%------------------------------------------------------------------------------
% File     : ITP019^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 syntactic 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]
%          : HL409001^4.p [TPAP]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.69 v8.1.0, 0.55 v7.5.0
% Syntax   : Number of formulae    : 63455 (25500 unt;29061 typ;   0 def)
%            Number of atoms       : 75853 (41113 equ;2792 cnn)
%            Maximal formula atoms :  912 (   2 avg)
%            Number of connectives : 1429068 (2792   ~;1460   |;12112   &;1395730   @)
%                                         (7052 <=>;9922  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  368 (   6 avg)
%            Number of types       :  169 ( 168 usr)
%            Number of type conns  : 84033 (84033   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 10206 (10204 usr;2108 con; 0-9 aty)
%            Number of variables   : 116791 (   0   ^;102665   !;14126   ?;116791   :)
% SPC      : TH0_THM_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002^4.ax').
include('Axioms/ITP001/ITP003^4.ax').
include('Axioms/ITP001/ITP004^4.ax').
include('Axioms/ITP001/ITP005^4.ax').
include('Axioms/ITP001/ITP006^4.ax').
include('Axioms/ITP001/ITP007^4.ax').
include('Axioms/ITP001/ITP008^4.ax').
include('Axioms/ITP001/ITP009^4.ax').
include('Axioms/ITP001/ITP010^4.ax').
include('Axioms/ITP001/ITP011^4.ax').
include('Axioms/ITP001/ITP012^4.ax').
include('Axioms/ITP001/ITP013^4.ax').
include('Axioms/ITP001/ITP014^4.ax').
include('Axioms/ITP001/ITP015^4.ax').
include('Axioms/ITP001/ITP016^4.ax').
include('Axioms/ITP001/ITP017^4.ax').
include('Axioms/ITP001/ITP018^4.ax').
include('Axioms/ITP001/ITP019^4.ax').
include('Axioms/ITP001/ITP020^4.ax').
include('Axioms/ITP001/ITP021^4.ax').
include('Axioms/ITP001/ITP022^4.ax').
include('Axioms/ITP001/ITP023^4.ax').
include('Axioms/ITP001/ITP024^4.ax').
include('Axioms/ITP001/ITP025^4.ax').
include('Axioms/ITP001/ITP026^4.ax').
include('Axioms/ITP001/ITP027^4.ax').
include('Axioms/ITP001/ITP028^4.ax').
include('Axioms/ITP001/ITP029^4.ax').
include('Axioms/ITP001/ITP030^4.ax').
include('Axioms/ITP001/ITP031^4.ax').
include('Axioms/ITP001/ITP032^4.ax').
include('Axioms/ITP001/ITP033^4.ax').
include('Axioms/ITP001/ITP034^4.ax').
include('Axioms/ITP001/ITP035^4.ax').
include('Axioms/ITP001/ITP036^4.ax').
include('Axioms/ITP001/ITP037^4.ax').
include('Axioms/ITP001/ITP038^4.ax').
include('Axioms/ITP001/ITP039^4.ax').
include('Axioms/ITP001/ITP040^4.ax').
include('Axioms/ITP001/ITP041^4.ax').
include('Axioms/ITP001/ITP042^4.ax').
include('Axioms/ITP001/ITP043^4.ax').
include('Axioms/ITP001/ITP044^4.ax').
include('Axioms/ITP001/ITP045^4.ax').
include('Axioms/ITP001/ITP046^4.ax').
include('Axioms/ITP001/ITP047^4.ax').
include('Axioms/ITP001/ITP048^4.ax').
include('Axioms/ITP001/ITP049^4.ax').
include('Axioms/ITP001/ITP050^4.ax').
include('Axioms/ITP001/ITP051^4.ax').
include('Axioms/ITP001/ITP052^4.ax').
include('Axioms/ITP001/ITP053^4.ax').
