ITP001 Axioms: ITP099^4.ax
%------------------------------------------------------------------------------
% File : ITP099^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : hreal.ax [Gau19]
% : HL4099^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 313 ( 116 unt; 147 typ; 0 def)
% Number of atoms : 322 ( 140 equ; 17 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1888 ( 17 ~; 7 |; 38 &;1764 @)
% ( 26 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg;1764 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 466 ( 466 >; 0 *; 0 +; 0 <<)
% Number of symbols : 144 ( 142 usr; 37 con; 0-4 aty)
% Number of variables : 379 ( 0 ^ 341 !; 38 ?; 379 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Ehrat_2Ehrat,type,
mono_2Etyop_2Ehrat_2Ehrat: $tType ).
thf(mono_2Etyop_2Ehreal_2Ehreal,type,
mono_2Etyop_2Ehreal_2Ehreal: $tType ).
thf(tyop_2Ehrat_2Ehrat,type,
tyop_2Ehrat_2Ehrat: d ).
thf(tyop_2Ehreal_2Ehreal,type,
tyop_2Ehreal_2Ehreal: d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > 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_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_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > 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_2Ehreal_2Ecut_2E0,type,
c_2Ehreal_2Ecut_2E0: u ).
thf(c_2Ehreal_2Ecut_2E1,type,
c_2Ehreal_2Ecut_2E1: du > u ).
thf(c_2Ehreal_2Ecut_2E2,type,
c_2Ehreal_2Ecut_2E2: du > du > u ).
thf(c_2Ehreal_2Ecut__of__hrat_2E0,type,
c_2Ehreal_2Ecut__of__hrat_2E0: u ).
thf(c_2Ehreal_2Ecut__of__hrat_2E1,type,
c_2Ehreal_2Ecut__of__hrat_2E1: du > u ).
thf(c_2Ehreal_2Ecut__of__hrat_2E2,type,
c_2Ehreal_2Ecut__of__hrat_2E2: du > du > u ).
thf(c_2Ehrat_2Ehrat__1_2E0,type,
c_2Ehrat_2Ehrat__1_2E0: u ).
thf(c_2Ehrat_2Ehrat__add_2E0,type,
c_2Ehrat_2Ehrat__add_2E0: u ).
thf(c_2Ehrat_2Ehrat__add_2E2,type,
c_2Ehrat_2Ehrat__add_2E2: du > du > u ).
thf(c_2Ehrat_2Ehrat__inv_2E0,type,
c_2Ehrat_2Ehrat__inv_2E0: u ).
thf(c_2Ehrat_2Ehrat__inv_2E1,type,
c_2Ehrat_2Ehrat__inv_2E1: du > u ).
thf(c_2Ehreal_2Ehrat__lt_2E0,type,
c_2Ehreal_2Ehrat__lt_2E0: u ).
thf(c_2Ehreal_2Ehrat__lt_2E2,type,
c_2Ehreal_2Ehrat__lt_2E2: du > du > u ).
thf(c_2Ehrat_2Ehrat__mul_2E0,type,
c_2Ehrat_2Ehrat__mul_2E0: u ).
thf(c_2Ehrat_2Ehrat__mul_2E2,type,
c_2Ehrat_2Ehrat__mul_2E2: du > du > u ).
thf(c_2Ehreal_2Ehreal_2E0,type,
c_2Ehreal_2Ehreal_2E0: u ).
thf(c_2Ehreal_2Ehreal_2E1,type,
c_2Ehreal_2Ehreal_2E1: du > u ).
thf(c_2Ehreal_2Ehreal__1_2E0,type,
c_2Ehreal_2Ehreal__1_2E0: u ).
thf(c_2Ehreal_2Ehreal__add_2E0,type,
c_2Ehreal_2Ehreal__add_2E0: u ).
thf(c_2Ehreal_2Ehreal__add_2E2,type,
c_2Ehreal_2Ehreal__add_2E2: du > du > u ).
thf(c_2Ehreal_2Ehreal__inv_2E0,type,
c_2Ehreal_2Ehreal__inv_2E0: u ).
thf(c_2Ehreal_2Ehreal__inv_2E1,type,
c_2Ehreal_2Ehreal__inv_2E1: du > u ).
