TPTP Problem File: ITP003^4.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP003^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Earithmetic_2EMOD__2.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_2Earithmetic_2EMOD__2.p [Gau20]
% : HL401001^4.p [TPAP]
% Status : Theorem
% Rating : 0.88 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0
% Syntax : Number of formulae : 3527 (1238 unt;1357 typ; 0 def)
% Number of atoms : 4814 (2051 equ; 213 cnn)
% Maximal formula atoms : 30 ( 2 avg)
% Number of connectives : 67428 ( 213 ~; 230 |; 665 &;64825 @)
% ( 626 <=>; 869 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 7 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 2358 (2358 >; 0 *; 0 +; 0 <<)
% Number of symbols : 594 ( 592 usr; 206 con; 0-4 aty)
% Number of variables : 7067 ( 0 ^;6869 !; 198 ?;7067 :)
% 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').
%------------------------------------------------------------------------------
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(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(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_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: u ).
thf(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_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_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: u ).
thf(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: du > du > 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_2Earithmetic_2E_3E_2E0,type,
c_2Earithmetic_2E_3E_2E0: u ).
thf(c_2Earithmetic_2E_3E_2E2,type,
c_2Earithmetic_2E_3E_2E2: du > du > u ).
thf(c_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: u ).
thf(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_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_2EABS__DIFF_2E0,type,
c_2Earithmetic_2EABS__DIFF_2E0: u ).
thf(c_2Earithmetic_2EABS__DIFF_2E2,type,
c_2Earithmetic_2EABS__DIFF_2E2: du > 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_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: u ).
thf(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: du > du > u ).
thf(c_2Earithmetic_2EDIV2_2E0,type,
c_2Earithmetic_2EDIV2_2E0: u ).
thf(c_2Earithmetic_2EDIV2_2E1,type,
c_2Earithmetic_2EDIV2_2E1: du > u ).
thf(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: u ).
thf(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: du > u ).
thf(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: u ).
thf(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: du > du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Earithmetic_2EFACT_2E0,type,
c_2Earithmetic_2EFACT_2E0: u ).
thf(c_2Earithmetic_2EFACT_2E1,type,
c_2Earithmetic_2EFACT_2E1: du > u ).
thf(c_2Earithmetic_2EFUNPOW_2E0,type,
c_2Earithmetic_2EFUNPOW_2E0: u ).
thf(c_2Earithmetic_2EFUNPOW_2E3,type,
c_2Earithmetic_2EFUNPOW_2E3: du > du > du > u ).
thf(c_2Earithmetic_2EMAX_2E0,type,
c_2Earithmetic_2EMAX_2E0: u ).
thf(c_2Earithmetic_2EMAX_2E2,type,
c_2Earithmetic_2EMAX_2E2: du > du > u ).
thf(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: u ).
thf(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: du > du > u ).
thf(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: u ).
thf(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: du > du > u ).
thf(c_2Earithmetic_2ENRC_2E0,type,
c_2Earithmetic_2ENRC_2E0: u ).
thf(c_2Earithmetic_2ENRC_2E4,type,
c_2Earithmetic_2ENRC_2E4: du > du > du > 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_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: u ).
thf(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: du > u ).
thf(c_2Ebool_2EONE__ONE_2E0,type,
c_2Ebool_2EONE__ONE_2E0: u ).
thf(c_2Ebool_2EONE__ONE_2E1,type,
c_2Ebool_2EONE__ONE_2E1: du > u ).
thf(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: u ).
thf(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: du > u ).
thf(c_2Erelation_2ERTC_2E0,type,
c_2Erelation_2ERTC_2E0: u ).
thf(c_2Erelation_2ERTC_2E1,type,
c_2Erelation_2ERTC_2E1: du > u ).
thf(c_2Erelation_2ERTC_2E3,type,
c_2Erelation_2ERTC_2E3: du > du > du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Erelation_2ETC_2E0,type,
c_2Erelation_2ETC_2E0: u ).
thf(c_2Erelation_2ETC_2E3,type,
c_2Erelation_2ETC_2E3: du > du > du > 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_2Eprim__rec_2Emeasure_2E0,type,
c_2Eprim__rec_2Emeasure_2E0: u ).
thf(c_2Eprim__rec_2Emeasure_2E1,type,
c_2Eprim__rec_2Emeasure_2E1: du > u ).
thf(c_2Earithmetic_2Enat__elim____magic_2E0,type,
c_2Earithmetic_2Enat__elim____magic_2E0: u ).
thf(c_2Earithmetic_2Enat__elim____magic_2E1,type,
c_2Earithmetic_2Enat__elim____magic_2E1: du > u ).
thf(c_2Earithmetic_2Enum__CASE_2E0,type,
c_2Earithmetic_2Enum__CASE_2E0: u ).
thf(c_2Earithmetic_2Enum__CASE_2E3,type,
c_2Earithmetic_2Enum__CASE_2E3: du > du > du > u ).
thf(c_2Erelation_2Etransitive_2E0,type,
c_2Erelation_2Etransitive_2E0: u ).
thf(c_2Erelation_2Etransitive_2E1,type,
c_2Erelation_2Etransitive_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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_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_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_2Ec_2Earithmetic_2E_2A,type,
mono_2Ec_2Earithmetic_2E_2A: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
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_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D,type,
mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Earithmetic_2E_3E,type,
mono_2Ec_2Earithmetic_2E_3E: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2E_3E_3D,type,
mono_2Ec_2Earithmetic_2E_3E_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EABS__DIFF,type,
mono_2Ec_2Earithmetic_2EABS__DIFF: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
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_2ECOND_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EDIV,type,
mono_2Ec_2Earithmetic_2EDIV: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EDIV2,type,
mono_2Ec_2Earithmetic_2EDIV2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EEVEN,type,
mono_2Ec_2Earithmetic_2EEVEN: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EEXP,type,
mono_2Ec_2Earithmetic_2EEXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Earithmetic_2EFACT,type,
mono_2Ec_2Earithmetic_2EFACT: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EMAX,type,
mono_2Ec_2Earithmetic_2EMAX: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EMIN,type,
mono_2Ec_2Earithmetic_2EMIN: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EMOD,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EODD,type,
mono_2Ec_2Earithmetic_2EODD: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o ).
thf(mono_2Ec_2Eprim__rec_2EPRE,type,
mono_2Ec_2Eprim__rec_2EPRE: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Erelation_2ERTC_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Erelation_2ERTC_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
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_2Earithmetic_2Enat__elim____magic,type,
mono_2Ec_2Earithmetic_2Enat__elim____magic: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Erelation_2Etransitive_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Erelation_2Etransitive_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).
