiom,(mem@c_2Ereal_2Epos@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Epos,type,(fo__c_2Ereal_2Epos:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Epos,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Epos @ X0)) = (ap @ c_2Ereal_2Epos @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
thf(mem_c_2Ereal_2Epow,axiom,(mem@c_2Ereal_2Epow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Epow @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Epow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ereal_2Ereal__ge,type,(c_2Ereal_2Ereal__ge:$i)).
thf(mem_c_2Ereal_2Ereal__ge,axiom,(mem@c_2Ereal_2Ereal__ge@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Ereal_2Ereal__gt,type,(c_2Ereal_2Ereal__gt:$i)).
thf(mem_c_2Ereal_2Ereal__gt,axiom,(mem@c_2Ereal_2Ereal__gt@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Ereal_2Ereal__lte,type,(c_2Ereal_2Ereal__lte:$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_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
thf(mem_c_2Ereal_2Ereal__of__num,axiom,(mem@c_2Ereal_2Ereal__of__num@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Ereal__of__num @ X0)) = (ap @ c_2Ereal_2Ereal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$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_2Ereal_2Esum,type,(c_2Ereal_2Esum:$i)).
thf(mem_c_2Ereal_2Esum,axiom,(mem@c_2Ereal_2Esum@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@(arr@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@ty_2Erealax_2Ereal)))).
thf(tp_c_2Ereal_2Esup,type,(c_2Ereal_2Esup:$i)).
thf(mem_c_2Ereal_2Esup,axiom,(mem@c_2Ereal_2Esup@(arr@(arr@ty_2Erealax_2Ereal@bool)@ty_2Erealax_2Ereal))).
thf(ax_thm_2Ereal_2Ereal__of__num,axiom,(((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Erealax_2Ereal__0) & ( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Erealax_2Ereal__1))))))).
thf(conj_thm_2Ereal_2EREAL__0,lemma,(fo__c_2Erealax_2Ereal__0 = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Ereal_2EREAL__1,lemma,(fo__c_2Erealax_2Ereal__1 = (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_2EREAL__10,lemma,(~~ ((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@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
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__ADD__ASSOC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Ereal_2EREAL__LDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__TOTAL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((V0x = V1y) | ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) | (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (~~ (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
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(conj_thm_2Ereal_2EREAL__SUP__ALLPOS,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => ((( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x))) => (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 @ V1x))))) & ((? [V2x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V2x)))) & (? [V3z:tp__ty_2Erealax_2Ereal] : ( ! [V4x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V4x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))) => (? [V5s:tp__ty_2Erealax_2Ereal] : ( ! [V6y:tp__ty_2Erealax_2Ereal] : ((? [V7x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V7x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6y))@(inj__ty_2Erealax_2Ereal @ V7x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6y))@(inj__ty_2Erealax_2Ereal @ V5s)))))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__COMM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__MUL__LINV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__INV__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(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(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(ax_thm_2Ereal_2Ereal__lte,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (~ (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(ax_thm_2Ereal_2Ereal__gt,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__gt@(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(ax_thm_2Ereal_2Ereal__ge,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__ge@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(ax_thm_2Ereal_2Ereal__div,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
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__ADD__RINV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
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__MUL__RINV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Einv@(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_2EREAL__RDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__LADD,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))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (V1y = V2z)))))).
thf(conj_thm_2Ereal_2EREAL__EQ__RADD,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))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (V0x = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__ADD__LID__UNIQ,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))) = V1y) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__RID__UNIQ,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))) = V0x) <=> (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__LNEG__UNIQ,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@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__RNEG__UNIQ,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@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
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__NEG__LMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__RMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__NEGNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__NEG__MUL2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__ENTIRE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) | (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RADD,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 @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__add@(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 @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__NOT__LT,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 @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ANTISYM,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_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__GT,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_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__NOT__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) | (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LET__TOTAL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) | (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LTE__TOTAL,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 @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))))).
thf(conj_thm_2Ereal_2EREAL__LE__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) | (V0x = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__LT__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))) & (~~ (V0x = V1y))))))).
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__LTE__TRANS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
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__LE__TRANS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (V0x = V1y))))).
thf(conj_thm_2Ereal_2EREAL__LET__ANTISYM,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 @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LTE__ANTISYM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (~~ ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LTE__ANTSYM,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (~~ ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__LT0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (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)))))).
thf(conj_thm_2Ereal_2EREAL__NEG__GT0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__LE0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (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_2EREAL__NEG__GE0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__LT__NEGTOTAL,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)))) | ((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@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__NEGTOTAL,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))) | (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__SQUARE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LE__01,lemma,(p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Ereal_2EREAL__LT__01,lemma,(p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(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_2EREAL__LE__LADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__RADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADD2,lemma,( ! [V0w:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__ADD2,lemma,( ! [V0w:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADDNEG,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))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2z))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADDNEG2,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))@(ap@c_2Erealax_2Ereal__neg@(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_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADD1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(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_2EREAL__SUB__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V1y))) = V0x)))).