thf(c_2Ehreal_2Ehreal__lt_2E0,type,
c_2Ehreal_2Ehreal__lt_2E0: u ).
thf(c_2Ehreal_2Ehreal__lt_2E2,type,
c_2Ehreal_2Ehreal__lt_2E2: du > du > u ).
thf(c_2Ehreal_2Ehreal__mul_2E0,type,
c_2Ehreal_2Ehreal__mul_2E0: u ).
thf(c_2Ehreal_2Ehreal__mul_2E2,type,
c_2Ehreal_2Ehreal__mul_2E2: du > du > u ).
thf(c_2Ehreal_2Ehreal__sub_2E0,type,
c_2Ehreal_2Ehreal__sub_2E0: u ).
thf(c_2Ehreal_2Ehreal__sub_2E2,type,
c_2Ehreal_2Ehreal__sub_2E2: du > du > u ).
thf(c_2Ehreal_2Ehreal__sup_2E0,type,
c_2Ehreal_2Ehreal__sup_2E0: u ).
thf(c_2Ehreal_2Ehreal__sup_2E1,type,
c_2Ehreal_2Ehreal__sup_2E1: du > u ).
thf(c_2Ehreal_2Eisacut_2E0,type,
c_2Ehreal_2Eisacut_2E0: u ).
thf(c_2Ehreal_2Eisacut_2E1,type,
c_2Ehreal_2Eisacut_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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal ) > ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal: ( ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal ) > ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ) > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Ehrat_2Ehrat,type,
mono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Ehrat_2Ehrat: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ) > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ) > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Ehreal_2Ehreal,type,
mono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Ehreal_2Ehreal: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ) > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,type,
mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ehreal_2Ecut,type,
mono_2Ec_2Ehreal_2Ecut: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Ec_2Ehreal_2Ecut__of__hrat,type,
mono_2Ec_2Ehreal_2Ecut__of__hrat: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Ec_2Ehrat_2Ehrat__1,type,
mono_2Ec_2Ehrat_2Ehrat__1: mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Ec_2Ehrat_2Ehrat__add,type,
mono_2Ec_2Ehrat_2Ehrat__add: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Ec_2Ehrat_2Ehrat__inv,type,
mono_2Ec_2Ehrat_2Ehrat__inv: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Ec_2Ehreal_2Ehrat__lt,type,
mono_2Ec_2Ehreal_2Ehrat__lt: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(mono_2Ec_2Ehrat_2Ehrat__mul,type,
mono_2Ec_2Ehrat_2Ehrat__mul: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(mono_2Ec_2Ehreal_2Ehreal,type,
mono_2Ec_2Ehreal_2Ehreal: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__1,type,
mono_2Ec_2Ehreal_2Ehreal__1: mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__add,type,
mono_2Ec_2Ehreal_2Ehreal__add: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__inv,type,
mono_2Ec_2Ehreal_2Ehreal__inv: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__lt,type,
mono_2Ec_2Ehreal_2Ehreal__lt: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o ).
thf(mono_2Ec_2Ehreal_2Ehreal__mul,type,
mono_2Ec_2Ehreal_2Ehreal__mul: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__sub,type,
mono_2Ec_2Ehreal_2Ehreal__sub: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Ehreal__sup,type,
mono_2Ec_2Ehreal_2Ehreal__sup: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(mono_2Ec_2Ehreal_2Eisacut,type,
mono_2Ec_2Ehreal_2Eisacut: ( mono_2Etyop_2Ehrat_2Ehrat > $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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29: ( ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29: ( ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29: ( mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ) > u ).
thf(i_mono_2Etyop_2Ehrat_2Ehrat,type,
i_mono_2Etyop_2Ehrat_2Ehrat: mono_2Etyop_2Ehrat_2Ehrat > u ).
thf(i_mono_2Etyop_2Ehreal_2Ehreal,type,
i_mono_2Etyop_2Ehreal_2Ehreal: mono_2Etyop_2Ehreal_2Ehreal > 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29: du > ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29: du > ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29: du > ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29: du > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29: du > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Ehreal_2Ehreal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29: du > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29: du > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal ).
thf(j_mono_2Etyop_2Ehrat_2Ehrat,type,
j_mono_2Etyop_2Ehrat_2Ehrat: du > mono_2Etyop_2Ehrat_2Ehrat ).
thf(j_mono_2Etyop_2Ehreal_2Ehreal,type,
j_mono_2Etyop_2Ehreal_2Ehreal: du > mono_2Etyop_2Ehreal_2Ehreal ).