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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > 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_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > 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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
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_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ 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_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(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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_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_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(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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ A_27a @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Earithmetic_2EFUNPOW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ A_27a @ X3_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Earithmetic_2ENRC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ERTC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Erelation_2ERTC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ETC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Erelation_2ETC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Eprim__rec_2Emeasure_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Eprim__rec_2Emeasure_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Earithmetic_2Enum__CASE_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ A_27a ) ) ) @ c_2Earithmetic_2Enum__CASE_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etransitive_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: $o,V1: mono_2Etyop_2Enum_2Enum,V2: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONE__ONE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EONE__ONE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EONE__ONE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Erelation_2ERTC_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Erelation_2ERTC_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Erelation_2ERTC_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Erelation_2ERTC_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( mono_2Ec_2Erelation_2ERTC_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ERTC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Erelation_2Etransitive_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Erelation_2Etransitive_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etransitive_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Erelation_2Etransitive_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > 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_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Earithmetic_2EADD,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ mono_2Ec_2Enum_2E0 @ V0n )
= V0n )
& ! [V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Enum_2ESUC @ V1m ) @ V2n )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2ENUMERAL__DEF,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0x )
= V0x ) ).
thf(thm_2Earithmetic_2EALT__ZERO,axiom,
mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0 ).
thf(thm_2Earithmetic_2EBIT1,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2EBIT2,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2Enat__elim____magic,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2Enat__elim____magic @ V0n )
= V0n ) ).
thf(thm_2Earithmetic_2ESUB,axiom,
( ! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ mono_2Ec_2Enum_2E0 @ V0m )
= mono_2Ec_2Enum_2E0 )
& ! [V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Enum_2ESUC @ V1m ) @ V2n )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V2n ) @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2D @ V1m @ V2n ) ) ) ) ) ).
thf(thm_2Earithmetic_2EMULT,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ mono_2Ec_2Enum_2E0 @ V0n )
= mono_2Ec_2Enum_2E0 )
& ! [V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V1m ) @ V2n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V2n ) @ V2n ) ) ) ).
thf(thm_2Earithmetic_2EEXP,axiom,
( ! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ V0m @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ! [V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ ( mono_2Ec_2Enum_2ESUC @ V2n ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2EGREATER__DEF,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ V1n )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__OR__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
| ( V0m = V1n ) ) ) ).
thf(thm_2Earithmetic_2EGREATER__OR__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E_3D @ V0m @ V1n )
<=> ( ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ V1n )
| ( V0m = V1n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN,axiom,
( ( ( mono_2Ec_2Earithmetic_2EEVEN @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
<=> ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EODD,axiom,
( ( ( mono_2Ec_2Earithmetic_2EODD @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
<=> ( (~) @ ( mono_2Ec_2Earithmetic_2EODD @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2Enum__case__def,axiom,
! [A_27a: d] :
( ! [V0v_2E0: u,V1f_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) ) )
= ( s @ A_27a @ V0v_2E0 ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3v_2E0: u,V4f_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V4f_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V4f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EFUNPOW,axiom,
! [A_27a: d] :
( ! [V0f_2E0: u,V1x_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ A_27a @ V1x_2E0 ) )
& ! [V2f_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4x_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V3n ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) )
= ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC,axiom,
! [A_27a: d] :
( ! [V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1x_2E0 )
= ( s @ A_27a @ V2y_2E0 ) ) )
& ! [V3R_2E0: u,V4n: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V3R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V4n ) ) ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) )
<=> ? [V7z_2E0: u] :
( ( 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 ) ) @ V3R_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V7z_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V3R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ A_27a @ V7z_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EFACT,axiom,
( ( ( mono_2Ec_2Earithmetic_2EFACT @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EFACT @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ ( mono_2Ec_2Earithmetic_2EFACT @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EDIVISION,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1k: mono_2Etyop_2Enum_2Enum] :
( ( V1k
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2EDIV @ V1k @ V0n ) @ V0n ) @ ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n ) ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EDIV2__def,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV2 @ V0n )
= ( mono_2Ec_2Earithmetic_2EDIV @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Earithmetic_2EMAX__DEF,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EMIN__DEF,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__def,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V1m @ V0n ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EONE,axiom,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2ETWO,axiom,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Earithmetic_2ENORM__0,axiom,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ mono_2Ec_2Earithmetic_2EZERO )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2Enum__case__compute,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V2n )
<=> ( V2n = mono_2Ec_2Enum_2E0 ) )
=> ! [V0g_2E0: u,V1f_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ A_27a @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0g_2E0 ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V2n ) ) ) @ ( s @ A_27a @ V1f_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eprim__rec_2EPRE @ V2n ) ) ) ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__NOT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( mono_2Ec_2Enum_2E0
= ( mono_2Ec_2Enum_2ESUC @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EADD__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ mono_2Ec_2Enum_2E0 )
= V0m ) ).
thf(thm_2Earithmetic_2EADD__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EADD__CLAUSES,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ mono_2Ec_2Enum_2E0 @ V1m )
= V1m )
& ( ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ mono_2Ec_2Enum_2E0 )
= V1m )
& ( ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Enum_2ESUC @ V1m ) @ V0n )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V0n ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__SYM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EADD__COMM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EADD__ASSOC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ V2p ) ) ).
thf(thm_2Earithmetic_2Enum__CASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( V0m = mono_2Ec_2Enum_2E0 )
| ? [V1n: mono_2Etyop_2Enum_2Enum] :
( V0m
= ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ENOT__ZERO__LT__ZERO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n ) ) ).
thf(thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n ) )
<=> ( V0n = mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2ELESS__OR__EQ__ALT,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0x @ V1y )
<=> ( V1y
= ( mono_2Ec_2Enum_2ESUC @ V0x ) ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D
= ( mono_2Ec_2Erelation_2ERTC_2Emono_2Etyop_2Enum_2Enum @ F0 ) ) ) ).
thf(thm_2Earithmetic_2ELESS__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m )
=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V1n )
= V0m ) ) ).
thf(thm_2Earithmetic_2Etransitive__LESS,axiom,
mono_2Ec_2Erelation_2Etransitive_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eprim__rec_2E_3C ).
thf(thm_2Earithmetic_2ELESS__TRANS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V2p ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V2p ) ) ).
thf(thm_2Earithmetic_2ELESS__ANTISYM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m ) ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__REV,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ ( mono_2Ec_2Enum_2ESUC @ V1n ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ ( mono_2Ec_2Enum_2ESUC @ V1n ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__MONO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ ( mono_2Ec_2Enum_2ESUC @ V1m ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m ) ) ).
thf(thm_2Earithmetic_2ELESS__LESS__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ ( mono_2Ec_2Enum_2ESUC @ V0m ) ) ) ) ).
thf(thm_2Earithmetic_2Etransitive__measure,axiom,
! [A_27a: d,V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Eprim__rec_2Emeasure_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__OR,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2EOR__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( mono_2Ec_2Enum_2ESUC @ V1m ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( mono_2Ec_2Enum_2ESUC @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ mono_2Ec_2Enum_2E0 @ V0n ) ).
thf(thm_2Earithmetic_2ELESS__SUC__EQ__COR,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( (~)
@ ( ( mono_2Ec_2Enum_2ESUC @ V0m )
= V1n ) ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__NOT__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( (~)
@ ( V1n
= ( mono_2Ec_2Enum_2ESUC @ V0m ) ) ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__0__CASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2E0 = V0m )
| ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__CASES__IMP,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) )
& ( (~) @ ( V0m = V1n ) ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__CASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EADD__INV__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= V0m )
=> ( V1n = mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m )
=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V1n )
= V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__STRONG__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m )
=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Enum_2ESUC @ V2p ) @ V1n )
= V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__SUC__REFL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ ( mono_2Ec_2Enum_2ESUC @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__ADD__NONZERO,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1n = mono_2Ec_2Enum_2E0 ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2ENOT__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ENOT__LESS__EQUAL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__ANTISYM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ mono_2Ec_2Enum_2E0 )
<=> ( V0n = mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2ESUB__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2D @ mono_2Ec_2Enum_2E0 @ V0m )
= mono_2Ec_2Enum_2E0 )
& ( ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ mono_2Ec_2Enum_2E0 )
= V0m ) ) ).
