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,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] : (((~~ (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)))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__RAT,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] : (((~~ (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__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(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__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(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)))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__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__div,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__DIV__REFL,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__div,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__SUB__INV2,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(ap(c_2Ecomplex_2Ecomplex__sub,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)))) = 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(V1w)),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(V0z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__RDIV__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] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (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 = 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)))) <=> (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)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__LDIV__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] : ( ! [V2v:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((~~ (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))))) => ((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(V2v))) = V1w) <=> (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(V1w)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2v))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__EQ,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y: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(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V1y)))) <=> (V0x = V1y)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__ADD,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__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__real,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V1y)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__NEG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__neg,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__MUL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__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__real,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V1y)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__INV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0x)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__SUB,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__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__real,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V1y)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__REAL__DIV,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V1y)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__NUM__EQ,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n: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(V0m))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(V1n)))) <=> (V0m = V1n)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__NUM__ADD,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (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(V0m))),ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__OF__NUM__MUL,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (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(V0m))),ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(V1n)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,ap(ap(c_2Earithmetic_2E_2A,inj__ty_2Enum_2Enum(V0m)),inj__ty_2Enum_2Enum(V1n))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__scalar__lmul,axiom,( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))) = 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__mul,inj__ty_2Erealax_2Ereal(V0k)),ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0k)),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__scalar__rmul,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1k:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Erealax_2Ereal(V1k))) = 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__mul,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__ty_2Erealax_2Ereal(V1k))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__ty_2Erealax_2Ereal(V1k)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__NEG,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0k))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0k))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__ADD,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__lmul,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__SUB,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__lmul,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l))),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__SCALAR__LMUL,lemma,(( ! [V0k:tp__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),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__add,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__SCALAR__LMUL,lemma,(( ! [V0k:tp__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),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__sub,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__SCALAR__LMUL2,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V3w: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l))),ap(ap(c_2Ecomplex_2Ecomplex__mul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3w))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__LMUL__SCALAR__LMUL,lemma,(( ! [V0k:tp__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))),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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),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(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__RMUL__SCALAR__LMUL,lemma,(( ! [V0k:tp__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] : (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(V1z)),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),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(V2w)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__ZERO,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__scalar__lmul,ap(c_2Ereal_2Ereal__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__ZERO__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),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__SCALAR__LMUL__ONE,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__scalar__lmul,ap(c_2Ereal_2Ereal__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__SCALAR__LMUL__NEG1,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__scalar__lmul,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__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__DOUBLE,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)),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__scalar__lmul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,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__SCALAR__LMUL__ENTIRE,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))) = 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)))) <=> ((V0k = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (V1z = 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__EQ__SCALAR__LMUL,lemma,(( ! [V0k:tp__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] : ((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)))) <=> ((V0k = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (V1z = V2w)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__EQ,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)))) <=> ((V0k = V1l) | (V2z = 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__SCALAR__LMUL__EQ1,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))) = V1z) <=> ((V0k = 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)))))) | (V1z = 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__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V0k = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V1z = 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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(c_2Erealax_2Einv,inj__ty_2Erealax_2Ereal(V0k))),ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__LMUL__DIV2,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V3w:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((~~ (V1l = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & (~~ (V3w = 