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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Ehrat_2Ehrat,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ ( j_mono_2Etyop_2Ehrat_2Ehrat @ ( s @ tyop_2Ehrat_2Ehrat @ V0_2E0 ) ) ) )
= ( s @ tyop_2Ehrat_2Ehrat @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ ( j_mono_2Etyop_2Ehreal_2Ehreal @ ( s @ tyop_2Ehreal_2Ehreal @ V0_2E0 ) ) ) )
= ( s @ tyop_2Ehreal_2Ehreal @ 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Ehrat_2Ehrat,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat] :
( ( j_mono_2Etyop_2Ehrat_2Ehrat @ ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal] :
( ( j_mono_2Etyop_2Ehreal_2Ehreal @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: mono_2Etyop_2Ehrat_2Ehrat > $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_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Ehreal_2Ehreal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Ehreal_2Ehreal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $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_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29_29 @ V0 ) ) @ ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Ehrat_2Ehrat,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Ehrat_2Ehrat @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Ehrat_2Ehrat ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29 @ V0 ) ) @ ( s @ tyop_2Ehrat_2Ehrat @ ( i_mono_2Etyop_2Ehrat_2Ehrat @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Ehreal_2Ehreal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ tyop_2Ehreal_2Ehreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29 @ V0 ) ) @ ( s @ tyop_2Ehreal_2Ehreal @ ( i_mono_2Etyop_2Ehreal_2Ehreal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Ehreal_2Ehreal @ ( tyop_2Emin_2Efun @ tyop_2Ehrat_2Ehrat @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
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_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o ) > ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: ( mono_2Etyop_2Ehrat_2Ehrat > $o ) > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o ) > $o,V1: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Ehrat_2Ehrat_29,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehrat_2Ehrat_20mono_2Etyop_2Ehrat_2Ehrat,axiom,
! [V0: mono_2Etyop_2Ehrat_2Ehrat > mono_2Etyop_2Ehrat_2Ehrat,V1: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ehreal_2Ehreal_20mono_2Etyop_2Ehreal_2Ehreal,axiom,
! [V0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal,V1: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Ehreal_2Ehrat__lt,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
<=> ? [V2d: mono_2Etyop_2Ehrat_2Ehrat] :
( V1y
= ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V2d ) ) ) ).
thf(thm_2Ehreal_2Eisacut,axiom,
! [V0C: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( mono_2Ec_2Ehreal_2Eisacut @ V0C )
<=> ( ? [V1x: mono_2Etyop_2Ehrat_2Ehrat] : ( V0C @ V1x )
& ? [V2x: mono_2Etyop_2Ehrat_2Ehrat] : ( (~) @ ( V0C @ V2x ) )
& ! [V3x: mono_2Etyop_2Ehrat_2Ehrat,V4y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( V0C @ V3x )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V4y @ V3x ) )
=> ( V0C @ V4y ) )
& ! [V5x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0C @ V5x )
=> ? [V6y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0C @ V6y )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V5x @ V6y ) ) ) ) ) ).
thf(thm_2Ehreal_2Ecut__of__hrat,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1x_27: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut__of__hrat @ V0x @ V1x_27 )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1x_27 @ V0x ) ) ).
thf(thm_2Ehreal_2Ehreal__TY__DEF,axiom,
? [V0rep: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] : ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ehrat_2Ehrat_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Ehreal_2Ehreal @ mono_2Ec_2Ehreal_2Eisacut @ V0rep ) ).
thf(thm_2Ehreal_2Ehreal__tybij,axiom,
( ! [V0a: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal @ ( mono_2Ec_2Ehreal_2Ecut @ V0a ) )
= V0a )
& ! [V1r: mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ( mono_2Ec_2Ehreal_2Eisacut @ V1r )
<=> ( ( mono_2Ec_2Ehreal_2Ecut @ ( mono_2Ec_2Ehreal_2Ehreal @ V1r ) )
= V1r ) ) ) ).