thf(thm_2Earithmetic_2ESUB__MONO__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ ( mono_2Ec_2Enum_2ESUC @ V1m ) )
= ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) ) ).
thf(thm_2Earithmetic_2ESUB__EQ__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n )
= mono_2Ec_2Enum_2E0 )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2EADD1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ V0m )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__SUB1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= V0m ) ).
thf(thm_2Earithmetic_2EPRE__SUB1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2EPRE @ V0m )
= ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Earithmetic_2EMULT__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2EMULT__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ ( mono_2Ec_2Enum_2ESUC @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EMULT__LEFT__1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0m )
= V0m ) ).
thf(thm_2Earithmetic_2EMULT__RIGHT__1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= V0m ) ).
thf(thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ mono_2Ec_2Enum_2E0 @ V0m )
= mono_2Ec_2Enum_2E0 )
& ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Enum_2E0 )
& ( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0m )
= V0m )
& ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= V0m )
& ( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ V1n ) )
& ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ ( mono_2Ec_2Enum_2ESUC @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) ).
thf(thm_2Earithmetic_2EMULT__SYM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EMULT__COMM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ERIGHT__ADD__DISTRIB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELEFT__ADD__DISTRIB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EMULT__ASSOC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ V2p ) ) ).
thf(thm_2Earithmetic_2ESUB__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m )
=> ( ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V1n )
= V0m ) ) ).
thf(thm_2Earithmetic_2EPRE__SUB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2EPRE @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2EADD__EQ__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= mono_2Ec_2Enum_2E0 )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
& ( V1n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EADD__EQ__1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
<=> ( ( ( V0m
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ( V1n = mono_2Ec_2Enum_2E0 ) )
| ( ( V0m = mono_2Ec_2Enum_2E0 )
& ( V1n
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__INV__0__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= V0m )
<=> ( V1n = mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EPRE__SUC__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ( ( V0m
= ( mono_2Ec_2Eprim__rec_2EPRE @ V1n ) )
<=> ( ( mono_2Ec_2Enum_2ESUC @ V0m )
= V1n ) ) ) ).
thf(thm_2Earithmetic_2EINV__PRE__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) )
=> ( ( ( mono_2Ec_2Eprim__rec_2EPRE @ V0m )
= ( mono_2Ec_2Eprim__rec_2EPRE @ V1n ) )
<=> ( V0m = V1n ) ) ) ).
thf(thm_2Earithmetic_2ELESS__SUC__NOT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
=> ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ ( mono_2Ec_2Enum_2ESUC @ V0m ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__EQ__SUB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p )
=> ( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= V2p )
<=> ( V0m
= ( mono_2Ec_2Earithmetic_2E_2D @ V2p @ V1n ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__ADD__INV,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__ADD__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELT__ADD__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELT__ADD__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V1n ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2EEQ__MONO__ADD__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
<=> ( V0m = V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V2p ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__LESS__TRANS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V2p ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V2p ) ) ).
thf(thm_2Earithmetic_2ELESS__LESS__EQ__TRANS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V2p ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum,V3q: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V2p )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V3q ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V3q ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__REFL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V0m ) ).
thf(thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__MULT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELESS__MONO__MULT2,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2i: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V2i )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V3j ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V2i @ V3j ) ) ) ).
thf(thm_2Earithmetic_2ERIGHT__SUB__DISTRIB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELEFT__SUB__DISTRIB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ELESS__ADD__1,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m )
=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( V0m
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EEXP__ADD,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ ( mono_2Ec_2Earithmetic_2E_2B @ V0p @ V1q ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ V0p ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ V1q ) ) ) ).
thf(thm_2Earithmetic_2ENOT__ODD__EQ__EVEN,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V0n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V1m ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQUAL__ANTISYM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) )
=> ( V0n = V1m ) ) ).
thf(thm_2Earithmetic_2ELESS__ADD__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ELESS__OR__EQ__ADD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m )
| ? [V2p: mono_2Etyop_2Enum_2Enum] :
( V0n
= ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EWOP,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ? [V1n: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1n )
=> ? [V2n: mono_2Etyop_2Enum_2Enum] :
( ( V0P @ V2n )
& ! [V3m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3m @ V2n )
=> ( (~) @ ( V0P @ V3m ) ) ) ) ) ).
thf(thm_2Earithmetic_2ECOMPLETE__INDUCTION,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ! [V2m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2m @ V1n )
=> ( V0P @ V2m ) )
=> ( V0P @ V1n ) )
=> ! [V3n: mono_2Etyop_2Enum_2Enum] : ( V0P @ V3n ) ) ).
thf(thm_2Earithmetic_2EFORALL__NUM__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1n )
<=> ( ( V0P @ mono_2Ec_2Enum_2E0 )
& ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( V0P @ V2n )
=> ( V0P @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__SUB,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Enum_2ESUC @ V0a ) @ V0a )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Earithmetic_2ESUB__PLUS,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum,V2c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ V0a @ ( mono_2Ec_2Earithmetic_2E_2B @ V1b @ V2c ) )
= ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2D @ V0a @ V1b ) @ V2c ) ) ).
thf(thm_2Earithmetic_2EINV__PRE__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0m ) @ ( mono_2Ec_2Eprim__rec_2EPRE @ V1n ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EINV__PRE__LESS__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Eprim__rec_2EPRE @ V1m ) @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0n ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EPRE__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0m ) @ ( mono_2Ec_2Eprim__rec_2EPRE @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LESS__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) @ V0n ) ).
thf(thm_2Earithmetic_2ESUB__EQ__EQ__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n )
= V0m )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
| ( V1n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LESS__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n )
= ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LESS__OR,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__SUB__ADD__LESS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V2i @ V1m ) @ V0n ) ) ).
thf(thm_2Earithmetic_2ETIMES2,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V0n ) ) ).
thf(thm_2Earithmetic_2ELESS__MULT__MONO,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1i: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2n ) @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2n ) @ V1i ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1i ) ) ).
thf(thm_2Earithmetic_2EMULT__MONO__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1i: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2n ) @ V0m )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2n ) @ V1i ) )
<=> ( V0m = V1i ) ) ).
thf(thm_2Earithmetic_2EMULT__SUC__EQ,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V2n @ ( mono_2Ec_2Enum_2ESUC @ V0p ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ ( mono_2Ec_2Enum_2ESUC @ V0p ) ) )
<=> ( V2n = V1m ) ) ).
thf(thm_2Earithmetic_2EMULT__EXP__MONO,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V2n @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V1q ) @ V0p ) )
= ( mono_2Ec_2Earithmetic_2E_2A @ V3m @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V1q ) @ V0p ) ) )
<=> ( V2n = V3m ) ) ).
thf(thm_2Earithmetic_2EEQ__ADD__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) )
<=> ( V1n = V2p ) ) ).
thf(thm_2Earithmetic_2EEQ__ADD__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
<=> ( V0m = V1n ) ) ).
thf(thm_2Earithmetic_2EEQ__MULT__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
| ( V1n = V2p ) ) ) ).
thf(thm_2Earithmetic_2EEQ__MULT__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V0m )
= ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V0m ) )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
| ( V1n = V2p ) ) ) ).
thf(thm_2Earithmetic_2EADD__SUB,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0a @ V1c ) @ V1c )
= V0a ) ).