thf(conj_thm_2Ereal_2EREAL__SUB__ADD2,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 @ V1y))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = V0x)))).
thf(conj_thm_2Ereal_2EREAL__SUB__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Ereal_2EREAL__SUB__0,lemma,( ! [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@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V0x = V1y))))).
thf(conj_thm_2Ereal_2EREAL__LE__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LE__NEGL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ 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_2EREAL__LE__NEGR,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__EQ0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
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__NEG__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
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__SUB__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V0x))) = V1y)))).
thf(conj_thm_2Ereal_2EREAL__EQ__LMUL,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))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) | (V1y = V2z))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__RMUL,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))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> ((V2z = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) | (V0x = V1y))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__LDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__RDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))) = V1y) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__MINUS1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(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__INV__NZ,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@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__INVINV,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@c_2Erealax_2Einv@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x)))).
thf(conj_thm_2Ereal_2EREAL__LT__IMP__NE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => (~~ (V0x = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__INV__POS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LT__LMUL__0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RMUL__0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (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)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__LMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__LMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))) & (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@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LINV__UNIQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) => (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__RINV__UNIQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) => (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__INV__INV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__INV__EQ__0,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__INV,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@c_2Erealax_2Ereal__neg@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ 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__LT__INV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LE__INV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LE__INV,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))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LE__ADDR,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__LE__ADDL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADDR,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__LT__ADDL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Ereal_2EREAL__POS,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Ereal_2EREAL__LE,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))).
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__ADD,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__MUL,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__INV1,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
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_2EREAL__DIV__LZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Ereal_2EREAL__LT__NZ,lemma,( ! [V0n: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 @ fo__c_2Enum_2E0))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(conj_thm_2Ereal_2EREAL__NZ__IMP__LT,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((~~ (V0n = fo__c_2Enum_2E0)) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RDIV__0,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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 @ V1z))) => ((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@(inj__ty_2Erealax_2Ereal @ V0y))@(inj__ty_2Erealax_2Ereal @ V1z)))) <=> (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 @ V0y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RDIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Ereal_2E_2F@(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 @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__FRACTION__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1d:tp__ty_2Erealax_2Ereal] : ((~~ (V0n = fo__c_2Enum_2E0)) => ((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@(inj__ty_2Erealax_2Ereal @ V1d))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))) <=> (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 @ V1d)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__MULTIPLE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1d:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1d))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1d)))) <=> (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 @ V1d)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__FRACTION,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1d:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1d))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n))))@(inj__ty_2Erealax_2Ereal @ V1d))) <=> (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 @ V1d)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__HALF1,lemma,( ! [V0d: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_2E_2F@(inj__ty_2Erealax_2Ereal @ V0d))@(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@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0d)))))).
thf(conj_thm_2Ereal_2EREAL__LT__HALF2,lemma,( ! [V0d:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0d))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0d))) <=> (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 @ V0d)))))).
thf(conj_thm_2Ereal_2EREAL__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__DIV__LMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((~~ (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = V0x))))).
thf(conj_thm_2Ereal_2EREAL__DIV__RMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((~~ (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V1y))) = V0x))))).
thf(conj_thm_2Ereal_2EREAL__HALF__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(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_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__DOWN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (? [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__DOWN2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (? [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y)))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y))))))).
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__SUB__RADD,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_2Ereal_2Ereal__sub@(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_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__SUB__LADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Ereal__sub@(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 @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__SUB__LADD,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))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__SUB__RADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(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__LE__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__ADD2__SUB2,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2c:tp__ty_2Erealax_2Ereal] : ( ! [V3d:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2c))@(inj__ty_2Erealax_2Ereal @ V3d)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V2c)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V3d)))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__LZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(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(conj_thm_2Ereal_2EREAL__LET__ADD2,lemma,( ! [V0w:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LTE__ADD2,lemma,( ! [V0w:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LET__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LTE__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__MUL2,lemma,( ! [V0x1:tp__ty_2Erealax_2Ereal] : ( ! [V1x2:tp__ty_2Erealax_2Ereal] : ( ! [V2y1:tp__ty_2Erealax_2Ereal] : ( ! [V3y2: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 @ V0x1))) & ((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 @ V2y1))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V1x2))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2y1))@(inj__ty_2Erealax_2Ereal @ V3y2)))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V2y1)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x2))@(inj__ty_2Erealax_2Ereal @ V3y2)))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__INV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__LNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__RNEG,lemma,( ! [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))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__NEG2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__TRIANGLE,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2c:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V2c)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V2c)))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__SUB__LADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__EQ__SUB__RADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = V2z) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__INV__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__LMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__RMUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__INV2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__SUB2,lemma,( ! [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))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = V1y)))).
