TPTP Problem File: ITP019_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP019_5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Ecomplex_2ECOMPLEX__INV__NZ.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ecomplex_2ECOMPLEX__INV__NZ.p [Gau20]
% : HL409001_5.p [TPAP]
% Status : Theorem
% Rating : 0.44 v8.2.0, 0.80 v8.1.0, 0.73 v7.5.0
% Syntax : Number of formulae : 23420 (5218 unt;5884 typ; 0 def)
% Number of atoms : 360248 (19072 equ)
% Maximal formula atoms : 5763 ( 15 avg)
% Number of connectives : 66433 (2135 ~; 995 |;24263 &)
% (5796 <=>;33244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 361 ( 7 avg)
% Maximal term depth : 132 ( 2 avg)
% Number of FOOLs : 278414 (278414 fml; 0 var)
% Number of types : 121 ( 119 usr)
% Number of type conns : 11381 (4880 >;6501 *; 0 +; 0 <<)
% Number of predicates : 33 ( 30 usr; 19 prp; 0-2 aty)
% Number of functors : 5763 (5763 usr; 885 con; 0-11 aty)
% Number of variables : 73969 (60258 !;13711 ?;73969 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001_2.ax').
include('Axioms/ITP001/ITP002_5.ax').
include('Axioms/ITP001/ITP003_5.ax').
include('Axioms/ITP001/ITP004_5.ax').
include('Axioms/ITP001/ITP007_5.ax').
include('Axioms/ITP001/ITP006_5.ax').
include('Axioms/ITP001/ITP005_5.ax').
include('Axioms/ITP001/ITP008_5.ax').
include('Axioms/ITP001/ITP009_5.ax').
include('Axioms/ITP001/ITP010_5.ax').
include('Axioms/ITP001/ITP012_5.ax').
include('Axioms/ITP001/ITP011_5.ax').
include('Axioms/ITP001/ITP013_5.ax').
include('Axioms/ITP001/ITP014_5.ax').
include('Axioms/ITP001/ITP015_5.ax').
include('Axioms/ITP001/ITP017_5.ax').
include('Axioms/ITP001/ITP016_5.ax').
include('Axioms/ITP001/ITP019_5.ax').
include('Axioms/ITP001/ITP018_5.ax').
include('Axioms/ITP001/ITP021_5.ax').
include('Axioms/ITP001/ITP022_5.ax').
include('Axioms/ITP001/ITP020_5.ax').
include('Axioms/ITP001/ITP024_5.ax').
include('Axioms/ITP001/ITP023_5.ax').
include('Axioms/ITP001/ITP025_5.ax').
include('Axioms/ITP001/ITP026_5.ax').
include('Axioms/ITP001/ITP027_5.ax').
include('Axioms/ITP001/ITP028_5.ax').
include('Axioms/ITP001/ITP031_5.ax').
include('Axioms/ITP001/ITP029_5.ax').
include('Axioms/ITP001/ITP033_5.ax').
include('Axioms/ITP001/ITP030_5.ax').
include('Axioms/ITP001/ITP032_5.ax').
include('Axioms/ITP001/ITP038_5.ax').
include('Axioms/ITP001/ITP035_5.ax').
include('Axioms/ITP001/ITP034_5.ax').
include('Axioms/ITP001/ITP036_5.ax').
include('Axioms/ITP001/ITP037_5.ax').
include('Axioms/ITP001/ITP039_5.ax').
include('Axioms/ITP001/ITP041_5.ax').
include('Axioms/ITP001/ITP042_5.ax').
include('Axioms/ITP001/ITP040_5.ax').
include('Axioms/ITP001/ITP044_5.ax').
include('Axioms/ITP001/ITP051_5.ax').
include('Axioms/ITP001/ITP045_5.ax').
include('Axioms/ITP001/ITP056_5.ax').
include('Axioms/ITP001/ITP046_5.ax').
include('Axioms/ITP001/ITP043_5.ax').
include('Axioms/ITP001/ITP052_5.ax').
include('Axioms/ITP001/ITP057_5.ax').
include('Axioms/ITP001/ITP048_5.ax').
include('Axioms/ITP001/ITP047_5.ax').
include('Axioms/ITP001/ITP055_5.ax').
include('Axioms/ITP001/ITP053_5.ax').
include('Axioms/ITP001/ITP054_5.ax').
include('Axioms/ITP001/ITP058_5.ax').
include('Axioms/ITP001/ITP049_5.ax').
include('Axioms/ITP001/ITP050_5.ax').
include('Axioms/ITP001/ITP061_5.ax').
include('Axioms/ITP001/ITP069_5.ax').
include('Axioms/ITP001/ITP062_5.ax').
include('Axioms/ITP001/ITP068_5.ax').
include('Axioms/ITP001/ITP078_5.ax').
include('Axioms/ITP001/ITP064_5.ax').
include('Axioms/ITP001/ITP060_5.ax').