thf(thm_2Ehreal_2Ehreal__1,axiom,
( mono_2Ec_2Ehreal_2Ehreal__1
= ( mono_2Ec_2Ehreal_2Ehreal @ ( mono_2Ec_2Ehreal_2Ecut__of__hrat @ mono_2Ec_2Ehrat_2Ehrat__1 ) ) ) ).
thf(thm_2Ehreal_2Ehreal__add,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat,V4y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V2w
= ( mono_2Ec_2Ehrat_2Ehrat__add @ V3x @ V4y ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V4y ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V1Y )
= ( mono_2Ec_2Ehreal_2Ehreal @ ( F0 @ V0X @ V1Y ) ) ) ) ).
thf(thm_2Ehreal_2Ehreal__mul,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat,V4y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V2w
= ( mono_2Ec_2Ehrat_2Ehrat__mul @ V3x @ V4y ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V4y ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ V1Y )
= ( mono_2Ec_2Ehreal_2Ehreal @ ( F0 @ V0X @ V1Y ) ) ) ) ).
thf(thm_2Ehreal_2Ehreal__inv,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1w )
<=> ? [V2d: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2d @ mono_2Ec_2Ehrat_2Ehrat__1 )
& ! [V3x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V1w @ V3x ) @ V2d ) ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__inv @ V0X )
= ( mono_2Ec_2Ehreal_2Ehreal @ ( F0 @ V0X ) ) ) ) ).
thf(thm_2Ehreal_2Ehreal__sup,axiom,
! [F0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0P: mono_2Etyop_2Ehreal_2Ehreal > $o,V1w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0P @ V1w )
<=> ? [V2X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0P @ V2X )
& ( mono_2Ec_2Ehreal_2Ecut @ V2X @ V1w ) ) )
=> ! [V0P: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( mono_2Ec_2Ehreal_2Ehreal__sup @ V0P )
= ( mono_2Ec_2Ehreal_2Ehreal @ ( F0 @ V0P ) ) ) ) ).
thf(thm_2Ehreal_2Ehreal__lt,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
<=> ( ( (~) @ ( V0X = V1Y ) )
& ! [V2x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2x )
=> ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V2x ) ) ) ) ).
thf(thm_2Ehreal_2Ehreal__sub,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V1X: mono_2Etyop_2Ehreal_2Ehreal,V0Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V1X @ V0Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V1X @ V3x ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V0Y @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V3x @ V2w ) ) ) )
=> ! [V0Y: mono_2Etyop_2Ehreal_2Ehreal,V1X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__sub @ V0Y @ V1X )
= ( mono_2Ec_2Ehreal_2Ehreal @ ( F0 @ V1X @ V0Y ) ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__REFL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat] : ( (~) @ ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V0x ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__TRANS,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V2z ) )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V2z ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__ANTISYM,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( (~)
@ ( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__TOTAL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V0x = V1y )
| ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
| ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V0x ) ) ).
thf(thm_2Ehreal_2EHRAT__MUL__RID,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ mono_2Ec_2Ehrat_2Ehrat__1 )
= V0x ) ).
thf(thm_2Ehreal_2EHRAT__MUL__RINV,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V0x ) )
= mono_2Ec_2Ehrat_2Ehrat__1 ) ).
thf(thm_2Ehreal_2EHRAT__RDISTRIB,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehrat_2Ehrat__mul @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Ehrat_2Ehrat__add @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V2z ) @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V1y @ V2z ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__ADDL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__ADDR,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__GT,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
=> ( (~) @ ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__NE,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
=> ( (~) @ ( V0x = V1y ) ) ) ).
thf(thm_2Ehreal_2EHRAT__EQ__LADD,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V1y )
= ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V2z ) )
<=> ( V1y = V2z ) ) ).