thf(conj_thm_2Ereal_2EREAL__ADD__SUB2,lemma,( ! [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))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__MEAN,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))) => (? [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__LMUL2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((V1y = V2z) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__MUL2,lemma,( ! [V0x1:tp__ty_2Erealax_2Ereal] : ( ! [V1x2:tp__ty_2Erealax_2Ereal] : ( ! [V2y1:tp__ty_2Erealax_2Ereal] : ( ! [V3y2: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 @ V0x1))) & ((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 @ V2y1))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V1x2))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2y1))@(inj__ty_2Erealax_2Ereal @ V3y2)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V2y1)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x2))@(inj__ty_2Erealax_2Ereal @ V3y2)))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__LDIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__RDIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__DIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__DIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LT__1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(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_2EREAL__LE__LMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__RMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__IMP__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((V0x = V1y) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__INV__LT1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(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))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__POS__NZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__RMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((~~ (V2z = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))) => (V0x = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__EQ__LMUL__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))) => (V1y = V2z)))))).
thf(conj_thm_2Ereal_2EREAL__FACT__NZ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__DIFFSQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__POASQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))) <=> (~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__SUMSQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (V1y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (V0x = V1y))))).
thf(conj_thm_2Ereal_2EREAL__DIV__MUL2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1z:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ (V1z = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V1z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1z)))))))))).
thf(conj_thm_2Ereal_2EREAL__MIDDLE1,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Ereal_2EREAL__MIDDLE2,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1b))))))).
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__ZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EABS__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(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_2EABS__1,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Ereal_2EABS__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EABS__TRIANGLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EABS__TRIANGLE__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EABS__TRIANGLE__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EABS__TRIANGLE__LT,lemma,( ! [V0e:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2y))))@(inj__ty_2Erealax_2Ereal @ V0e))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y))))@(inj__ty_2Erealax_2Ereal @ V0e)))))))).
thf(conj_thm_2Ereal_2EABS__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)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EABS__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EABS__LT__MUL2,lemma,( ! [V0w:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0w)))@(inj__ty_2Erealax_2Ereal @ V2y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V3z)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0w))@(inj__ty_2Erealax_2Ereal @ V1x))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z)))))))))).
thf(conj_thm_2Ereal_2EABS__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EABS__NZ,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))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EABS__INV,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@c_2Ereal_2Eabs@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EABS__ABS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EABS__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Eabs@(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_2EABS__N,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(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 @ V0n)))))).
thf(conj_thm_2Ereal_2EABS__BETWEEN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2d: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 @ V2d))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2d)))@(inj__ty_2Erealax_2Ereal @ V1y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2d)))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))@(inj__ty_2Erealax_2Ereal @ V2d)))))))).
thf(conj_thm_2Ereal_2EABS__BOUND,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2d:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(inj__ty_2Erealax_2Ereal @ V2d))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2d))))))))).
thf(conj_thm_2Ereal_2EABS__STILLNZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))) => (~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2Ereal_2EABS__CASES,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)))) | (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EABS__BETWEEN1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))).
thf(conj_thm_2Ereal_2EABS__SIGN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(inj__ty_2Erealax_2Ereal @ V1y))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EABS__SIGN2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EABS__DIV,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((~~ (V0y = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0y))))))))).
thf(conj_thm_2Ereal_2EABS__CIRCLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2h:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2h)))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2h))))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__ABS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EABS__SUB__ABS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EABS__BETWEEN2,lemma,( ! [V0x0:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y0:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x0))@(inj__ty_2Erealax_2Ereal @ V2y0))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0x0))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2y0))@(inj__ty_2Erealax_2Ereal @ V0x0)))@(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@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V3y))@(inj__ty_2Erealax_2Ereal @ V2y0))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2y0))@(inj__ty_2Erealax_2Ereal @ V0x0)))@(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@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V3y))))))))).
thf(conj_thm_2Ereal_2EABS__BOUNDS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1k:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1k))) <=> ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1k)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1k)))))))).
thf(ax_thm_2Ereal_2Epow,axiom,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ereal_2EPOW__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((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_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Ereal_2EPOW__NZ,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ (V0c = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => (~~ ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2Ereal_2EPOW__INV,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ((~~ (V0c = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0c)))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EPOW__ABS,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0c)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EPOW__PLUS1,lemma,( ! [V0e: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 @ V0e))) => ( ! [V1n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Erealax_2Ereal @ V0e))))@(ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Erealax_2Ereal__add@(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 @ V0e)))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EPOW__ADD,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Enum_2Enum @ V1m)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ereal_2EPOW__1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x))).
thf(conj_thm_2Ereal_2EPOW__2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EPOW__ONE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V0n))) = (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_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_2EPOW__LE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y: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 @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Enum_2Enum @ V0n))))))))).
thf(conj_thm_2Ereal_2EPOW__M1,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Enum_2Enum @ V0n)))) = (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_2EPOW__MUL,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Enum_2Enum @ V0n))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__POW2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Ereal_2EABS__POW2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Ereal_2EREAL__POW2__ABS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Ereal_2EREAL__LE1__POW2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(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))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Ereal_2EREAL__LT1__POW2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(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))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Ereal_2EPOW__POS__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))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Ereal_2EPOW__2__LE1,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(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)))))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Ereal_2EPOW__2__LT,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(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)))))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Ereal_2EPOW__MINUS1,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n)))) = (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_2EPOW__LT,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y: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 @ V1x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))))))))).