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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V1l)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3w)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l))),ap(ap(c_2Ecomplex_2Ecomplex__div,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3w)))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__MUL__COMM,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V0k)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__RMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__rmul,ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0k))),inj__ty_2Erealax_2Ereal(V1l))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__RMUL__NEG,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V0k)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0k))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__NEG__SCALAR__RMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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__scalar__rmul,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))),inj__ty_2Erealax_2Ereal(V0k))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0k))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__RMUL__ADD,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0k))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1l)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__RSCALAR__RMUL__SUB,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2z: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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0k)),inj__ty_2Erealax_2Ereal(V1l)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V0k))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2z)),inj__ty_2Erealax_2Ereal(V1l)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__ADD__RSCALAR__RMUL,lemma,(( ! [V0k:tp__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,ap(ap(c_2Ecomplex_2Ecomplex__add,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w))),inj__ty_2Erealax_2Ereal(V0k))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__add,ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V0k))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)),inj__ty_2Erealax_2Ereal(V0k)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SUB__SCALAR__RMUL,lemma,(( ! [V0k:tp__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,ap(ap(c_2Ecomplex_2Ecomplex__sub,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w))),inj__ty_2Erealax_2Ereal(V0k))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__sub,ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Erealax_2Ereal(V0k))),ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)),inj__ty_2Erealax_2Ereal(V0k)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__RMUL__ZERO,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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ereal_2Ereal__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__ZERO__SCALAR__RMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__rmul,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V0k))) = 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__SCALAR__RMUL__ONE,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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__SCALAR__RMUL__NEG1,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__scalar__rmul,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),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))))))) = 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(ax_thm_2Ecomplex_2Econj,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_2Econj,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_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(conj_thm_2Ecomplex_2ECONJ__REAL__REFL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Econj,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ecomplex_2ECONJ__NUM__REFL,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Econj,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__num,inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ecomplex_2ECONJ__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_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__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_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECONJ__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_2Econj,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(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__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] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__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_2Econj,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,ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ECONJ__DIV,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_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z: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_2Econj,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__CONJ,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_2Econj,ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECONJ__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_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2ECONJ__EQ2,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_2Econj,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_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) <=> (V0z = V1w)))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RCONJ,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_2Econj,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__real,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(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LCONJ,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_2Econj,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__real,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(conj_thm_2Ecomplex_2ECONJ__ZERO,lemma,((surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Econj,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(ax_thm_2Ecomplex_2Emodu,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Etransc_2Esqrt,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_2Earg,axiom,( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = 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))),ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Etransc_2Eacs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,ap(c_2Etransc_2Eacs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))),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(fo__c_2Etransc_2Epi)))))))).
tff(conj_thm_2Ecomplex_2EMODU__POW2,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2Emodu,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(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(conj_thm_2Ecomplex_2ERE__IM__LE__MODU,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2EMODU__POS,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_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_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RCONJ1,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_2Econj,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__real,ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2Emodu,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(conj_thm_2Ecomplex_2ECOMPLEX__MUL__LCONJ1,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_2Econj,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__real,ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2Emodu,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(conj_thm_2Ecomplex_2EMODU__NEG,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__neg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))).
tff(conj_thm_2Ecomplex_2EMODU__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__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,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__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,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_2EMODU__CONJ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Econj,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))).
tff(conj_thm_2Ecomplex_2EMODU__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] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,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__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w))))))))).
tff(conj_thm_2Ecomplex_2EMODU__0,lemma,((surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__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_2Ecomplex_2EMODU__1,lemma,((surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__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_2Ecomplex_2EMODU__COMPLEX__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__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Einv,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2EMODU__DIV,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] : ((~~ (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__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,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__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2EMODU__SCALAR__LMUL,lemma,(( ! [V0k:tp__ty_2Erealax_2Ereal] : ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(ap(c_2Ecomplex_2Ecomplex__scalar__lmul,inj__ty_2Erealax_2Ereal(V0k)),inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0k))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z))))))))).
tff(conj_thm_2Ecomplex_2EMODU__REAL,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__of__real,inj__ty_2Erealax_2Ereal(V0x)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))))))).
tff(conj_thm_2Ecomplex_2EMODU__NUM,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(c_2Ecomplex_2Ecomplex__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_2Ecomplex_2EMODU__ZERO,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(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))).
tff(conj_thm_2Ecomplex_2EMODU__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))))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2EMODU__CASES,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)))) | p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))))).
tff(conj_thm_2Ecomplex_2ERE__DIV__MODU__BOUNDS,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))))) => (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ecomplex_2EIM__DIV__MODU__BOUNDS,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))))) => (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ecomplex_2ERE__DIV__MODU__ACS__BOUNDS,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))))) => (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Etransc_2Eacs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Eacs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))),inj__ty_2Erealax_2Ereal(fo__c_2Etransc_2Epi)))))))).