thf(thm_2Ehreal_2EHRAT__EQ__LMUL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V1y )
= ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V2z ) )
<=> ( V1y = V2z ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__ADD2,axiom,
! [V0u: mono_2Etyop_2Ehrat_2Ehrat,V1v: mono_2Etyop_2Ehrat_2Ehrat,V2x: mono_2Etyop_2Ehrat_2Ehrat,V3y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0u @ V2x )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1v @ V3y ) )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V0u @ V1v ) @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V2x @ V3y ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__LADD,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V2z @ V0x ) @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V2z @ V1y ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__RADD,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V0x @ V2z ) @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V1y @ V2z ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__MUL2,axiom,
! [V0u: mono_2Etyop_2Ehrat_2Ehrat,V1v: mono_2Etyop_2Ehrat_2Ehrat,V2x: mono_2Etyop_2Ehrat_2Ehrat,V3y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0u @ V2x )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1v @ V3y ) )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0u @ V1v ) @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V2x @ V3y ) ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__LMUL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V2z @ V0x ) @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V2z @ V1y ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__RMUL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat,V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V2z ) @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V1y @ V2z ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__LMUL1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V1y ) @ V1y )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ mono_2Ec_2Ehrat_2Ehrat__1 ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__RMUL1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V1y ) @ V0x )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ mono_2Ec_2Ehrat_2Ehrat__1 ) ) ).
thf(thm_2Ehreal_2EHRAT__GT__LMUL1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V1y ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ mono_2Ec_2Ehrat_2Ehrat__1 @ V0x ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__L1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V0x ) @ V1y ) @ mono_2Ec_2Ehrat_2Ehrat__1 )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V0x ) ) ).
thf(thm_2Ehreal_2EHRAT__LT__R1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V1y ) ) @ mono_2Ec_2Ehrat_2Ehrat__1 )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__GT__L1,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ mono_2Ec_2Ehrat_2Ehrat__1 @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V0x ) @ V1y ) )
= ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__INV__MUL,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehrat_2Ehrat__inv @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V0x @ V1y ) )
= ( mono_2Ec_2Ehrat_2Ehrat__mul @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V0x ) @ ( mono_2Ec_2Ehrat_2Ehrat__inv @ V1y ) ) ) ).
thf(thm_2Ehreal_2EHRAT__UP,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat] :
? [V1y: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y ) ).
thf(thm_2Ehreal_2EHRAT__DOWN,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat] :
? [V1y: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1y @ V0x ) ).
thf(thm_2Ehreal_2EHRAT__DOWN2,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
? [V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2z @ V0x )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2z @ V1y ) ) ).
thf(thm_2Ehreal_2EHRAT__MEAN,axiom,
! [V0x: mono_2Etyop_2Ehrat_2Ehrat,V1y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V1y )
=> ? [V2z: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V0x @ V2z )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2z @ V1y ) ) ) ).
thf(thm_2Ehreal_2EISACUT__HRAT,axiom,
! [V0h: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Eisacut @ ( mono_2Ec_2Ehreal_2Ecut__of__hrat @ V0h ) ) ).
thf(thm_2Ehreal_2EEQUAL__CUTS,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( ( mono_2Ec_2Ehreal_2Ecut @ V0X )
= ( mono_2Ec_2Ehreal_2Ecut @ V1Y ) )
=> ( V0X = V1Y ) ) ).
thf(thm_2Ehreal_2ECUT__ISACUT,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal] : ( mono_2Ec_2Ehreal_2Eisacut @ ( mono_2Ec_2Ehreal_2Ecut @ V0X ) ) ).
thf(thm_2Ehreal_2ECUT__NONEMPTY,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal] :
? [V1x: mono_2Etyop_2Ehrat_2Ehrat] : ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x ) ).
thf(thm_2Ehreal_2ECUT__BOUNDED,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal] :
? [V1x: mono_2Etyop_2Ehrat_2Ehrat] : ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x ) ) ).
thf(thm_2Ehreal_2ECUT__DOWN,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1x: mono_2Etyop_2Ehrat_2Ehrat,V2y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2y @ V1x ) )
=> ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2y ) ) ).
thf(thm_2Ehreal_2ECUT__UP,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x )
=> ? [V2y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2y )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1x @ V2y ) ) ) ).
thf(thm_2Ehreal_2ECUT__UBOUND,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1x: mono_2Etyop_2Ehrat_2Ehrat,V2y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x ) )
& ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1x @ V2y ) )
=> ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2y ) ) ) ).