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_2EPOW__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y: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 @ V1x))) & ((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 @ V2y))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))))) => (V1x = V2y)))))).
thf(conj_thm_2Ereal_2EPOW__ZERO,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) => (V1x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EPOW__ZERO__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V1x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__POW__LT2,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : (((~~ (V0n = fo__c_2Enum_2E0)) & ((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 @ V1x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Enum_2Enum @ V0n))))))))).
thf(conj_thm_2Ereal_2EREAL__POW__MONO__LT,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(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 @ V2x))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2x))@(inj__ty_2Enum_2Enum @ V0m)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2x))@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Ereal_2EREAL__POW__POW,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V1m)))@(inj__ty_2Enum_2Enum @ V2n))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__SOMEPOS,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x))) & (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 @ V1x))))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => (? [V4s:tp__ty_2Erealax_2Ereal] : ( ! [V5y:tp__ty_2Erealax_2Ereal] : ((? [V6x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V6x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V6x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V4s)))))))))).
thf(conj_thm_2Ereal_2ESUP__LEMMA1,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1s:tp__ty_2Erealax_2Ereal] : ( ! [V2d:tp__ty_2Erealax_2Ereal] : (( ! [V3y:tp__ty_2Erealax_2Ereal] : ((? [V4x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(lam@ty_2Erealax_2Ereal@(^ [V5x:$i] : (ap@V0P@(ap@(ap@c_2Erealax_2Ereal__add@V5x)@(inj__ty_2Erealax_2Ereal @ V2d)))))@(inj__ty_2Erealax_2Ereal @ V4x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3y))@(inj__ty_2Erealax_2Ereal @ V4x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3y))@(inj__ty_2Erealax_2Ereal @ V1s))))) => ( ! [V6y:tp__ty_2Erealax_2Ereal] : ((? [V7x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V7x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6y))@(inj__ty_2Erealax_2Ereal @ V7x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1s))@(inj__ty_2Erealax_2Ereal @ V2d)))))))))))).
thf(conj_thm_2Ereal_2ESUP__LEMMA2,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => ((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) => (? [V2d:tp__ty_2Erealax_2Ereal] : (? [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(lam@ty_2Erealax_2Ereal@(^ [V4x:$i] : (ap@V0P@(ap@(ap@c_2Erealax_2Ereal__add@V4x)@(inj__ty_2Erealax_2Ereal @ V2d)))))@(inj__ty_2Erealax_2Ereal @ V3x))) & (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 @ V3x)))))))))).
thf(conj_thm_2Ereal_2ESUP__LEMMA3,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1d:tp__ty_2Erealax_2Ereal] : ((? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z)))))) => (? [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(lam@ty_2Erealax_2Ereal@(^ [V6x:$i] : (ap@V0P@(ap@(ap@c_2Erealax_2Ereal__add@V6x)@(inj__ty_2Erealax_2Ereal @ V1d)))))@(inj__ty_2Erealax_2Ereal @ V5x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V5x))@(inj__ty_2Erealax_2Ereal @ V4z))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__EXISTS,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => (? [V4s:tp__ty_2Erealax_2Ereal] : ( ! [V5y:tp__ty_2Erealax_2Ereal] : ((? [V6x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V6x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V6x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V4s)))))))))).
thf(ax_thm_2Ereal_2Esup,axiom,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Esup@V0P)) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1s:$i] : (ap@(c_2Ebool_2E_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V2y:$i] : (ap@(ap@(c_2Emin_2E_3D@bool)@(ap@(c_2Ebool_2E_3F@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V3x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@V0P@V3x))@(ap@(ap@c_2Erealax_2Ereal__lt@V2y)@V3x))))))@(ap@(ap@c_2Erealax_2Ereal__lt@V2y)@V1s))))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => ( ! [V4y:tp__ty_2Erealax_2Ereal] : ((? [V5x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V5x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V4y))@(inj__ty_2Erealax_2Ereal @ V5x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V4y))@(ap@c_2Ereal_2Esup@V0P))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__UBOUND,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => ( ! [V4y:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V4y))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4y))@(ap@c_2Ereal_2Esup@V0P))))))))).
thf(conj_thm_2Ereal_2ESETOK__LE__LT,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) <=> ((? [V4x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V4x)))) & (? [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V6x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6x))@(inj__ty_2Erealax_2Ereal @ V5z))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__LE,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => ( ! [V4y:tp__ty_2Erealax_2Ereal] : ((? [V5x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V5x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V4y))@(inj__ty_2Erealax_2Ereal @ V5x))))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V4y))@(ap@c_2Ereal_2Esup@V0P))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__UBOUND__LE,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => ( ! [V4y:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0P@(inj__ty_2Erealax_2Ereal @ V4y))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4y))@(ap@c_2Ereal_2Esup@V0P))))))))).
thf(conj_thm_2Ereal_2EREAL__ARCH,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ( ! [V1y:tp__ty_2Erealax_2Ereal] : (? [V2n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Erealax_2Ereal @ V0x))))))))).
