include('Axioms/basis_emit_2.ax').
tff(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
tff(mem_c_2Ereal_2E_2F,axiom,mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2E_2F,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2E_2F(X0,X1)) = ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2ENUM__CEILING,type,(c_2Ereal_2ENUM__CEILING:$i)).
tff(mem_c_2Ereal_2ENUM__CEILING,axiom,mem(c_2Ereal_2ENUM__CEILING,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ereal_2ENUM__CEILING,type,(fo__c_2Ereal_2ENUM__CEILING:(tp__ty_2Erealax_2Ereal) > tp__ty_2Enum_2Enum)).
tff(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))))).
tff(tp_c_2Ereal_2ENUM__FLOOR,type,(c_2Ereal_2ENUM__FLOOR:$i)).
tff(mem_c_2Ereal_2ENUM__FLOOR,axiom,mem(c_2Ereal_2ENUM__FLOOR,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ereal_2ENUM__FLOOR,type,(fo__c_2Ereal_2ENUM__FLOOR:(tp__ty_2Erealax_2Ereal) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ereal_2ENUM__FLOOR,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Enum_2Enum(fo__c_2Ereal_2ENUM__FLOOR(X0)) = ap(c_2Ereal_2ENUM__FLOOR,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ereal_2Eabs,type,(c_2Ereal_2Eabs:$i)).
tff(mem_c_2Ereal_2Eabs,axiom,mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ereal_2Eabs,type,(fo__c_2Ereal_2Eabs:(tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Eabs,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Eabs(X0)) = ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ereal_2Einf,type,(c_2Ereal_2Einf:$i)).
tff(mem_c_2Ereal_2Einf,axiom,mem(c_2Ereal_2Einf,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal))).
tff(tp_c_2Ereal_2Emax,type,(c_2Ereal_2Emax:$i)).
tff(mem_c_2Ereal_2Emax,axiom,mem(c_2Ereal_2Emax,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Emax,type,(fo__c_2Ereal_2Emax:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(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)))))).
tff(tp_c_2Ereal_2Emin,type,(c_2Ereal_2Emin:$i)).
tff(mem_c_2Ereal_2Emin,axiom,mem(c_2Ereal_2Emin,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Emin,type,(fo__c_2Ereal_2Emin:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Emin,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Emin(X0,X1)) = ap(ap(c_2Ereal_2Emin,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2Epos,type,(c_2Ereal_2Epos:$i)).
tff(mem_c_2Ereal_2Epos,axiom,mem(c_2Ereal_2Epos,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ereal_2Epos,type,(fo__c_2Ereal_2Epos:(tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(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))))).
tff(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
tff(mem_c_2Ereal_2Epow,axiom,mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal * tp__ty_2Enum_2Enum) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Epow(X0,X1)) = ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Enum_2Enum(X1)))))).
tff(tp_c_2Ereal_2Ereal__ge,type,(c_2Ereal_2Ereal__ge:$i)).
tff(mem_c_2Ereal_2Ereal__ge,axiom,mem(c_2Ereal_2Ereal__ge,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))).
tff(stp_fo_c_2Ereal_2Ereal__ge,type,(fo__c_2Ereal_2Ereal__ge:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Ereal_2Ereal__ge,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Ereal_2Ereal__ge(X0,X1)) = ap(ap(c_2Ereal_2Ereal__ge,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2Ereal__gt,type,(c_2Ereal_2Ereal__gt:$i)).
tff(mem_c_2Ereal_2Ereal__gt,axiom,mem(c_2Ereal_2Ereal__gt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))).
tff(stp_fo_c_2Ereal_2Ereal__gt,type,(fo__c_2Ereal_2Ereal__gt:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Ereal_2Ereal__gt,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Ereal_2Ereal__gt(X0,X1)) = ap(ap(c_2Ereal_2Ereal__gt,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2Ereal__lte,type,(c_2Ereal_2Ereal__lte:$i)).
tff(mem_c_2Ereal_2Ereal__lte,axiom,mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))).
tff(stp_fo_c_2Ereal_2Ereal__lte,type,(fo__c_2Ereal_2Ereal__lte:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Ereal_2Ereal__lte,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Ereal_2Ereal__lte(X0,X1)) = ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
tff(mem_c_2Ereal_2Ereal__of__num,axiom,mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__of__num(X0)) = ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$i)).
tff(mem_c_2Ereal_2Ereal__sub,axiom,mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(stp_fo_c_2Ereal_2Ereal__sub,type,(fo__c_2Ereal_2Ereal__sub:(tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ereal_2Ereal__sub(X0,X1)) = ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))).
tff(tp_c_2Ereal_2Esum,type,(c_2Ereal_2Esum:$i)).
tff(mem_c_2Ereal_2Esum,axiom,mem(c_2Ereal_2Esum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)))).
tff(tp_c_2Ereal_2Esup,type,(c_2Ereal_2Esup:$i)).