thf(thm_2Earithmetic_2ELESS__EQ__ADD__SUB,axiom,
! [V0c: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0c @ V1b )
=> ! [V2a: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V2a @ V1b ) @ V0c )
= ( mono_2Ec_2Earithmetic_2E_2B @ V2a @ ( mono_2Ec_2Earithmetic_2E_2D @ V1b @ V0c ) ) ) ) ).
thf(thm_2Earithmetic_2ESUB__EQUAL__0,axiom,
! [V0c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ V0c @ V0c )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2ELESS__EQ__SUB__LESS,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1b @ V0a )
=> ! [V2c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2D @ V0a @ V1b ) @ V2c )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0a @ ( mono_2Ec_2Earithmetic_2E_2B @ V1b @ V2c ) ) ) ) ).
thf(thm_2Earithmetic_2ENOT__SUC__LESS__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ V1m ) )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ).
thf(thm_2Earithmetic_2ESUB__SUB,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum,V1c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1c @ V0b )
=> ! [V2a: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ V2a @ ( mono_2Ec_2Earithmetic_2E_2D @ V0b @ V1c ) )
= ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V2a @ V1c ) @ V0b ) ) ) ).
thf(thm_2Earithmetic_2ELESS__IMP__LESS__ADD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m )
=> ! [V2p: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LESS__EQ__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1p )
=> ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V1p @ V0m ) @ V2n )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1p @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LESS__SUC,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2D @ V0p @ V1m ) @ ( mono_2Ec_2Enum_2ESUC @ V0p ) ) ).
thf(thm_2Earithmetic_2ESUB__CANCEL,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0p )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2m @ V0p ) )
=> ( ( ( mono_2Ec_2Earithmetic_2E_2D @ V0p @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2D @ V0p @ V2m ) )
<=> ( V1n = V2m ) ) ) ).
thf(thm_2Earithmetic_2ECANCEL__SUB,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0p @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0p @ V2m ) )
=> ( ( ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V0p )
= ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V0p ) )
<=> ( V1n = V2m ) ) ) ).
thf(thm_2Earithmetic_2ENOT__EXP__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V0m )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EZERO__LESS__EXP,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V0m ) ) ).
thf(thm_2Earithmetic_2EODD__OR__EVEN,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
? [V1m: mono_2Etyop_2Enum_2Enum] :
( ( V0n
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) @ V1m ) )
| ( V0n
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EXP__SUC__MONO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ V1m ) ) @ V0n ) @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ V1m ) ) @ ( mono_2Ec_2Enum_2ESUC @ V0n ) ) ) ).
thf(thm_2Earithmetic_2ELESS__LESS__CASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( V0m = V1n )
| ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n )
| ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EGREATER__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E_3D @ V0n @ V1m )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__CASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__EQUAL__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( V1n
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__EXISTS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
<=> ? [V2p: mono_2Etyop_2Enum_2Enum] :
( V1n
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2EMULT__EQ__0,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n )
= mono_2Ec_2Enum_2E0 )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
| ( V1n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EMULT__EQ__1,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V0x @ V1y )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
<=> ( ( V0x
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ( V1y
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Earithmetic_2EMULT__EQ__ID,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n )
= V1n )
<=> ( ( V0m
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
| ( V1n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ELESS__MULT2,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EZERO__LESS__MULT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EZERO__LESS__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
| ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EFACT__LESS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2EFACT @ V0n ) ) ).
thf(thm_2Earithmetic_2EEVEN__ODD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
<=> ( (~) @ ( mono_2Ec_2Earithmetic_2EODD @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EODD__EVEN,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ V0n )
<=> ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__OR__ODD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
| ( mono_2Ec_2Earithmetic_2EODD @ V0n ) ) ).
thf(thm_2Earithmetic_2EEVEN__AND__ODD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
& ( mono_2Ec_2Earithmetic_2EODD @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
<=> ( ( mono_2Ec_2Earithmetic_2EEVEN @ V0m )
= ( mono_2Ec_2Earithmetic_2EEVEN @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__MULT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) )
<=> ( ( mono_2Ec_2Earithmetic_2EEVEN @ V0m )
| ( mono_2Ec_2Earithmetic_2EEVEN @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EODD__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
<=> ( (~)
@ ( ( mono_2Ec_2Earithmetic_2EODD @ V0m )
= ( mono_2Ec_2Earithmetic_2EODD @ V1n ) ) ) ) ).
thf(thm_2Earithmetic_2EODD__MULT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) )
<=> ( ( mono_2Ec_2Earithmetic_2EODD @ V0m )
& ( mono_2Ec_2Earithmetic_2EODD @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__DOUBLE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n ) ) ).
thf(thm_2Earithmetic_2EODD__DOUBLE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__ODD__EXISTS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
=> ? [V1m: mono_2Etyop_2Enum_2Enum] :
( V0n
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1m ) ) )
& ( ( mono_2Ec_2Earithmetic_2EODD @ V0n )
=> ? [V2m: mono_2Etyop_2Enum_2Enum] :
( V0n
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V2m ) ) ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
<=> ? [V1m: mono_2Etyop_2Enum_2Enum] :
( V0n
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EODD__EXISTS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ V0n )
<=> ? [V1m: mono_2Etyop_2Enum_2Enum] :
( V0n
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1m ) ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__EXP__IFF,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( mono_2Ec_2Earithmetic_2EEVEN @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EEVEN__EXP,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Earithmetic_2EEVEN @ V0m ) )
=> ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2EEXP @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EODD__EXP__IFF,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ V0n ) )
<=> ( ( V0n = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Earithmetic_2EODD @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EODD__EXP,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Earithmetic_2EODD @ V0m ) )
=> ( mono_2Ec_2Earithmetic_2EODD @ ( mono_2Ec_2Earithmetic_2EEXP @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( V0m = V1n )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ) ).
thf(thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ).
thf(thm_2Earithmetic_2ELE__ADD__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ).
thf(thm_2Earithmetic_2ELE__ADD__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2p @ V0m ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ).
thf(thm_2Earithmetic_2ENOT__LEQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V0m ) ) ).
thf(thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0m = V1n ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V0m ) ) ) ).
thf(thm_2Earithmetic_2ENOT__GREATER,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ V1n ) )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2ENOT__GREATER__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Earithmetic_2E_3E_3D @ V0m @ V1n ) )
<=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n ) ) ).
thf(thm_2Earithmetic_2ESUC__ADD__SYM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V0m ) ) ).
thf(thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) ) @ V0m ) ) ).