thf(conj_thm_2Ereal_2EREAL__ARCH__LEAST,lemma,( ! [V0y: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 @ V0y))) => ( ! [V1x: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 @ V1x))) => (? [V2n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Erealax_2Ereal @ V0y)))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n))))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(conj_thm_2Ereal_2Esum__ind,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@(ty_2Epair_2Eprod@ty_2Enum_2Enum@ty_2Enum_2Enum)@(arr@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@bool))) => ((( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => (p@(ap@(ap@V0P@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V2f))))) & ( ! [V3n:tp__ty_2Enum_2Enum] : ( ! [V4m:tp__ty_2Enum_2Enum] : ( ! [V5f:$i] : ((mem@V5f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@V0P@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V3n))@(inj__ty_2Enum_2Enum @ V4m)))@V5f)) => (p@(ap@(ap@V0P@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V4m))))@V5f)))))))) => ( ! [V6v:tp__ty_2Enum_2Enum] : ( ! [V7v1:tp__ty_2Enum_2Enum] : ( ! [V8v2:$i] : ((mem@V8v2@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => (p@(ap@(ap@V0P@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V6v))@(inj__ty_2Enum_2Enum @ V7v1)))@V8v2)))))))))).
thf(conj_thm_2Ereal_2Esum,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1f)) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))) & ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : ( ! [V4f:$i] : ((mem@V4f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2n))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V3m))))@V4f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))@V4f))@(ap@V4f@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))))))).
thf(conj_thm_2Ereal_2Esum__compute,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1f)) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : ( ! [V4f:$i] : ((mem@V4f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))))@V4f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2n))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@V4f))@(ap@V4f@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2n))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))) & ( ! [V5n:tp__ty_2Enum_2Enum] : ( ! [V6m:tp__ty_2Enum_2Enum] : ( ! [V7f:$i] : ((mem@V7f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V5n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V6m)))))@V7f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V5n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V6m)))))@V7f))@(ap@V7f@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V5n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V6m))))))))))))))).
thf(conj_thm_2Ereal_2ESUM__TWO,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))@V0f))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p))))@V0f)))))))).
thf(conj_thm_2Ereal_2ESUM__DIFF,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n))))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1m)))@V0f))))))))).
thf(conj_thm_2Ereal_2EABS__SUM,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@V0f)))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@c_2Ereal_2Eabs@(ap@V0f@V3n)))))))))))).
thf(conj_thm_2Ereal_2ESUM__LE,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : (( ! [V4r:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V4r))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4r))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V3n))@(inj__ty_2Enum_2Enum @ V2m))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@V0f@(inj__ty_2Enum_2Enum @ V4r)))@(ap@V1g@(inj__ty_2Enum_2Enum @ V4r)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V1g))))))))))).
thf(conj_thm_2Ereal_2ESUM__EQ,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : (( ! [V4r:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V4r))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4r))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V3n))@(inj__ty_2Enum_2Enum @ V2m))))) => ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Enum_2Enum @ V4r))) = (surj__ty_2Erealax_2Ereal @ (ap@V1g@(inj__ty_2Enum_2Enum @ V4r)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V1g))))))))))).
thf(conj_thm_2Ereal_2ESUM__POS,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => (( ! [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@V0f@(inj__ty_2Enum_2Enum @ V1n))))) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n: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_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))))))))).
thf(conj_thm_2Ereal_2ESUM__POS__GEN,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : (( ! [V2n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@V0f@(inj__ty_2Enum_2Enum @ V2n)))))) => ( ! [V3n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))))))))).
thf(conj_thm_2Ereal_2ESUM__ABS,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@c_2Ereal_2Eabs@(ap@V0f@V3m))))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@(lam@ty_2Enum_2Enum@(^ [V4m:$i] : (ap@c_2Ereal_2Eabs@(ap@V0f@V4m)))))))))))).
thf(conj_thm_2Ereal_2ESUM__ABS__LE,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@V0f)))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@c_2Ereal_2Eabs@(ap@V0f@V3n)))))))))))).
thf(conj_thm_2Ereal_2ESUM__ZERO,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1N:tp__ty_2Enum_2Enum] : (( ! [V2n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V1N))) => ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Enum_2Enum @ V2n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ( ! [V3m:tp__ty_2Enum_2Enum] : ( ! [V4n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V3m))@(inj__ty_2Enum_2Enum @ V1N))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V3m))@(inj__ty_2Enum_2Enum @ V4n)))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2Ereal_2ESUM__ADD,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V4n:$i] : (ap@(ap@c_2Erealax_2Ereal__add@(ap@V0f@V4n))@(ap@V1g@V4n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V1g))))))))))).
thf(conj_thm_2Ereal_2ESUM__CMUL,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1c:tp__ty_2Erealax_2Ereal] : ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V4n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1c))@(ap@V0f@V4n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1c))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f)))))))))).
thf(conj_thm_2Ereal_2ESUM__NEG,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2d:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2d)))@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@c_2Erealax_2Ereal__neg@(ap@V0f@V3n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2d)))@V0f))))))))).