tff(mem_c_2Ereal_2Esup,axiom,mem(c_2Ereal_2Esup,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal))).
tff(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))))))).
tff(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)))))).
tff(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)))))))).
tff(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))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__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)))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__ASSOC,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__LDISTRIB,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__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))))))))).
tff(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))))))).
tff(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))))).
tff(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))))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__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)))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__MUL__LINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(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)))))).
tff(ax_thm_2Ereal_2Ereal__sub,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(ax_thm_2Ereal_2Ereal__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)))))))).
tff(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))))))).
tff(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))))))).
tff(ax_thm_2Ereal_2Ereal__div,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(conj_thm_2Ereal_2EREAL__ADD__RID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__ADD__RINV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__RID,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0x)))).
tff(conj_thm_2Ereal_2EREAL__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)))))))))).
tff(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)))))))))).
tff(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))))))).
tff(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))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))).
tff(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__MUL__RZERO,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(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))))))))).
tff(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)))).
tff(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)))))))).
tff(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)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__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))))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))).
tff(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) | p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(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)))))))).
tff(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x)))))).
tff(conj_thm_2Ereal_2EREAL__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))))))).
tff(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)))))))).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__LE,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))))))).
tff(conj_thm_2Ereal_2EREAL__LTE__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LET__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__TRANS,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))) <=> (V0x = V1y)))))).
tff(conj_thm_2Ereal_2EREAL__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))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))).
tff(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)))))))).
tff(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))))))).
tff(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)))))))).
tff(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))))))))).
tff(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)))))))).
tff(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__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))))))).
tff(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)))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))))).
tff(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))))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))))))))).
tff(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))))).
tff(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))))).
tff(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))))))).
tff(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)))))).
tff(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))))))).
tff(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))))))).
tff(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)))))))).
tff(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)))))))).
tff(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)))))).
tff(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)))))))).
tff(conj_thm_2Ereal_2EREAL__SUB__LT,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(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))))).
tff(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)))))))).
tff(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)))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(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))))))).
tff(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))))))))).
tff(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))))).
tff(conj_thm_2Ereal_2EREAL__LT__IMP__NE,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) => (~~ (V0x = V1y))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(conj_thm_2Ereal_2EREAL__LT__RMUL__IMP,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))).
tff(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)))))))).
tff(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))))))))).
tff(conj_thm_2Ereal_2EREAL__INV__1OVER,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__LT__INV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__LE__INV__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(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)))))))).
tff(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)))))))).
tff(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)))))))).
tff(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)))))))).
tff(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)))))))))).
tff(conj_thm_2Ereal_2EREAL__POS,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ereal_2EREAL__LE,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Ereal_2EREAL__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)))))))).
tff(conj_thm_2Ereal_2EREAL__INJ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> (V0m = V1n)))))).
tff(conj_thm_2Ereal_2EREAL__ADD,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__MUL,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ereal_2EREAL__INV1,lemma,((surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))).
tff(conj_thm_2Ereal_2EREAL__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)))).
tff(conj_thm_2Ereal_2EREAL__DIV__REFL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ereal_2EREAL__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))))))).
tff(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)))))))).
tff(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)))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))).
tff(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))))))).
tff(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))))))).
tff(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)))))).
tff(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)))))).
tff(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)))).
tff(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))))))))).
tff(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))))))))))).
tff(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)))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))))).
tff(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)))))))).
tff(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))))))))))).
tff(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))))))).
tff(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)))).
tff(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))))))))))).
tff(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))))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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))))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))).
tff(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)))))))))).
tff(conj_thm_2Ereal_2EREAL__INV__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((~~ (V0x = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V1y = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__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)))))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(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))))).
tff(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)))))))).
tff(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)))))))))).
tff(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))))))))))).
tff(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))))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__DIV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1y)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ereal_2EREAL__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))))))))))).
tff(conj_thm_2Ereal_2EREAL__LE__LMUL__IMP,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))) & p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1y)),inj__ty_2Erealax_2Ereal(V2z)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V2z)))))))))).
tff(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)))))))))).
tff(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)))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))).
tff(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))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))).
tff(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))))))))))).
tff(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)))))))))))).
tff(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)))))))).
tff(ax_thm_2Ereal_2Eabs,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0x))),inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))))).
tff(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)))))))).
tff(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)))))).
tff(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)))))))).
tff(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))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(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))))))).
tff(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))))))))).
tff(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))))))))))).
tff(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))))))))).
tff(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)))))))).
tff(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))))))))).
tff(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))))))).
tff(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))))))).
tff(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))))))).
tff(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))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(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)))))))).
tff(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))))))))).
tff(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)))))))).
tff(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))))))))).
tff(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)))))))))).
tff(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)))))))))).
tff(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))))))))).
tff(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))))))))).
tff(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)))))))))).
tff(conj_thm_2Ereal_2EABS__BOUNDS,conjecture,(( ! [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))))))))).
