include('Axioms/HolSmt_2.ax').
tff(tp_c_2Ecomplex_2EIM,type,(c_2Ecomplex_2EIM:$i)).
tff(mem_c_2Ecomplex_2EIM,axiom,mem(c_2Ecomplex_2EIM,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ecomplex_2EIM,type,(fo__c_2Ecomplex_2EIM:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ecomplex_2EIM,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ecomplex_2EIM(X0)) = ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ecomplex_2ERE,type,(c_2Ecomplex_2ERE:$i)).
tff(mem_c_2Ecomplex_2ERE,axiom,mem(c_2Ecomplex_2ERE,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ecomplex_2ERE,type,(fo__c_2Ecomplex_2ERE:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ecomplex_2ERE,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ecomplex_2ERE(X0)) = ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ecomplex_2Earg,type,(c_2Ecomplex_2Earg:$i)).
tff(mem_c_2Ecomplex_2Earg,axiom,mem(c_2Ecomplex_2Earg,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ecomplex_2Earg,type,(fo__c_2Ecomplex_2Earg:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ecomplex_2Earg,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ecomplex_2Earg(X0)) = ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ecomplex_2Ecomplex__add,type,(c_2Ecomplex_2Ecomplex__add:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__add,axiom,mem(c_2Ecomplex_2Ecomplex__add,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__div,type,(c_2Ecomplex_2Ecomplex__div:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__div,axiom,mem(c_2Ecomplex_2Ecomplex__div,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__exp,type,(c_2Ecomplex_2Ecomplex__exp:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__exp,axiom,mem(c_2Ecomplex_2Ecomplex__exp,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ecomplex__inv,type,(c_2Ecomplex_2Ecomplex__inv:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__inv,axiom,mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ecomplex__mul,type,(c_2Ecomplex_2Ecomplex__mul:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__mul,axiom,mem(c_2Ecomplex_2Ecomplex__mul,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__neg,type,(c_2Ecomplex_2Ecomplex__neg:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__neg,axiom,mem(c_2Ecomplex_2Ecomplex__neg,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ecomplex__of__num,type,(c_2Ecomplex_2Ecomplex__of__num:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__of__num,axiom,mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ecomplex__of__real,type,(c_2Ecomplex_2Ecomplex__of__real:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__of__real,axiom,mem(c_2Ecomplex_2Ecomplex__of__real,arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ecomplex__pow,type,(c_2Ecomplex_2Ecomplex__pow:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__pow,axiom,mem(c_2Ecomplex_2Ecomplex__pow,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__scalar__lmul,type,(c_2Ecomplex_2Ecomplex__scalar__lmul:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__scalar__lmul,axiom,mem(c_2Ecomplex_2Ecomplex__scalar__lmul,arr(ty_2Erealax_2Ereal,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__scalar__rmul,type,(c_2Ecomplex_2Ecomplex__scalar__rmul:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__scalar__rmul,axiom,mem(c_2Ecomplex_2Ecomplex__scalar__rmul,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Ecomplex__sub,type,(c_2Ecomplex_2Ecomplex__sub:$i)).
tff(mem_c_2Ecomplex_2Ecomplex__sub,axiom,mem(c_2Ecomplex_2Ecomplex__sub,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))))).
tff(tp_c_2Ecomplex_2Econj,type,(c_2Ecomplex_2Econj:$i)).
tff(mem_c_2Ecomplex_2Econj,axiom,mem(c_2Ecomplex_2Econj,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)))).
tff(tp_c_2Ecomplex_2Ei,type,(c_2Ecomplex_2Ei:$i)).
tff(mem_c_2Ecomplex_2Ei,axiom,mem(c_2Ecomplex_2Ei,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))).
tff(tp_c_2Ecomplex_2Emodu,type,(c_2Ecomplex_2Emodu:$i)).
tff(mem_c_2Ecomplex_2Emodu,axiom,mem(c_2Ecomplex_2Emodu,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))).
tff(stp_fo_c_2Ecomplex_2Emodu,type,(fo__c_2Ecomplex_2Emodu:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) > tp__ty_2Erealax_2Ereal)).
tff(stp_eq_fo_c_2Ecomplex_2Emodu,axiom,( ! [X0:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (inj__ty_2Erealax_2Ereal(fo__c_2Ecomplex_2Emodu(X0)) = ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__LEMMA1,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_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V2c))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V3d)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V3d))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1b)),inj__ty_2Erealax_2Ereal(V2c)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1b)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V2c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V3d)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__LEMMA2,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(c_2Etransc_2Esqrt,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,inj__ty_2Erealax_2Ereal(V1y)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))))).
tff(ax_thm_2Ecomplex_2ERE,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Epair_2EFST(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))).
tff(ax_thm_2Ecomplex_2EIM,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Epair_2ESND(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__RE__IM__EQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((V0z = V1w) <=> ((surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) & (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__of__real,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(V0x)),ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ERE__COMPLEX__OF__REAL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2ERE,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = V0x)))).
tff(conj_thm_2Ecomplex_2EIM__COMPLEX__OF__REAL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2EIM,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__of__num,axiom,( ! [V0n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(V0n))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__0,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__1,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,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_2Ecomplex_2ECOMPLEX__10,lemma,((~~ (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__0__THM,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,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(ax_thm_2Ecomplex_2Ei,axiom,(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(c_2Ecomplex_2Ei) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),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(ax_thm_2Ecomplex_2Ecomplex__add,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__neg,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Erealax_2Ereal__neg,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__mul,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__inv,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Erealax_2Ereal__neg,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__sub,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__div,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__COMM,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RID,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__LID,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RINV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__LINV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__COMM,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RID,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LID,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RINV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LINV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__LADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) <=> (V1w = V2v))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__RADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) <=> (V0z = V1w))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = V0z) <=> (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = V1w) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEGNEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__EQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = V1w) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__NEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) <=> (V0z = V1w)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__ADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RZERO,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LZERO,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__LMUL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__RMUL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__MUL2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ENTIRE,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> ((V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__0,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__EQ0,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__REFL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__RZERO,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__LZERO,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__LNEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__NEG2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__SUB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__RNEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__ADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = V0z))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__ADD2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = V0z))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__SUB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = V1w))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__SUB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__SUB2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = V1w))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__SUB2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2u:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V3v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2u)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2u))),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3v))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__0,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V0z = V1w)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) <=> (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))) = V1w))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = V2v) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RNEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LNEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIFFSQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__LMUL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) <=> ((V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (V1w = V2v)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__RMUL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) <=> ((V2v = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (V0z = V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => ((V1w = V2v) <=> (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))) => (V1w = V2v))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))) => (V1w = V2v))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__INV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__MUL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INVINV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = V0z))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__LINV__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__RINV__UNIQ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__0,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV1,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__INV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__NEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (~~ (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__INJ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) <=> (V0z = V1w)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__LDIV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__RDIV,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__DIV2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__1OVER,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV1,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__ADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__SUB,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__RMUL__CANCEL,lemma,(( ! [V0v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0v = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0v))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__LMUL__CANCEL,lemma,(( ! [V0v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0v = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__DENOM__CANCEL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__INNER__CANCEL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__OUTER__CANCEL,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__MUL2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V0z = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RAT,conjecture,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2u:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V3v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V1w = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V3v = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2u)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3v)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3v))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2u)))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3v)))))))))))).