thf(thm_2Earithmetic_2EMULT__LESS__EQ__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2p ) @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V2p ) @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ELE__MULT__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) )
<=> ( ( V0m = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELE__MULT__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V1n ) )
<=> ( ( V1n = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELT__MULT__LCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V2p ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELT__MULT__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V2p @ V1n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n ) ) )
& ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ V1m ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) @ V1m )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1m )
& ( V0n = mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) @ V0n )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( V1m = mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ V1m ) )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) @ V1m )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V1m @ V0n ) @ V0n )
<=> ( ( V0n = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) @ V2p @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__SUB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__SUC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Enum_2ESUC @ V0m ) @ V1n ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E_3D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2E_3E_3D @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
<=> ( ( mono_2Ec_2Earithmetic_2E_3E_3D @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
| ( mono_2Ec_2Earithmetic_2E_3E_3D @ mono_2Ec_2Enum_2E0 @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__GREATER,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3E @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__GREATER,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( mono_2Ec_2Earithmetic_2E_3E @ V0m @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( V0m
= ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2p ) )
<=> ( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p )
= V1n )
| ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ mono_2Ec_2Enum_2E0 )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n )
= V2p )
<=> ( ( V0m
= ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2p ) )
| ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2ELE,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ mono_2Ec_2Enum_2E0 )
<=> ( V0n = mono_2Ec_2Enum_2E0 ) )
& ! [V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ ( mono_2Ec_2Enum_2ESUC @ V2n ) )
<=> ( ( V1m
= ( mono_2Ec_2Enum_2ESUC @ V2n ) )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2EDA,axiom,
! [V0k: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ? [V2r: mono_2Etyop_2Enum_2Enum,V3q: mono_2Etyop_2Enum_2Enum] :
( ( V0k
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3q @ V1n ) @ V2r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V2r @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EMOD__ONE,axiom,
! [V0k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ V0k @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2EMOD__1,axiom,
! [V0k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ V0k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2EDIV__LESS__EQ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1k: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EDIV @ V1k @ V0n ) @ V1k ) ) ).
thf(thm_2Earithmetic_2EDIV__UNIQUE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1k: mono_2Etyop_2Enum_2Enum,V2q: mono_2Etyop_2Enum_2Enum] :
( ? [V3r: mono_2Etyop_2Enum_2Enum] :
( ( V1k
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V2q @ V0n ) @ V3r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V3r @ V0n ) )
=> ( ( mono_2Ec_2Earithmetic_2EDIV @ V1k @ V0n )
= V2q ) ) ).
thf(thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1k: mono_2Etyop_2Enum_2Enum,V2r: mono_2Etyop_2Enum_2Enum] :
( ? [V3q: mono_2Etyop_2Enum_2Enum] :
( ( V1k
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3q @ V0n ) @ V2r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V2r @ V0n ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n )
= V2r ) ) ).
thf(thm_2Earithmetic_2EDIV__MULT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1r: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1r @ V0n )
=> ! [V2q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V2q @ V0n ) @ V1r ) @ V0n )
= V2q ) ) ).
thf(thm_2Earithmetic_2ELESS__MOD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1k @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n )
= V1k ) ) ).
thf(thm_2Earithmetic_2EMOD__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2A @ V1k @ V0n ) @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EZERO__MOD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ mono_2Ec_2Enum_2E0 @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EZERO__DIV,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EDIV @ mono_2Ec_2Enum_2E0 @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EMOD__MULT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1r: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1r @ V0n )
=> ! [V2q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V2q @ V0n ) @ V1r ) @ V0n )
= V1r ) ) ).
thf(thm_2Earithmetic_2EMOD__TIMES,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1q: mono_2Etyop_2Enum_2Enum,V2r: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V1q @ V0n ) @ V2r ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V2r @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EMOD__TIMES__SUB,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum,V2r: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1q )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2r @ V0n ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2E_2A @ V1q @ V0n ) @ V2r ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V2r ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EMOD__PLUS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1j: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EMOD @ V1j @ V0n ) @ ( mono_2Ec_2Earithmetic_2EMOD @ V2k @ V0n ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V1j @ V2k ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EMOD__MOD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n ) ) ) ).
thf(thm_2Earithmetic_2ELESS__DIV__EQ__ZERO,axiom,
! [V0r: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0r @ V1n )
=> ( ( mono_2Ec_2Earithmetic_2EDIV @ V0r @ V1n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EMULT__DIV,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2A @ V1q @ V0n ) @ V0n )
= V1q ) ) ).
thf(thm_2Earithmetic_2EADD__DIV__ADD__DIV,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1x: mono_2Etyop_2Enum_2Enum,V2r: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V1x @ V0n ) @ V2r ) @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V1x @ ( mono_2Ec_2Earithmetic_2EDIV @ V2r @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__DIV__RWT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Earithmetic_2EMOD @ V1m @ V0n )
= mono_2Ec_2Enum_2E0 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ V2p @ V0n )
= mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2p ) @ V0n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EDIV @ V1m @ V0n ) @ ( mono_2Ec_2Earithmetic_2EDIV @ V2p @ V0n ) ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__MULT__MOD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m ) )
=> ! [V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2EMOD @ V2x @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V0m ) ) @ V1n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V2x @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EDIV__ONE,axiom,
! [V0q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV @ V0q @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
= V0q ) ).
thf(thm_2Earithmetic_2EDIV__1,axiom,
! [V0q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV @ V0q @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= V0q ) ).
thf(thm_2Earithmetic_2EDIVMOD__ID,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( ( mono_2Ec_2Earithmetic_2EDIV @ V0n @ V0n )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD @ V0n @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EDIV__DIV__DIV__MULT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) )
=> ! [V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2EDIV @ V2x @ V0m ) @ V1n )
= ( mono_2Ec_2Earithmetic_2EDIV @ V2x @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__PRE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m )
<=> ( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0m ) )
= V0m ) ) ).
thf(thm_2Earithmetic_2EDIV__LESS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1d: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1d ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EDIV @ V0n @ V1d ) @ V0n ) ) ).
thf(thm_2Earithmetic_2EMOD__LESS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EMOD @ V0m @ V1n ) @ V1n ) ) ).
thf(thm_2Earithmetic_2EADD__MODULUS,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V1x @ V0n ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0n ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V2n @ V3x ) @ V2n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V3x @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__MODULUS__LEFT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V1x @ V0n ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EADD__MODULUS__RIGHT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V1x ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EDIV__P,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1p: mono_2Etyop_2Enum_2Enum,V2q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2q )
=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2EDIV @ V1p @ V2q ) )
<=> ? [V3k: mono_2Etyop_2Enum_2Enum,V4r: mono_2Etyop_2Enum_2Enum] :
( ( V1p
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3k @ V2q ) @ V4r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V4r @ V2q )
& ( V0P @ V3k ) ) ) ) ).
thf(thm_2Earithmetic_2EDIV__P__UNIV,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2n )
=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2EDIV @ V1m @ V2n ) )
<=> ! [V3q: mono_2Etyop_2Enum_2Enum,V4r: mono_2Etyop_2Enum_2Enum] :
( ( ( V1m
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3q @ V2n ) @ V4r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V4r @ V2n ) )
=> ( V0P @ V3q ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__P,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1p: mono_2Etyop_2Enum_2Enum,V2q: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2q )
=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2EMOD @ V1p @ V2q ) )
<=> ? [V3k: mono_2Etyop_2Enum_2Enum,V4r: mono_2Etyop_2Enum_2Enum] :
( ( V1p
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3k @ V2q ) @ V4r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V4r @ V2q )
& ( V0P @ V4r ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__P__UNIV,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2n )
=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2EMOD @ V1m @ V2n ) )
<=> ! [V3q: mono_2Etyop_2Enum_2Enum,V4r: mono_2Etyop_2Enum_2Enum] :
( ( ( V1m
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V3q @ V2n ) @ V4r ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V4r @ V2n ) )
=> ( V0P @ V4r ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__TIMES2,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ! [V1j: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2EMOD @ V1j @ V0n ) @ ( mono_2Ec_2Earithmetic_2EMOD @ V2k @ V0n ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2A @ V1j @ V2k ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EMOD__COMMON__FACTOR,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1p: mono_2Etyop_2Enum_2Enum,V2q: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2q ) )
=> ( ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ ( mono_2Ec_2Earithmetic_2EMOD @ V1p @ V2q ) )
= ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ V1p ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ V2q ) ) ) ) ).