thf(conj_thm_2Ereal_2ESUM__SUB,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V4n:$i] : (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0f@V4n))@(ap@V1g@V4n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V1g))))))))))).
thf(conj_thm_2Ereal_2ESUM__SUBST,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : (( ! [V4p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V4p))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4p))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n))))) => ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Enum_2Enum @ V4p))) = (surj__ty_2Erealax_2Ereal @ (ap@V1g@(inj__ty_2Enum_2Enum @ V4p)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V1g))))))))))).
thf(conj_thm_2Ereal_2ESUM__NSUB,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2c:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n)))@V1f))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V2c)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n)))@(lam@ty_2Enum_2Enum@(^ [V3p:$i] : (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V1f@V3p))@(inj__ty_2Erealax_2Ereal @ V2c)))))))))))).
thf(conj_thm_2Ereal_2ESUM__BOUND,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1k:tp__ty_2Erealax_2Ereal] : ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : (( ! [V4p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V4p))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4p))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@V0f@(inj__ty_2Enum_2Enum @ V4p)))@(inj__ty_2Erealax_2Ereal @ V1k))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V2m))@(inj__ty_2Enum_2Enum @ V3n)))@V0f))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V3n)))@(inj__ty_2Erealax_2Ereal @ V1k))))))))))).
thf(conj_thm_2Ereal_2ESUM__GROUP,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1k:tp__ty_2Enum_2Enum] : ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(ap@(ap@c_2Earithmetic_2E_2A@V3m)@(inj__ty_2Enum_2Enum @ V1k)))@(inj__ty_2Enum_2Enum @ V1k)))@V2f))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1k))))@V2f)))))))).
thf(conj_thm_2Ereal_2ESUM__1,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2ESUM__2,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@V0f@(inj__ty_2Enum_2Enum @ V1n)))@(ap@V0f@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))))).
thf(conj_thm_2Ereal_2ESUM__OFFSET,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2k:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@V0f@(ap@(ap@c_2Earithmetic_2E_2B@V3m)@(inj__ty_2Enum_2Enum @ V2k))))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2k))))@V0f))@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V2k)))@V0f))))))))).
thf(conj_thm_2Ereal_2ESUM__REINDEX,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2k:tp__ty_2Enum_2Enum] : ( ! [V3n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2k)))@(inj__ty_2Enum_2Enum @ V3n)))@V0f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V4r:$i] : (ap@V0f@(ap@(ap@c_2Earithmetic_2E_2B@V4r)@(inj__ty_2Enum_2Enum @ V2k)))))))))))))).
thf(conj_thm_2Ereal_2ESUM__0,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(lam@ty_2Enum_2Enum@(^ [V2r:$i] : (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2ESUM__PERMUTE__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1p:$i] : ((mem@V1p@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)) => (( ! [V2y:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V2y))@(inj__ty_2Enum_2Enum @ V0n))) => (p@(ap@(c_2Ebool_2E_3F_21@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V3x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Eprim__rec_2E_3C@V3x)@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@(ap@V1p@V3x))@(inj__ty_2Enum_2Enum @ V2y))))))))) => ( ! [V4f:$i] : ((mem@V4f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n)))@(lam@ty_2Enum_2Enum@(^ [V5n:$i] : (ap@V4f@(ap@V1p@V5n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n)))@V4f)))))))))).
thf(conj_thm_2Ereal_2ESUM__CANCEL,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2d:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2d)))@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0f@(ap@c_2Enum_2ESUC@V3n)))@(ap@V0f@V3n)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0f@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2d))))@(ap@V0f@(inj__ty_2Enum_2Enum @ V1n)))))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__RNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__MUL__LNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2Ereal__lt,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0y))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(inj__ty_2Erealax_2Ereal @ V1x)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__LADD__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__LNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__LE__NEG2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__NEG__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__LE__RNEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Ereal_2EREAL__POW__INV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__POW__DIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Enum_2Enum @ V2n))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V2n)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ereal_2EREAL__POW__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V1m)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__RDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__LDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__RDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__LDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__RDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) = V1y))))))).
thf(conj_thm_2Ereal_2EREAL__EQ__LDIV__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2z))) => (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))) = V1y) <=> (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__POW,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0x)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V0x))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__LDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__ADD,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__LE,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__SUC,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(conj_thm_2Ereal_2EREAL__OF__NUM__EQ,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__EQ__MUL__LCANCEL,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))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> ((V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) | (V1y = V2z))))))).
thf(conj_thm_2Ereal_2EREAL__ABS__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(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__ABS__TRIANGLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__ABS__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__ABS__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)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__LE__EPSILON,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (( ! [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))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2e)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__BIGNUM,lemma,( ! [V0r:tp__ty_2Erealax_2Ereal] : (? [V1n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0r))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Ereal_2EREAL__INV__LT__ANTIMONO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Einv@(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__INV__INJ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (V0x = V1y))))).
thf(conj_thm_2Ereal_2EREAL__DIV__RMUL__CANCEL,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((~~ (V0c = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V0c)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2b))@(inj__ty_2Erealax_2Ereal @ V0c)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b))))))))).