include('Axioms/ITP001/ITP054^4.ax').
include('Axioms/ITP001/ITP055^4.ax').
include('Axioms/ITP001/ITP056^4.ax').
include('Axioms/ITP001/ITP057^4.ax').
include('Axioms/ITP001/ITP058^4.ax').
include('Axioms/ITP001/ITP059^4.ax').
include('Axioms/ITP001/ITP060^4.ax').
include('Axioms/ITP001/ITP061^4.ax').
include('Axioms/ITP001/ITP062^4.ax').
include('Axioms/ITP001/ITP063^4.ax').
include('Axioms/ITP001/ITP064^4.ax').
include('Axioms/ITP001/ITP065^4.ax').
include('Axioms/ITP001/ITP066^4.ax').
include('Axioms/ITP001/ITP067^4.ax').
include('Axioms/ITP001/ITP068^4.ax').
include('Axioms/ITP001/ITP069^4.ax').
include('Axioms/ITP001/ITP070^4.ax').
include('Axioms/ITP001/ITP071^4.ax').
include('Axioms/ITP001/ITP072^4.ax').
include('Axioms/ITP001/ITP073^4.ax').
include('Axioms/ITP001/ITP074^4.ax').
include('Axioms/ITP001/ITP075^4.ax').
include('Axioms/ITP001/ITP076^4.ax').
include('Axioms/ITP001/ITP077^4.ax').
include('Axioms/ITP001/ITP078^4.ax').
include('Axioms/ITP001/ITP079^4.ax').
include('Axioms/ITP001/ITP080^4.ax').
include('Axioms/ITP001/ITP081^4.ax').
include('Axioms/ITP001/ITP082^4.ax').
include('Axioms/ITP001/ITP083^4.ax').
include('Axioms/ITP001/ITP084^4.ax').
include('Axioms/ITP001/ITP085^4.ax').
include('Axioms/ITP001/ITP086^4.ax').
include('Axioms/ITP001/ITP087^4.ax').
include('Axioms/ITP001/ITP088^4.ax').
include('Axioms/ITP001/ITP089^4.ax').
include('Axioms/ITP001/ITP090^4.ax').
include('Axioms/ITP001/ITP091^4.ax').
include('Axioms/ITP001/ITP092^4.ax').
include('Axioms/ITP001/ITP093^4.ax').
include('Axioms/ITP001/ITP094^4.ax').
include('Axioms/ITP001/ITP095^4.ax').
include('Axioms/ITP001/ITP096^4.ax').
include('Axioms/ITP001/ITP097^4.ax').
include('Axioms/ITP001/ITP098^4.ax').
include('Axioms/ITP001/ITP099^4.ax').
include('Axioms/ITP001/ITP100^4.ax').
include('Axioms/ITP001/ITP101^4.ax').
include('Axioms/ITP001/ITP102^4.ax').
include('Axioms/ITP001/ITP103^4.ax').
include('Axioms/ITP001/ITP104^4.ax').
include('Axioms/ITP001/ITP105^4.ax').
include('Axioms/ITP001/ITP106^4.ax').
include('Axioms/ITP001/ITP107^4.ax').
include('Axioms/ITP001/ITP108^4.ax').
include('Axioms/ITP001/ITP109^4.ax').
include('Axioms/ITP001/ITP110^4.ax').
include('Axioms/ITP001/ITP111^4.ax').
include('Axioms/ITP001/ITP112^4.ax').
include('Axioms/ITP001/ITP113^4.ax').
include('Axioms/ITP001/ITP114^4.ax').
include('Axioms/ITP001/ITP116^4.ax').
include('Axioms/ITP001/ITP117^4.ax').
include('Axioms/ITP001/ITP118^4.ax').
include('Axioms/ITP001/ITP119^4.ax').
include('Axioms/ITP001/ITP120^4.ax').
include('Axioms/ITP001/ITP121^4.ax').
include('Axioms/ITP001/ITP123^4.ax').
include('Axioms/ITP001/ITP124^4.ax').
include('Axioms/ITP001/ITP126^4.ax').
include('Axioms/ITP001/ITP127^4.ax').
include('Axioms/ITP001/ITP128^4.ax').
include('Axioms/ITP001/ITP129^4.ax').
include('Axioms/ITP001/ITP130^4.ax').
include('Axioms/ITP001/ITP131^4.ax').
include('Axioms/ITP001/ITP132^4.ax').
include('Axioms/ITP001/ITP133^4.ax').
include('Axioms/ITP001/ITP134^4.ax').
%------------------------------------------------------------------------------
thf(u,type,
    u: $tType ).