include('Axioms/ITP001/ITP067_5.ax').
include('Axioms/ITP001/ITP075_5.ax').
include('Axioms/ITP001/ITP074_5.ax').
include('Axioms/ITP001/ITP063_5.ax').
include('Axioms/ITP001/ITP059_5.ax').
include('Axioms/ITP001/ITP065_5.ax').
include('Axioms/ITP001/ITP076_5.ax').
include('Axioms/ITP001/ITP066_5.ax').
include('Axioms/ITP001/ITP077_5.ax').
include('Axioms/ITP001/ITP070_5.ax').
include('Axioms/ITP001/ITP071_5.ax').
include('Axioms/ITP001/ITP072_5.ax').
include('Axioms/ITP001/ITP073_5.ax').
include('Axioms/ITP001/ITP080_5.ax').
include('Axioms/ITP001/ITP083_5.ax').
include('Axioms/ITP001/ITP088_5.ax').
include('Axioms/ITP001/ITP082_5.ax').
include('Axioms/ITP001/ITP081_5.ax').
include('Axioms/ITP001/ITP079_5.ax').
include('Axioms/ITP001/ITP087_5.ax').
include('Axioms/ITP001/ITP085_5.ax').
include('Axioms/ITP001/ITP086_5.ax').
include('Axioms/ITP001/ITP090_5.ax').
include('Axioms/ITP001/ITP089_5.ax').
include('Axioms/ITP001/ITP084_5.ax').
include('Axioms/ITP001/ITP104_5.ax').
include('Axioms/ITP001/ITP097_5.ax').
include('Axioms/ITP001/ITP094_5.ax').
include('Axioms/ITP001/ITP095_5.ax').
include('Axioms/ITP001/ITP093_5.ax').
include('Axioms/ITP001/ITP102_5.ax').
include('Axioms/ITP001/ITP091_5.ax').
include('Axioms/ITP001/ITP098_5.ax').
include('Axioms/ITP001/ITP096_5.ax').
include('Axioms/ITP001/ITP100_5.ax').
include('Axioms/ITP001/ITP092_5.ax').
include('Axioms/ITP001/ITP105_5.ax').
include('Axioms/ITP001/ITP101_5.ax').
include('Axioms/ITP001/ITP103_5.ax').
include('Axioms/ITP001/ITP099_5.ax').
include('Axioms/ITP001/ITP111_5.ax').
include('Axioms/ITP001/ITP108_5.ax').
include('Axioms/ITP001/ITP106_5.ax').
include('Axioms/ITP001/ITP107_5.ax').
include('Axioms/ITP001/ITP114_5.ax').
include('Axioms/ITP001/ITP110_5.ax').
include('Axioms/ITP001/ITP109_5.ax').
include('Axioms/ITP001/ITP112_5.ax').
include('Axioms/ITP001/ITP113_5.ax').
include('Axioms/ITP001/ITP117_5.ax').
include('Axioms/ITP001/ITP116_5.ax').
include('Axioms/ITP001/ITP118_5.ax').
include('Axioms/ITP001/ITP120_5.ax').
include('Axioms/ITP001/ITP119_5.ax').
include('Axioms/ITP001/ITP121_5.ax').
include('Axioms/ITP001/ITP123_5.ax').
include('Axioms/ITP001/ITP124_5.ax').
include('Axioms/ITP001/ITP126_5.ax').
include('Axioms/ITP001/ITP127_5.ax').
include('Axioms/ITP001/ITP129_5.ax').
include('Axioms/ITP001/ITP128_5.ax').
include('Axioms/ITP001/ITP130_5.ax').
include('Axioms/ITP001/ITP131_5.ax').
include('Axioms/ITP001/ITP132_5.ax').
include('Axioms/ITP001/ITP134_5.ax').
include('Axioms/ITP001/ITP133_5.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,axiom,
! [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,axiom,
! [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,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_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,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] :
( ( 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,axiom,
! [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,axiom,
! [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,axiom,
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,axiom,
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,axiom,
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,axiom,
! [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,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_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,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,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,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__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,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__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,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__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,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__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,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_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,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,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,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__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,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__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,axiom,
! [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,axiom,
! [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,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,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,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,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,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,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,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,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,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))) = 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,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))) = 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,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,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,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(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,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(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,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(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,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(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,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(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,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__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,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__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,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(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,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(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,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,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,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(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,axiom,
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,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(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,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__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,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__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,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__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,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,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,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,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,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(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,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)),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,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,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,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(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,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,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,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,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,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)),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,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)),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,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,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,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,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,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(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( V0z = V1w ) ) ).
tff(conj_thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD,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,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,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,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,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)),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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,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,axiom,
! [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,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] :
( ( ( 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,axiom,
! [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,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(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,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(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,axiom,
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,axiom,
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,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,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,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,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,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(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,conjecture,
! [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))) ) ) ).
%------------------------------------------------------------------------------