thf(conj_thm_2Ereal_2EREAL__DIV__LMUL__CANCEL,lemma,( ! [V0c:tp__ty_2Erealax_2Ereal] : ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((~~ (V0c = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Erealax_2Ereal @ V1a)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0c))@(inj__ty_2Erealax_2Ereal @ V2b)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b))))))))).
thf(conj_thm_2Ereal_2EREAL__DIV__ADD,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@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Ereal_2EREAL__ADD__RAT,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2c:tp__ty_2Erealax_2Ereal] : ( ! [V3d:tp__ty_2Erealax_2Ereal] : (((~~ (V1b = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ (V3d = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2c))@(inj__ty_2Erealax_2Ereal @ V3d)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V3d)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V2c))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V3d))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB__RAT,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2c:tp__ty_2Erealax_2Ereal] : ( ! [V3d:tp__ty_2Erealax_2Ereal] : (((~~ (V1b = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ (V3d = (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_2Ereal__sub@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V2c))@(inj__ty_2Erealax_2Ereal @ V3d)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V3d)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V2c))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1b))@(inj__ty_2Erealax_2Ereal @ V3d))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUB,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0m)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m)))))@(ap@c_2Ereal_2Ereal__of__num@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(ax_thm_2Ereal_2Epos__def,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Epos@(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_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__POS__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)))@(ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__POS__ID,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))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x)))).
thf(conj_thm_2Ereal_2EREAL__POS__INFLATE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__POS__MONO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Ereal_2EREAL__POS__EQ__ZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Ereal_2EREAL__POS__LE__ZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Epos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(ax_thm_2Ereal_2Emin__def,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(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_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__LE__MIN,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) <=> ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V2y))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__LE,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z))) <=> ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z))) | (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__LE1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Ereal_2EREAL__MIN__LE2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V1y)))))).
thf(conj_thm_2Ereal_2EREAL__LT__MIN,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 @ V2z))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__LT,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_2Ereal_2Emin@(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))@(inj__ty_2Erealax_2Ereal @ V2z))) | (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__ALT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = V0x)) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = V1y)))))).
thf(conj_thm_2Ereal_2EREAL__MIN__LE__LIN,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y: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 @ V0z))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(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@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Ereal__sub@(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 @ V0z)))@(inj__ty_2Erealax_2Ereal @ V2y)))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__ADD,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z)))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__SUB,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z)))))))).
thf(conj_thm_2Ereal_2EREAL__IMP__MIN__LE2,lemma,( ! [V0x1:tp__ty_2Erealax_2Ereal] : ( ! [V1x2:tp__ty_2Erealax_2Ereal] : ( ! [V2y1:tp__ty_2Erealax_2Ereal] : ( ! [V3y2:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V2y1))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x2))@(inj__ty_2Erealax_2Ereal @ V3y2)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V1x2)))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V2y1))@(inj__ty_2Erealax_2Ereal @ V3y2)))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__ACI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))))))).
thf(ax_thm_2Ereal_2Emax__def,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(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_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__REFL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__LE__MAX,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) <=> ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V1x))) | (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V2y))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__MAX1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__LE__MAX2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__LE,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z))) <=> ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z))))))))).
thf(conj_thm_2Ereal_2EREAL__LT__MAX,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 @ V2z))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))) | (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__LT,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_2Ereal_2Emax@(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))@(inj__ty_2Erealax_2Ereal @ V2z))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__ALT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = V1y)) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = V0x)))))).
thf(conj_thm_2Ereal_2EREAL__MAX__MIN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2Emin@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__MIN__MAX,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emin@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2Emax@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Ereal_2EREAL__LIN__LE__MAX,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y: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 @ V0z))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0z))@(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@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Ereal__sub@(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 @ V0z)))@(inj__ty_2Erealax_2Ereal @ V2y))))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y))))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__ADD,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z)))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__SUB,lemma,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V0z)))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V0z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0z)))))))).
thf(conj_thm_2Ereal_2EREAL__IMP__MAX__LE2,lemma,( ! [V0x1:tp__ty_2Erealax_2Ereal] : ( ! [V1x2:tp__ty_2Erealax_2Ereal] : ( ! [V2y1:tp__ty_2Erealax_2Ereal] : ( ! [V3y2:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V2y1))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x2))@(inj__ty_2Erealax_2Ereal @ V3y2)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x1))@(inj__ty_2Erealax_2Ereal @ V1x2)))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V2y1))@(inj__ty_2Erealax_2Ereal @ V3y2)))))))))).
thf(conj_thm_2Ereal_2EREAL__MAX__ACI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x)))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))) & (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Emax@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))))))).