thf(d,type,
    d: $tType ).

thf(du,type,
    du: $tType ).

thf(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Etyop_2Erealax_2Ereal: $tType ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(tyop_2Erealax_2Ereal,type,
    tyop_2Erealax_2Ereal: d ).

thf(s,type,
    s: d > u > du ).

thf(app_2E2,type,
    app_2E2: du > du > u ).

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

thf(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: du > du > u ).

thf(c_2Ereal_2E_2F_2E0,type,
    c_2Ereal_2E_2F_2E0: u ).

thf(c_2Ereal_2E_2F_2E2,type,
    c_2Ereal_2E_2F_2E2: du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

thf(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

thf(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

thf(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: du > u ).

thf(c_2Ecomplex_2EIM_2E0,type,
    c_2Ecomplex_2EIM_2E0: u ).

thf(c_2Ecomplex_2EIM_2E1,type,
    c_2Ecomplex_2EIM_2E1: du > u ).

thf(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

thf(c_2Ecomplex_2ERE_2E0,type,
    c_2Ecomplex_2ERE_2E0: u ).

thf(c_2Ecomplex_2ERE_2E1,type,
    c_2Ecomplex_2ERE_2E1: du > u ).

thf(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

thf(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(c_2Ereal_2Eabs_2E0,type,
    c_2Ereal_2Eabs_2E0: u ).

thf(c_2Ereal_2Eabs_2E1,type,
    c_2Ereal_2Eabs_2E1: du > u ).

thf(c_2Ecomplex_2Ecomplex__add_2E0,type,
    c_2Ecomplex_2Ecomplex__add_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__add_2E2,type,
    c_2Ecomplex_2Ecomplex__add_2E2: du > du > u ).

thf(c_2Ecomplex_2Ecomplex__div_2E0,type,
    c_2Ecomplex_2Ecomplex__div_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__div_2E2,type,
    c_2Ecomplex_2Ecomplex__div_2E2: du > du > u ).

thf(c_2Ecomplex_2Ecomplex__inv_2E0,type,
    c_2Ecomplex_2Ecomplex__inv_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__inv_2E1,type,
    c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).

thf(c_2Ecomplex_2Ecomplex__mul_2E0,type,
    c_2Ecomplex_2Ecomplex__mul_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__mul_2E2,type,
    c_2Ecomplex_2Ecomplex__mul_2E2: du > du > u ).

thf(c_2Ecomplex_2Ecomplex__neg_2E0,type,
    c_2Ecomplex_2Ecomplex__neg_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__neg_2E1,type,
    c_2Ecomplex_2Ecomplex__neg_2E1: du > u ).

thf(c_2Ecomplex_2Ecomplex__of__num_2E0,type,
    c_2Ecomplex_2Ecomplex__of__num_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__of__num_2E1,type,
    c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).

thf(c_2Ecomplex_2Ecomplex__of__real_2E0,type,
    c_2Ecomplex_2Ecomplex__of__real_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__of__real_2E1,type,
    c_2Ecomplex_2Ecomplex__of__real_2E1: du > u ).

thf(c_2Ecomplex_2Ecomplex__sub_2E0,type,
    c_2Ecomplex_2Ecomplex__sub_2E0: u ).

thf(c_2Ecomplex_2Ecomplex__sub_2E2,type,
    c_2Ecomplex_2Ecomplex__sub_2E2: du > du > u ).

thf(c_2Ecomplex_2Ei_2E0,type,
    c_2Ecomplex_2Ei_2E0: u ).

thf(c_2Ereal_2Epow_2E0,type,
    c_2Ereal_2Epow_2E0: u ).

thf(c_2Ereal_2Epow_2E2,type,
    c_2Ereal_2Epow_2E2: du > du > u ).

thf(c_2Erealax_2Ereal__add_2E0,type,
    c_2Erealax_2Ereal__add_2E0: u ).

thf(c_2Erealax_2Ereal__add_2E2,type,
    c_2Erealax_2Ereal__add_2E2: du > du > u ).

thf(c_2Ereal_2Ereal__lte_2E0,type,
    c_2Ereal_2Ereal__lte_2E0: u ).

thf(c_2Ereal_2Ereal__lte_2E2,type,
    c_2Ereal_2Ereal__lte_2E2: du > du > u ).

thf(c_2Erealax_2Ereal__mul_2E0,type,
    c_2Erealax_2Ereal__mul_2E0: u ).

thf(c_2Erealax_2Ereal__mul_2E2,type,
    c_2Erealax_2Ereal__mul_2E2: du > du > u ).

thf(c_2Erealax_2Ereal__neg_2E0,type,
    c_2Erealax_2Ereal__neg_2E0: u ).