thf(thm_2Earithmetic_2EX__MOD__Y__EQ__X,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1y )
=> ( ( ( mono_2Ec_2Earithmetic_2EMOD @ V0x @ V1y )
= V0x )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ V1y ) ) ) ).
thf(thm_2Earithmetic_2EDIV__LE__MONOTONE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum,V2y: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1x @ V2y ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EDIV @ V1x @ V0n ) @ ( mono_2Ec_2Earithmetic_2EDIV @ V2y @ V0n ) ) ) ).
thf(thm_2Earithmetic_2ELE__LT1,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0x @ V1y )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ ( mono_2Ec_2Earithmetic_2E_2B @ V1y @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Earithmetic_2EX__LE__DIV,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2z )
=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0x @ ( mono_2Ec_2Earithmetic_2EDIV @ V1y @ V2z ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0x @ V2z ) @ V1y ) ) ) ).
thf(thm_2Earithmetic_2EX__LT__DIV,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2z )
=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ ( mono_2Ec_2Earithmetic_2EDIV @ V1y @ V2z ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2z ) @ V1y ) ) ) ).
thf(thm_2Earithmetic_2EDIV__LT__X,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2z )
=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EDIV @ V1y @ V2z ) @ V0x )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1y @ ( mono_2Ec_2Earithmetic_2E_2A @ V0x @ V2z ) ) ) ) ).
thf(thm_2Earithmetic_2EDIV__LE__X,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2z )
=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EDIV @ V1y @ V2z ) @ V0x )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1y @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V2z ) ) ) ) ).
thf(thm_2Earithmetic_2EDIV__EQ__X,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2z )
=> ( ( ( mono_2Ec_2Earithmetic_2EDIV @ V1y @ V2z )
= V0x )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2A @ V0x @ V2z ) @ V1y )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1y @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ V0x ) @ V2z ) ) ) ) ) ).
thf(thm_2Earithmetic_2EDIV__MOD__MOD__DIV,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2k ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2EDIV @ V0m @ V1n ) @ V2k )
= ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2EMOD @ V0m @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V2k ) ) @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EMULT__EQ__DIV,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2x )
=> ( ( ( mono_2Ec_2Earithmetic_2E_2A @ V2x @ V1y )
= V0z )
<=> ( ( V1y
= ( mono_2Ec_2Earithmetic_2EDIV @ V0z @ V2x ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD @ V0z @ V2x )
= mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2x ) ) @ V1y )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) )
<=> ( ( V1y
= ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2x ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2x ) ) )
= mono_2Ec_2Enum_2E0 ) ) )
& ( ( ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2x ) ) @ V1y )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) )
<=> ( ( V1y
= ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2x ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0z ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2x ) ) )
= mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__EQ__0__DIVISOR,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
=> ( ( ( mono_2Ec_2Earithmetic_2EMOD @ V1k @ V0n )
= mono_2Ec_2Enum_2E0 )
<=> ? [V2d: mono_2Etyop_2Enum_2Enum] :
( V1k
= ( mono_2Ec_2Earithmetic_2E_2A @ V2d @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__SUC,axiom,
! [V0y: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0y )
& ( (~)
@ ( ( mono_2Ec_2Enum_2ESUC @ V1x )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2EDIV @ V1x @ V0y ) ) @ V0y ) ) ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Enum_2ESUC @ V1x ) @ V0y )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0y ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__SUC__IFF,axiom,
! [V0y: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0y )
=> ( ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Enum_2ESUC @ V1x ) @ V0y )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0y ) ) )
<=> ( (~)
@ ( ( mono_2Ec_2Enum_2ESUC @ V1x )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2EDIV @ V1x @ V0y ) ) @ V0y ) ) ) ) ) ).
thf(thm_2Earithmetic_2EONE__MOD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Earithmetic_2EONE__MOD__IFF,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
& ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Earithmetic_2EMOD__LESS__EQ,axiom,
! [V0y: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0y )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EMOD @ V1x @ V0y ) @ V1x ) ) ).
thf(thm_2Earithmetic_2EMOD__LIFT__PLUS,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V2k @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ ( mono_2Ec_2Earithmetic_2EMOD @ V0x @ V1n ) ) ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V2k ) @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EMOD @ V0x @ V1n ) @ V2k ) ) ) ).
thf(thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ( ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V2k ) @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EMOD @ V0x @ V1n ) @ V2k ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ V2k @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ ( mono_2Ec_2Earithmetic_2EMOD @ V0x @ V1n ) ) ) ) ) ).
thf(thm_2Earithmetic_2Enum__case__cong,axiom,
! [A_27a: d,V0v_27_2E0: u,V1f_27_2E0: u,V2M: mono_2Etyop_2Enum_2Enum,V3M_27: mono_2Etyop_2Enum_2Enum,V4v_2E0: u,V5f_2E0: u] :
( ( ( V2M = V3M_27 )
& ( ( V3M_27 = mono_2Ec_2Enum_2E0 )
=> ( ( s @ A_27a @ V4v_2E0 )
= ( s @ A_27a @ V0v_27_2E0 ) ) )
& ! [V6n: mono_2Etyop_2Enum_2Enum] :
( ( V3M_27
= ( mono_2Ec_2Enum_2ESUC @ V6n ) )
=> ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V5f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_27_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2M ) ) @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V5f_2E0 ) ) )
= ( s @ A_27a @ ( c_2Earithmetic_2Enum__CASE_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3M_27 ) ) @ ( s @ A_27a @ V0v_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_27_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__ELIM__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ V1n )
<=> ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2n )
=> ( V0P @ V2n @ ( mono_2Ec_2Earithmetic_2E_2D @ V2n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUC__ELIM__NUMERALS,axiom,
! [A_27a: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) ) )
<=> ( ! [V3n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) ) ) )
& ! [V4n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V4n ) ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V4n ) ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V4n ) ) ) ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum,V2P: mono_2Etyop_2Enum_2Enum > $o] :
( ( V2P @ ( mono_2Ec_2Earithmetic_2E_2D @ V1a @ V0b ) )
<=> ! [V3d: mono_2Etyop_2Enum_2Enum] :
( ( ( V0b
= ( mono_2Ec_2Earithmetic_2E_2B @ V1a @ V3d ) )
=> ( V2P @ mono_2Ec_2Enum_2E0 ) )
& ( ( V1a
= ( mono_2Ec_2Earithmetic_2E_2B @ V0b @ V3d ) )
=> ( V2P @ V3d ) ) ) ) ).
thf(thm_2Earithmetic_2EPRE__ELIM__THM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1P: mono_2Etyop_2Enum_2Enum > $o] :
( ( V1P @ ( mono_2Ec_2Eprim__rec_2EPRE @ V0n ) )
<=> ! [V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( V0n = mono_2Ec_2Enum_2E0 )
=> ( V1P @ mono_2Ec_2Enum_2E0 ) )
& ( ( V0n
= ( mono_2Ec_2Enum_2ESUC @ V2m ) )
=> ( V1P @ V2m ) ) ) ) ).
thf(thm_2Earithmetic_2EMULT__INCREASES,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Enum_2ESUC @ V1n ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0b )
=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
? [V2m: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V2m ) ) ) ).