thf(ax_thm_2Ereal_2Einf__def,axiom,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Einf@V0p)) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Esup@(lam@ty_2Erealax_2Ereal@(^ [V1r:$i] : (ap@V0p@(ap@c_2Erealax_2Ereal__neg@V1r))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__EXISTS__UNIQUE,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => (((? [V1x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V1x)))) & (? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V2z))))))) => (p@(ap@(c_2Ebool_2E_3F_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V4s:$i] : (ap@(c_2Ebool_2E_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V5y:$i] : (ap@(ap@(c_2Emin_2E_3D@bool)@(ap@(c_2Ebool_2E_3F@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V6x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@V0p@V6x))@(ap@(ap@c_2Erealax_2Ereal__lt@V5y)@V6x))))))@(ap@(ap@c_2Erealax_2Ereal__lt@V5y)@V4s))))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__MAX,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1z:tp__ty_2Erealax_2Ereal] : (((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V1z))) & ( ! [V2x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2x))@(inj__ty_2Erealax_2Ereal @ V1z)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Esup@V0p)) = V1z)))))).
thf(conj_thm_2Ereal_2EREAL__IMP__SUP__LE,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((? [V2r:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2r)))) & ( ! [V3r:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3r))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3r))@(inj__ty_2Erealax_2Ereal @ V1x)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Esup@V0p))@(inj__ty_2Erealax_2Ereal @ V1x)))))))).
thf(conj_thm_2Ereal_2EREAL__IMP__LE__SUP,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((? [V2r:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2r)))) & ((? [V3z:tp__ty_2Erealax_2Ereal] : ( ! [V4r:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V4r))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4r))@(inj__ty_2Erealax_2Ereal @ V3z)))))) & (? [V5r:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V5r))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V5r))))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Ereal_2Esup@V0p)))))))).
thf(conj_thm_2Ereal_2EREAL__INF__MIN,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1z:tp__ty_2Erealax_2Ereal] : (((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V1z))) & ( ! [V2x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1z))@(inj__ty_2Erealax_2Ereal @ V2x)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Einf@V0p)) = V1z)))))).
thf(conj_thm_2Ereal_2EREAL__IMP__LE__INF,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1r:tp__ty_2Erealax_2Ereal] : (((? [V2x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x)))) & ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1r))@(inj__ty_2Erealax_2Ereal @ V3x)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1r))@(ap@c_2Ereal_2Einf@V0p)))))))).
thf(conj_thm_2Ereal_2EREAL__IMP__INF__LE,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1r:tp__ty_2Erealax_2Ereal] : (((? [V2z:tp__ty_2Erealax_2Ereal] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V3x)))))) & (? [V4x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V4x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Erealax_2Ereal @ V1r)))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Einf@V0p))@(inj__ty_2Erealax_2Ereal @ V1r)))))))).
thf(conj_thm_2Ereal_2EREAL__INF__LT,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1z:tp__ty_2Erealax_2Ereal] : (((? [V2x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Einf@V0p))@(inj__ty_2Erealax_2Ereal @ V1z)))) => (? [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(inj__ty_2Erealax_2Ereal @ V1z)))))))))).
thf(conj_thm_2Ereal_2EREAL__INF__CLOSE,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1e:tp__ty_2Erealax_2Ereal] : (((? [V2x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1e)))) => (? [V3x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V3x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V3x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Einf@V0p))@(inj__ty_2Erealax_2Ereal @ V1e))))))))))).
thf(conj_thm_2Ereal_2ESUP__EPSILON,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1e: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 @ V1e))) & ((? [V2x:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2x)))) & (? [V3z:tp__ty_2Erealax_2Ereal] : ( ! [V4x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V4x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Erealax_2Ereal @ V3z)))))))) => (? [V5x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V5x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Esup@V0p))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V5x))@(inj__ty_2Erealax_2Ereal @ V1e))))))))))).
thf(conj_thm_2Ereal_2EREAL__LE__SUP,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((? [V2y:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2y)))) & (? [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V4z))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4z))@(inj__ty_2Erealax_2Ereal @ V3y))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Ereal_2Esup@V0p))) <=> ( ! [V5y:tp__ty_2Erealax_2Ereal] : (( ! [V6z:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V6z))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V6z))@(inj__ty_2Erealax_2Ereal @ V5y))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V5y))))))))))).
thf(conj_thm_2Ereal_2EREAL__INF__LE,lemma,( ! [V0p:$i] : ((mem@V0p@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((? [V2y:tp__ty_2Erealax_2Ereal] : (p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V2y)))) & (? [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V4z))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V3y))@(inj__ty_2Erealax_2Ereal @ V4z))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Einf@V0p))@(inj__ty_2Erealax_2Ereal @ V1x))) <=> ( ! [V5y:tp__ty_2Erealax_2Ereal] : (( ! [V6z:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0p@(inj__ty_2Erealax_2Ereal @ V6z))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V6z))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V5y))@(inj__ty_2Erealax_2Ereal @ V1x))))))))))).
thf(conj_thm_2Ereal_2EREAL__SUP__CONST,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Esup@(lam@ty_2Erealax_2Ereal@(^ [V1r:$i] : (ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@V1r)@(inj__ty_2Erealax_2Ereal @ V0x)))))) = V0x))).
thf(conj_thm_2Ereal_2EREAL__MUL__SUB2__CANCEL,conjecture,( ! [V0z:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V2y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0z))@(inj__ty_2Erealax_2Ereal @ V2y)))))))).