thf(c_2Erealax_2Ereal__neg_2E1,type,
    c_2Erealax_2Ereal__neg_2E1: du > u ).

thf(c_2Ereal_2Ereal__of__num_2E0,type,
    c_2Ereal_2Ereal__of__num_2E0: u ).

thf(c_2Ereal_2Ereal__of__num_2E1,type,
    c_2Ereal_2Ereal__of__num_2E1: du > u ).

thf(c_2Ereal_2Ereal__sub_2E0,type,
    c_2Ereal_2Ereal__sub_2E0: u ).

thf(c_2Ereal_2Ereal__sub_2E2,type,
    c_2Ereal_2Ereal__sub_2E2: du > du > u ).

thf(c_2Etransc_2Esqrt_2E0,type,
    c_2Etransc_2Esqrt_2E0: u ).

thf(c_2Etransc_2Esqrt_2E1,type,
    c_2Etransc_2Esqrt_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ereal_2E_2F,type,
    mono_2Ec_2Ereal_2E_2F: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Earithmetic_2EBIT1,type,
    mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2EBIT2,type,
    mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ecomplex_2EIM,type,
    mono_2Ec_2Ecomplex_2EIM: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
    mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ecomplex_2ERE,type,
    mono_2Ec_2Ecomplex_2ERE: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
    mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Earithmetic_2EZERO,type,
    mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2Ereal_2Eabs,type,
    mono_2Ec_2Ereal_2Eabs: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__add,type,
    mono_2Ec_2Ecomplex_2Ecomplex__add: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__div,type,
    mono_2Ec_2Ecomplex_2Ecomplex__div: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__mul,type,
    mono_2Ec_2Ecomplex_2Ecomplex__mul: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__neg,type,
    mono_2Ec_2Ecomplex_2Ecomplex__neg: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__real,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__real: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__sub,type,
    mono_2Ec_2Ecomplex_2Ecomplex__sub: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ei,type,
    mono_2Ec_2Ecomplex_2Ei: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ereal_2Epow,type,
    mono_2Ec_2Ereal_2Epow: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Erealax_2Ereal__add,type,
    mono_2Ec_2Erealax_2Ereal__add: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ereal_2Ereal__lte,type,
    mono_2Ec_2Ereal_2Ereal__lte: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(mono_2Ec_2Erealax_2Ereal__mul,type,
    mono_2Ec_2Erealax_2Ereal__mul: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Erealax_2Ereal__neg,type,
    mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ereal_2Ereal__of__num,type,
    mono_2Ec_2Ereal_2Ereal__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ereal_2Ereal__sub,type,
    mono_2Ec_2Ereal_2Ereal__sub: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Etransc_2Esqrt,type,
    mono_2Ec_2Etransc_2Esqrt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ebool_2E_7E,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).

thf(i_mono_2Etyop_2Erealax_2Ereal,type,
    i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).

thf(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
    j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Erealax_2Ereal,type,
    j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).

thf(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).

thf(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(reserved_2Elogic_2E_7E,axiom,
    ! [V0: $o] :
      ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
    <=> ( ( s @ A_27a @ V0_2E0 )
        = ( s @ A_27a @ V1_2E0 ) ) ) ).

thf(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
      = V0 ) ).

thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( ( s @ A_27a @ X0_2E0 )
        = ( s @ A_27a @ X1_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ c_2Epair_2EFST_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ c_2Epair_2ESND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) ) ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Ecomplex_2ERE,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2ERE @ V0z )
      = ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0z ) ) ).

thf(thm_2Ecomplex_2EIM,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2EIM @ V0z )
      = ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0z ) ) ).

thf(thm_2Ecomplex_2Ecomplex__of__real,axiom,
    ! [V0x: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ V0x )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__of__num,axiom,
    ! [V0n: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ V0n )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ V0n ) ) ) ).

thf(thm_2Ecomplex_2Ei,axiom,
    ( mono_2Ec_2Ecomplex_2Ei
    = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__add,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Ecomplex_2ERE @ V1w ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Ecomplex_2EIM @ V1w ) ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__neg,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__mul,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Ecomplex_2ERE @ V1w ) ) @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Ecomplex_2EIM @ V1w ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Ecomplex_2EIM @ V1w ) ) @ ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Ecomplex_2ERE @ V1w ) ) ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__inv,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( mono_2Ec_2Ereal_2E_2F @ ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__sub,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ) ).