thf(thm_2Earithmetic_2EEXP__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ V1m )
= mono_2Ec_2Enum_2E0 )
<=> ( ( V0n = mono_2Ec_2Enum_2E0 )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1m ) ) ) ).
thf(thm_2Earithmetic_2EZERO__LT__EXP,axiom,
! [V0y: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2EEXP @ V1x @ V0y ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1x )
| ( V0y = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EEXP__1,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0n )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ( ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= V0n ) ) ).
thf(thm_2Earithmetic_2EEXP__EQ__1,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ V1m )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
<=> ( ( V0n
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
| ( V1m = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__LE__MONO,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0b )
=> ! [V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V2m ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__LT__MONO,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0b )
=> ! [V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V2m ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V1n ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V2m @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__INJECTIVE,axiom,
! [V0b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0b )
=> ! [V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V1n )
= ( mono_2Ec_2Earithmetic_2EEXP @ V0b @ V2m ) )
<=> ( V1n = V2m ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2b )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V1m ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V2b ) @ V1m ) @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Enum_2ESUC @ V2b ) @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__LE__IFF,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V1m ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V0n ) )
<=> ( ( ( V2b = mono_2Ec_2Enum_2E0 )
& ( V0n = mono_2Ec_2Enum_2E0 ) )
| ( ( V2b = mono_2Ec_2Enum_2E0 )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1m ) )
| ( V2b
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
| ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V2b )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EX__LE__X__EXP,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0x @ ( mono_2Ec_2Earithmetic_2EEXP @ V0x @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EX__LT__EXP__X,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1b )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ ( mono_2Ec_2Earithmetic_2EEXP @ V1b @ V0x ) ) ) ).
thf(thm_2Earithmetic_2EZERO__EXP,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0x )
<=> ( V0x = mono_2Ec_2Enum_2E0 ) )
=> ! [V0x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ mono_2Ec_2Enum_2E0 @ V0x )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V0x ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EX__LT__EXP__X__IFF,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ ( mono_2Ec_2Earithmetic_2EEXP @ V1b @ V0x ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1b )
| ( V0x = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EEXP__EXP__LT__MONO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EEXP @ V1a @ V0n ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V0n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1a @ V2b )
& ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n ) ) ) ).
thf(thm_2Earithmetic_2EEXP__EXP__LE__MONO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EEXP @ V1a @ V0n ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2b @ V0n ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1a @ V2b )
| ( V0n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EEXP__EXP__INJECTIVE,axiom,
! [V0b1: mono_2Etyop_2Enum_2Enum,V1b2: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEXP @ V0b1 @ V2x )
= ( mono_2Ec_2Earithmetic_2EEXP @ V1b2 @ V2x ) )
<=> ( ( V2x = mono_2Ec_2Enum_2E0 )
| ( V0b1 = V1b2 ) ) ) ).
thf(thm_2Earithmetic_2EEXP__SUB,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V2n )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1q @ V0p ) )
=> ( ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ ( mono_2Ec_2Earithmetic_2E_2D @ V0p @ V1q ) )
= ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ V0p ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2n @ V1q ) ) ) ) ).
thf(thm_2Earithmetic_2EEXP__SUB__NUMERAL,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1n )
=> ( ( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0x ) ) ) @ V1n )
= ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0x ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0x ) ) ) @ V1n )
= ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0x ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EEXP__BASE__MULT,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum,V2y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Earithmetic_2E_2A @ V1x @ V2y ) @ V0z )
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2EEXP @ V1x @ V0z ) @ ( mono_2Ec_2Earithmetic_2EEXP @ V2y @ V0z ) ) ) ).
thf(thm_2Earithmetic_2EEXP__EXP__MULT,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum,V2y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP @ V1x @ ( mono_2Ec_2Earithmetic_2E_2A @ V2y @ V0z ) )
= ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Earithmetic_2EEXP @ V1x @ V2y ) @ V0z ) ) ).
thf(thm_2Earithmetic_2EMAX__COMM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2EMAX @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EMIN__COMM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2EMIN @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EMAX__ASSOC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ ( mono_2Ec_2Earithmetic_2EMAX @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2EMAX @ ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n ) @ V2p ) ) ).
thf(thm_2Earithmetic_2EMIN__ASSOC,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ ( mono_2Ec_2Earithmetic_2EMIN @ V1n @ V2p ) )
= ( mono_2Ec_2Earithmetic_2EMIN @ ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n ) @ V2p ) ) ).
thf(thm_2Earithmetic_2EMIN__MAX__EQ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n ) )
<=> ( V0m = V1n ) ) ).
thf(thm_2Earithmetic_2EMIN__MAX__LT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n ) )
<=> ( (~) @ ( V0m = V1n ) ) ) ).
thf(thm_2Earithmetic_2EMIN__MAX__LE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n ) @ ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n ) ) ).
thf(thm_2Earithmetic_2EMIN__MAX__PRED,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( V0P @ V1m )
& ( V0P @ V2n ) )
=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V2n ) )
& ( V0P @ ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2EMIN__LT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V0n ) @ V2p )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V2p )
| ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V2p ) ) )
& ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ V1m )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EMAX__LT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ V1m )
| ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ V0n ) ) )
& ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V0n ) @ V2p )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V2p )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V2p ) ) ) ) ).
thf(thm_2Earithmetic_2EMIN__LE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V0n ) @ V2p )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V2p )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V2p ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ V1m )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EMAX__LE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V0n ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ V1m )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2p @ V0n ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V0n ) @ V2p )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V2p )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V2p ) ) ) ) ).
thf(thm_2Earithmetic_2EMIN__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMIN @ V0n @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Enum_2E0 )
& ( ( mono_2Ec_2Earithmetic_2EMIN @ mono_2Ec_2Enum_2E0 @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EMAX__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMAX @ V0n @ mono_2Ec_2Enum_2E0 )
= V0n )
& ( ( mono_2Ec_2Earithmetic_2EMAX @ mono_2Ec_2Enum_2E0 @ V0n )
= V0n ) ) ).
thf(thm_2Earithmetic_2EMAX__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMAX @ V1m @ V0n )
= mono_2Ec_2Enum_2E0 )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
& ( V0n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EMIN__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMIN @ V1m @ V0n )
= mono_2Ec_2Enum_2E0 )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
| ( V0n = mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2EMIN__IDEM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN @ V0n @ V0n )
= V0n ) ).
thf(thm_2Earithmetic_2EMAX__IDEM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX @ V0n @ V0n )
= V0n ) ).
thf(thm_2Earithmetic_2EEXISTS__GREATEST,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ( ? [V1x: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1x )
& ? [V2x: mono_2Etyop_2Enum_2Enum] :
! [V3y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E @ V3y @ V2x )
=> ( (~) @ ( V0P @ V3y ) ) ) )
<=> ? [V4x: mono_2Etyop_2Enum_2Enum] :
( ( V0P @ V4x )
& ! [V5y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E @ V5y @ V4x )
=> ( (~) @ ( V0P @ V5y ) ) ) ) ) ).
thf(thm_2Earithmetic_2EEXISTS__NUM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ? [V1n: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1n )
<=> ( ( V0P @ mono_2Ec_2Enum_2E0 )
| ? [V2m: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Enum_2ESUC @ V2m ) ) ) ) ).
thf(thm_2Earithmetic_2EFORALL__NUM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1n )
<=> ( ( V0P @ mono_2Ec_2Enum_2E0 )
& ! [V2n: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) ).