thf(thm_2Ehreal_2ECUT__STRADDLE,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1x: mono_2Etyop_2Ehrat_2Ehrat,V2y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V1x )
& ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2y ) ) )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ V1x @ V2y ) ) ).
thf(thm_2Ehreal_2ECUT__NEARTOP__ADD,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1e: mono_2Etyop_2Ehrat_2Ehrat] :
? [V2x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2x )
& ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V2x @ V1e ) ) ) ) ).
thf(thm_2Ehreal_2ECUT__NEARTOP__MUL,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1u: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ mono_2Ec_2Ehrat_2Ehrat__1 @ V1u )
=> ? [V2x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2x )
& ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V1u @ V2x ) ) ) ) ) ).
thf(thm_2Ehreal_2EHREAL__INV__ISACUT,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1w )
<=> ? [V2d: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ehrat__lt @ V2d @ mono_2Ec_2Ehrat_2Ehrat__1 )
& ! [V3x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
=> ( mono_2Ec_2Ehreal_2Ehrat__lt @ ( mono_2Ec_2Ehrat_2Ehrat__mul @ V1w @ V3x ) @ V2d ) ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal] : ( mono_2Ec_2Ehreal_2Eisacut @ ( F0 @ V0X ) ) ) ).
thf(thm_2Ehreal_2EHREAL__ADD__ISACUT,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat,V4y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V2w
= ( mono_2Ec_2Ehrat_2Ehrat__add @ V3x @ V4y ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V4y ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] : ( mono_2Ec_2Ehreal_2Eisacut @ ( F0 @ V0X @ V1Y ) ) ) ).
thf(thm_2Ehreal_2EHREAL__MUL__ISACUT,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat,V4y: mono_2Etyop_2Ehrat_2Ehrat] :
( ( V2w
= ( mono_2Ec_2Ehrat_2Ehrat__mul @ V3x @ V4y ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V4y ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] : ( mono_2Ec_2Ehreal_2Eisacut @ ( F0 @ V0X @ V1Y ) ) ) ).
thf(thm_2Ehreal_2EHREAL__ADD__SYM,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V1Y )
= ( mono_2Ec_2Ehreal_2Ehreal__add @ V1Y @ V0X ) ) ).
thf(thm_2Ehreal_2EHREAL__MUL__SYM,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ V1Y )
= ( mono_2Ec_2Ehreal_2Ehreal__mul @ V1Y @ V0X ) ) ).
thf(thm_2Ehreal_2EHREAL__ADD__ASSOC,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2Z: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ ( mono_2Ec_2Ehreal_2Ehreal__add @ V1Y @ V2Z ) )
= ( mono_2Ec_2Ehreal_2Ehreal__add @ ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V1Y ) @ V2Z ) ) ).
thf(thm_2Ehreal_2EHREAL__MUL__ASSOC,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2Z: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ ( mono_2Ec_2Ehreal_2Ehreal__mul @ V1Y @ V2Z ) )
= ( mono_2Ec_2Ehreal_2Ehreal__mul @ ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ V1Y ) @ V2Z ) ) ).
thf(thm_2Ehreal_2EHREAL__LDISTRIB,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2Z: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ ( mono_2Ec_2Ehreal_2Ehreal__add @ V1Y @ V2Z ) )
= ( mono_2Ec_2Ehreal_2Ehreal__add @ ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ V1Y ) @ ( mono_2Ec_2Ehreal_2Ehreal__mul @ V0X @ V2Z ) ) ) ).
thf(thm_2Ehreal_2EHREAL__MUL__LID,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ mono_2Ec_2Ehreal_2Ehreal__1 @ V0X )
= V0X ) ).
thf(thm_2Ehreal_2EHREAL__MUL__LINV,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__mul @ ( mono_2Ec_2Ehreal_2Ehreal__inv @ V0X ) @ V0X )
= mono_2Ec_2Ehreal_2Ehreal__1 ) ).
thf(thm_2Ehreal_2EHREAL__NOZERO,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( (~)
@ ( ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V1Y )
= V0X ) ) ).
thf(thm_2Ehreal_2EHREAL__LT__LEMMA,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
=> ? [V2x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V2x ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ V2x ) ) ) ).