thf(thm_2Ecomplex_2Ecomplex__div,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__div @ V0z @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__LEMMA1,axiom,
    ! [V0a: mono_2Etyop_2Erealax_2Ereal,V1b: mono_2Etyop_2Erealax_2Ereal,V2c: mono_2Etyop_2Erealax_2Ereal,V3d: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ereal_2Ereal__sub @ ( mono_2Ec_2Erealax_2Ereal__mul @ V0a @ V2c ) @ ( mono_2Ec_2Erealax_2Ereal__mul @ V1b @ V3d ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__mul @ V0a @ V3d ) @ ( mono_2Ec_2Erealax_2Ereal__mul @ V1b @ V2c ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__mul @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ V0a @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ V1b @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ V2c @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ V3d @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__LEMMA2,axiom,
    ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1y: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Eabs @ V0x ) @ ( mono_2Ec_2Etransc_2Esqrt @ ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ V0x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ V1y @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__RE__IM__EQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0z = V1w )
    <=> ( ( ( mono_2Ec_2Ecomplex_2ERE @ V0z )
          = ( mono_2Ec_2Ecomplex_2ERE @ V1w ) )
        & ( ( mono_2Ec_2Ecomplex_2EIM @ V0z )
          = ( mono_2Ec_2Ecomplex_2EIM @ V1w ) ) ) ) ).

thf(thm_2Ecomplex_2ERE__COMPLEX__OF__REAL,axiom,
    ! [V0x: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2ERE @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ V0x ) )
      = V0x ) ).

thf(thm_2Ecomplex_2EIM__COMPLEX__OF__REAL,axiom,
    ! [V0x: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2EIM @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ V0x ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__0,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__1,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__10,axiom,
    ( (~)
    @ ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__0__THM,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2ERE @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Ereal_2Epow @ ( mono_2Ec_2Ecomplex_2EIM @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__COMM,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V1w @ V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V1w @ V2v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) @ V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__RID,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__LID,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ V0z )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__RINV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__LINV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ V0z )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__COMM,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V2v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) @ V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__RID,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__LID,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V0z )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__RINV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__LINV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) @ V0z )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V1w @ V2v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) @ V2v )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V2v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__LADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V2v ) )
    <=> ( V1w = V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__RADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V2v )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V1w @ V2v ) )
    <=> ( V0z = V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
        = V0z )
    <=> ( V1w
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
        = V1w )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEGNEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__EQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z )
        = V1w )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__NEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) )
    <=> ( V0z = V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( V1w
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__ADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__RZERO,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__LZERO,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ V0z )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__LMUL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__RMUL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__MUL2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ENTIRE,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( V1w
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__0,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__EQ0,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__REFL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V0z )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__RZERO,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__LZERO,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ V0z )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__LNEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__NEG2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__SUB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__RNEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__ADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) @ V1w )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__ADD2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V1w @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__SUB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) @ V0z )
      = V1w ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__SUB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) @ V0z )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__SUB2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) )
      = V1w ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD__SUB2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2u: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V3v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V2u @ V3v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V2u ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V3v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V2v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__0,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( V0z = V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V2v ) )
    <=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V2v )
        = V1w ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w )
        = V2v )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V2v @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__RNEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__MUL__LNEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) @ V1w )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V1w @ V2v ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) @ V2v )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V2v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__DIFFSQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ V0z @ V1w ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ V0z @ V1w ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V0z ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__LMUL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) )
    <=> ( ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( V1w = V2v ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__RMUL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V2v ) )
    <=> ( ( V2v
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( V0z = V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( V1w = V2v )
      <=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( (~)
          @ ( V0z
            = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V1w @ V0z )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V2v @ V0z ) ) )
     => ( V1w = V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V2v: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( (~)
          @ ( V0z
            = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V2v ) ) )
     => ( V1w = V2v ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__NEG__INV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__MUL,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( (~)
          @ ( V0z
            = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
        & ( (~)
          @ ( V1w
            = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V1w ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INVINV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) )
        = V0z ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__LINV__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
     => ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V1w ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__RINV__UNIQ,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1w: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ V0z @ V1w )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
     => ( V1w
        = ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__0,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV1,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__INV,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) )
      = V0z ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__NEG,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ V0z ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( V0z
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
    ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( (~)
        @ ( V0z
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( (~)
        @ ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).

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