thf(thm_2Earithmetic_2EBOUNDED__FORALL__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1c )
=> ( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ V1c )
=> ( V0P @ V2n ) )
<=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2E_2D @ V1c @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3n @ ( mono_2Ec_2Earithmetic_2E_2D @ V1c @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
=> ( V0P @ V3n ) ) ) ) ) ).
thf(thm_2Earithmetic_2EBOUNDED__EXISTS__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o,V1c: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1c )
=> ( ? [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ V1c )
& ( V0P @ V2n ) )
<=> ( ( V0P @ ( mono_2Ec_2Earithmetic_2E_2D @ V1c @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
| ? [V3n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3n @ ( mono_2Ec_2Earithmetic_2E_2D @ V1c @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ( V0P @ V3n ) ) ) ) ) ).
thf(thm_2Earithmetic_2Etransitive__monotone,axiom,
! [A_27a: d,V0R_2E0: u,V1f_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum] : ( 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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) ) ) ) ) )
=> ! [V3m: mono_2Etyop_2Enum_2Enum,V4n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3m @ V4n )
=> ( 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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ESTRICTLY__INCREASING__TC,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( V0f @ V1n ) @ ( V0f @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) )
=> ! [V2m: mono_2Etyop_2Enum_2Enum,V3n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2m @ V3n )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( V0f @ V2m ) @ ( V0f @ V3n ) ) ) ) ).
thf(thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( V0f @ V1n ) @ ( V0f @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) )
=> ( mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0f ) ) ).
thf(thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0f )
=> ! [V1b: mono_2Etyop_2Enum_2Enum] :
? [V2a: mono_2Etyop_2Enum_2Enum] :
! [V3x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( V0f @ V3x ) @ V1b )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V3x @ V2a ) ) ) ).
thf(thm_2Earithmetic_2EONE__ONE__UNBOUNDED,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0f )
=> ! [V1b: mono_2Etyop_2Enum_2Enum] :
? [V2n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ V1b @ ( V0f @ V2n ) ) ) ).
thf(thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( V0f @ V1n ) @ ( V0f @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) )
=> ! [V2b: mono_2Etyop_2Enum_2Enum] :
? [V3n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ V2b @ ( V0f @ V3n ) ) ) ).
thf(thm_2Earithmetic_2ENOT__STRICTLY__DECREASING,axiom,
! [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( (~)
@ ! [V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ ( V0f @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) @ ( V0f @ V1n ) ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__SYM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m )
= ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V1m @ V0n ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__COMM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m )
= ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V1m @ V0n ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__EQS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V0n )
= mono_2Ec_2Enum_2E0 ) ).
thf(thm_2Earithmetic_2EABS__DIFF__EQ__0,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m )
= mono_2Ec_2Enum_2E0 )
<=> ( V0n = V1m ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__ZERO,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ mono_2Ec_2Enum_2E0 )
= V0n )
& ( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ mono_2Ec_2Enum_2E0 @ V0n )
= V0n ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__SUC,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ ( mono_2Ec_2Enum_2ESUC @ V0n ) @ ( mono_2Ec_2Enum_2ESUC @ V1m ) )
= ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__SUC__LE,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1z: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ ( mono_2Ec_2Enum_2ESUC @ V1z ) ) @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ V1z ) ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__PLUS__LE,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1z: mono_2Etyop_2Enum_2Enum,V2y: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ ( mono_2Ec_2Earithmetic_2E_2B @ V2y @ V1z ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2y @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ V1z ) ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__LE__SUM,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V1x @ V0z ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1x @ V0z ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0x @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ V1y ) @ V1y ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__TRIANGLE,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ V2z ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0x @ V1y ) @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V1y @ V2z ) ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__ADD__SAME,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EABS__DIFF @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V2p ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2p ) )
= ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n @ V1m ) ) ).
thf(thm_2Earithmetic_2ELE__SUB__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V2p @ V0m ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELT__SUB__RCANCEL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V0m ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V2p @ V0m ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ V2p )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ELE__SUB__LCANCEL,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2E_2D @ V2x @ V1y ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V2x @ V0z ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0z @ V1y )
| ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2x @ V1y ) ) ) ).
thf(thm_2Earithmetic_2ELT__SUB__LCANCEL,axiom,
! [V0z: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2D @ V2x @ V1y ) @ ( mono_2Ec_2Earithmetic_2E_2D @ V2x @ V0z ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0z @ V1y )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V0z @ V2x ) ) ) ).
thf(thm_2Earithmetic_2EABS__DIFF__SUMS,axiom,
! [V0n1: mono_2Etyop_2Enum_2Enum,V1n2: mono_2Etyop_2Enum_2Enum,V2m1: mono_2Etyop_2Enum_2Enum,V3m2: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n1 @ V1n2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2m1 @ V3m2 ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V0n1 @ V2m1 ) @ ( mono_2Ec_2Earithmetic_2EABS__DIFF @ V1n2 @ V3m2 ) ) ) ).
thf(thm_2Earithmetic_2EFUNPOW__SUC,axiom,
! [A_27a: d,V0f_2E0: u,V1n: mono_2Etyop_2Enum_2Enum,V2x_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EFUNPOW__0,axiom,
! [A_27a: d,V0x_2E0: u,V1f_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(thm_2Earithmetic_2EFUNPOW__ADD,axiom,
! [A_27a: d,V0x_2E0: u,V1f_2E0: u,V2m: mono_2Etyop_2Enum_2Enum,V3n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V2m @ V3n ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2EFUNPOW__1,axiom,
! [A_27a: d,V0x_2E0: u,V1f_2E0: u] :
( ( s @ A_27a @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__0,axiom,
! [A_27a: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1x_2E0 )
= ( s @ A_27a @ V2y_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ENRC__1,axiom,
! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V0y_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 ) ) @ V2R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__ADD__I,axiom,
! [A_27a: d,V0R_2E0: u,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum,V3x_2E0: u,V4y_2E0: u,V5z_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ A_27a @ V4y_2E0 ) @ ( s @ A_27a @ V5z_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V5z_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__ADD__E,axiom,
! [A_27a: d,V0R_2E0: u,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum,V3x_2E0: u,V4z_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V1m @ V2n ) ) ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
=> ? [V5y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__ADD__EQN,axiom,
! [A_27a: d,V0z_2E0: u,V1x_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum,V4R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V3m @ V2n ) ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V0z_2E0 ) ) ) )
<=> ? [V5y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ A_27a @ V0z_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT,axiom,
! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V3R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V0y_2E0 ) ) ) )
<=> ? [V4z_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V3R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V4z_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 ) ) @ V3R_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) ).
thf(thm_2Earithmetic_2ENRC__RTC,axiom,
! [A_27a: d,V0R_2E0: u,V1n: mono_2Etyop_2Enum_2Enum,V2x_2E0: u,V3y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ERTC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ERTC__NRC,axiom,
! [A_27a: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ERTC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
=> ? [V3n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ERTC__eq__NRC,axiom,
! [A_27a: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ERTC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
<=> ? [V3n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ETC__eq__NRC,axiom,
! [A_27a: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2ETC_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
<=> ? [V3n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2ENRC_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V3n ) ) ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQUAL__DIFF,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n )
=> ? [V2k: mono_2Etyop_2Enum_2Enum] :
( V0m
= ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2k ) ) ) ).
thf(thm_2Earithmetic_2EMOD__2,conjecture,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0n ) @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
%------------------------------------------------------------------------------