thf(thm_2Ehreal_2EHREAL__SUB__ISACUT,axiom,
! [F0: mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehreal_2Ehreal > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal,V2w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0X @ V1Y @ V2w )
<=> ? [V3x: mono_2Etyop_2Ehrat_2Ehrat] :
( ( (~) @ ( mono_2Ec_2Ehreal_2Ecut @ V0X @ V3x ) )
& ( mono_2Ec_2Ehreal_2Ecut @ V1Y @ ( mono_2Ec_2Ehrat_2Ehrat__add @ V3x @ V2w ) ) ) )
=> ! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
=> ( mono_2Ec_2Ehreal_2Eisacut @ ( F0 @ V0X @ V1Y ) ) ) ) ).
thf(thm_2Ehreal_2EHREAL__SUB__ADD,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
=> ( ( mono_2Ec_2Ehreal_2Ehreal__add @ ( mono_2Ec_2Ehreal_2Ehreal__sub @ V1Y @ V0X ) @ V0X )
= V1Y ) ) ).
thf(thm_2Ehreal_2EHREAL__LT__TOTAL,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0X = V1Y )
| ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
| ( mono_2Ec_2Ehreal_2Ehreal__lt @ V1Y @ V0X ) ) ).
thf(thm_2Ehreal_2EHREAL__LT,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( mono_2Ec_2Ehreal_2Ehreal__lt @ V0X @ V1Y )
<=> ? [V2D: mono_2Etyop_2Ehreal_2Ehreal] :
( V1Y
= ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V2D ) ) ) ).
thf(thm_2Ehreal_2EHREAL__ADD__TOTAL,axiom,
! [V0X: mono_2Etyop_2Ehreal_2Ehreal,V1Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0X = V1Y )
| ? [V2D: mono_2Etyop_2Ehreal_2Ehreal] :
( V1Y
= ( mono_2Ec_2Ehreal_2Ehreal__add @ V0X @ V2D ) )
| ? [V3D: mono_2Etyop_2Ehreal_2Ehreal] :
( V0X
= ( mono_2Ec_2Ehreal_2Ehreal__add @ V1Y @ V3D ) ) ) ).
thf(thm_2Ehreal_2EHREAL__SUP__ISACUT,axiom,
! [F0: ( mono_2Etyop_2Ehreal_2Ehreal > $o ) > mono_2Etyop_2Ehrat_2Ehrat > $o] :
( ! [V0P: mono_2Etyop_2Ehreal_2Ehreal > $o,V4w: mono_2Etyop_2Ehrat_2Ehrat] :
( ( F0 @ V0P @ V4w )
<=> ? [V5X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0P @ V5X )
& ( mono_2Ec_2Ehreal_2Ecut @ V5X @ V4w ) ) )
=> ! [V0P: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( ? [V1X: mono_2Etyop_2Ehreal_2Ehreal] : ( V0P @ V1X )
& ? [V2Y: mono_2Etyop_2Ehreal_2Ehreal] :
! [V3X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0P @ V3X )
=> ( mono_2Ec_2Ehreal_2Ehreal__lt @ V3X @ V2Y ) ) )
=> ( mono_2Ec_2Ehreal_2Eisacut @ ( F0 @ V0P ) ) ) ) ).
thf(thm_2Ehreal_2EHREAL__SUP,axiom,
! [V0P: mono_2Etyop_2Ehreal_2Ehreal > $o] :
( ( ? [V1X: mono_2Etyop_2Ehreal_2Ehreal] : ( V0P @ V1X )
& ? [V2Y: mono_2Etyop_2Ehreal_2Ehreal] :
! [V3X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0P @ V3X )
=> ( mono_2Ec_2Ehreal_2Ehreal__lt @ V3X @ V2Y ) ) )
=> ! [V4Y: mono_2Etyop_2Ehreal_2Ehreal] :
( ? [V5X: mono_2Etyop_2Ehreal_2Ehreal] :
( ( V0P @ V5X )
& ( mono_2Ec_2Ehreal_2Ehreal__lt @ V4Y @ V5X ) )
<=> ( mono_2Ec_2Ehreal_2Ehreal__lt @ V4Y @ ( mono_2Ec_2Ehreal_2Ehreal__sup @ V0P ) ) ) ) ).
%------------------------------------------------------------------------------