tff(conj_thm_2Ecomplex_2EIM__DIV__MODU__ASN__BOUNDS,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))))) => (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(fo__c_2Etransc_2Epi)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),ap(c_2Etransc_2Easn,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Etransc_2Easn,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))),ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(fo__c_2Etransc_2Epi)),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_2Ecomplex_2ERE__DIV__MODU__ACS__COS,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(c_2Etransc_2Ecos,ap(c_2Etransc_2Eacs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2ERE,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))) = surj__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(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2EIM__DIV__MODU__ASN__SIN,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(c_2Etransc_2Esin,ap(c_2Etransc_2Easn,ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2EARG__COS,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(c_2Etransc_2Ecos,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__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(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2EARG__SIN,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(c_2Etransc_2Esin,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(c_2Ecomplex_2EIM,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2ERE__MODU__ARG,lemma,(( ! [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(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Etransc_2Ecos,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2EIM__MODU__ARG,lemma,(( ! [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(ap(c_2Erealax_2Ereal__mul,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(c_2Etransc_2Esin,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__TRIANGLE,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__scalar__lmul,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))),ap(c_2Etransc_2Esin,ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)))))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__MODU__ARG__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_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))) & (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))) = surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Earg,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1w)))))))))).
tff(conj_thm_2Ecomplex_2EMODU__UNIT,lemma,(( ! [A_27a:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:$i] : (mem(V1y,A_27a) => (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Etransc_2Esin,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_2Ecomplex_2ECOMPLEX__MUL__ARG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Etransc_2Esin,inj__ty_2Erealax_2Ereal(V0x)))),ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Etransc_2Esin,inj__ty_2Erealax_2Ereal(V1y))))) = 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_2Etransc_2Ecos,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(c_2Etransc_2Esin,ap(ap(c_2Erealax_2Ereal__add,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__INV__ARG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Etransc_2Esin,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),ap(c_2Etransc_2Ecos,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x)))),ap(c_2Etransc_2Esin,ap(c_2Erealax_2Ereal__neg,inj__ty_2Erealax_2Ereal(V0x))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__DIV__ARG,lemma,(( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__div,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Etransc_2Esin,inj__ty_2Erealax_2Ereal(V0x)))),ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ap(c_2Etransc_2Ecos,inj__ty_2Erealax_2Ereal(V1y))),ap(c_2Etransc_2Esin,inj__ty_2Erealax_2Ereal(V1y))))) = 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_2Etransc_2Ecos,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))),ap(c_2Etransc_2Esin,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V0x)),inj__ty_2Erealax_2Ereal(V1y)))))))))).
tff(ax_thm_2Ecomplex_2Ecomplex__pow__def,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(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),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,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V2n)))) = 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(V1z)),ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Enum_2Enum(V2n))))))))).
tff(conj_thm_2Ecomplex_2Ecomplex__pow__def__compute,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__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),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,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & (( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V2n))))) = 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(V1z)),ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V2n)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))))))) & ( ! [V3z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V4n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V4n))))) = 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(V3z)),ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V3z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V4n))))))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__0,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V0n)))) = 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__POW__NZ,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~~ (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__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V1n))) = 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__POWINV,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))))) => ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V1n)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ecomplex_2EMODU__COMPLEX__POW,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Emodu,ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V1n)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2Epow,ap(c_2Ecomplex_2Emodu,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__ty_2Enum_2Enum(V1n)))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__ADD,lemma,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1m)),inj__ty_2Enum_2Enum(V2n)))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V1m))),ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V2n)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__1,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__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = V0z)))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__2,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__pow,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__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(V0z))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__ONE,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,ap(c_2Ecomplex_2Ecomplex__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Enum_2Enum(V0n))) = 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__POW__MUL,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V2w: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__pow,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(V2w))),inj__ty_2Enum_2Enum(V0n))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__mul,ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V1z)),inj__ty_2Enum_2Enum(V0n))),ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V2w)),inj__ty_2Enum_2Enum(V0n)))))))))).
tff(conj_thm_2Ecomplex_2ECOMPLEX__POW__INV,conjecture,(( ! [V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(ap(c_2Ecomplex_2Ecomplex__pow,ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z))),inj__ty_2Enum_2Enum(V1n))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,ap(ap(c_2Ecomplex_2Ecomplex__pow,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(V0z)),inj__ty_2Enum_2Enum(V1n))))))))).
