ITP001 Axioms: ITP058^4.ax


%------------------------------------------------------------------------------
% File     : ITP058^4 : TPTP v9.0.0. 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    : wot.ax [Gau19]
%          : HL4058^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  155 (  49 unt;  91 typ;   0 def)
%            Number of atoms       :  136 (  53 equ;   2 cnn)
%            Maximal formula atoms :    7 (   0 avg)
%            Number of connectives : 1876 (   2   ~;   2   |;   8   &;1841   @)
%                                         (  15 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg;1841 nst)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   85 (  85   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   90 (  88 usr;  42 con; 0-3 aty)
%            Number of variables   :  154 (   0   ^ 151   !;   3   ?; 154   :)
% 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(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: 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_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

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

thf(c_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_2Epred__set_2EBIGUNION_2E0,type,
    c_2Epred__set_2EBIGUNION_2E0: u ).

thf(c_2Epred__set_2EBIGUNION_2E1,type,
    c_2Epred__set_2EBIGUNION_2E1: du > u ).

thf(c_2Epred__set_2ECHOICE_2E0,type,
    c_2Epred__set_2ECHOICE_2E0: u ).

thf(c_2Epred__set_2ECHOICE_2E1,type,
    c_2Epred__set_2ECHOICE_2E1: du > u ).

thf(c_2Epred__set_2ECOMPL_2E0,type,
    c_2Epred__set_2ECOMPL_2E0: u ).

thf(c_2Epred__set_2ECOMPL_2E1,type,
    c_2Epred__set_2ECOMPL_2E1: du > u ).

thf(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

thf(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: du > du > u ).

thf(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

thf(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: du > du > u ).

thf(c_2Erelation_2ESTRORD_2E0,type,
    c_2Erelation_2ESTRORD_2E0: u ).

thf(c_2Erelation_2ESTRORD_2E1,type,
    c_2Erelation_2ESTRORD_2E1: du > u ).

thf(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

thf(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: du > du > u ).

thf(c_2Erelation_2EStrongLinearOrder_2E0,type,
    c_2Erelation_2EStrongLinearOrder_2E0: u ).

thf(c_2Erelation_2EStrongLinearOrder_2E1,type,
    c_2Erelation_2EStrongLinearOrder_2E1: du > u ).

thf(c_2Ewot_2EStrongWellOrder_2E0,type,
    c_2Ewot_2EStrongWellOrder_2E0: u ).

thf(c_2Ewot_2EStrongWellOrder_2E1,type,
    c_2Ewot_2EStrongWellOrder_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

thf(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: du > u ).

thf(c_2Erelation_2EWeakOrder_2E0,type,
    c_2Erelation_2EWeakOrder_2E0: u ).

thf(c_2Erelation_2EWeakOrder_2E1,type,
    c_2Erelation_2EWeakOrder_2E1: du > u ).

thf(c_2Ewot_2EWeakWellOrder_2E0,type,
    c_2Ewot_2EWeakWellOrder_2E0: u ).

thf(c_2Ewot_2EWeakWellOrder_2E1,type,
    c_2Ewot_2EWeakWellOrder_2E1: 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_2Ewot_2Echain_2E0,type,
    c_2Ewot_2Echain_2E0: u ).

thf(c_2Ewot_2Echain_2E1,type,
    c_2Ewot_2Echain_2E1: du > u ).

thf(c_2Ewot_2Ecpl_2E0,type,
    c_2Ewot_2Ecpl_2E0: u ).

thf(c_2Ewot_2Ecpl_2E2,type,
    c_2Ewot_2Ecpl_2E2: du > du > u ).

thf(c_2Ewot_2Emex_2E0,type,
    c_2Ewot_2Emex_2E0: u ).

thf(c_2Ewot_2Emex_2E1,type,
    c_2Ewot_2Emex_2E1: du > u ).

thf(c_2Ewot_2Emex__less_2E0,type,
    c_2Ewot_2Emex__less_2E0: u ).

thf(c_2Ewot_2Emex__less__eq_2E0,type,
    c_2Ewot_2Emex__less__eq_2E0: u ).

thf(c_2Ewot_2Emex__less__eq_2E2,type,
    c_2Ewot_2Emex__less__eq_2E2: du > du > u ).

thf(c_2Ewot_2Epreds_2E0,type,
    c_2Ewot_2Epreds_2E0: u ).

thf(c_2Ewot_2Epreds_2E1,type,
    c_2Ewot_2Epreds_2E1: du > u ).

thf(c_2Ewot_2Epreds__image_2E0,type,
    c_2Ewot_2Epreds__image_2E0: u ).

thf(c_2Ewot_2Epreds__image_2E1,type,
    c_2Ewot_2Epreds__image_2E1: du > u ).

thf(c_2Ewot_2Esetsuc_2E0,type,
    c_2Ewot_2Esetsuc_2E0: u ).

thf(c_2Ewot_2Esetsuc_2E1,type,
    c_2Ewot_2Esetsuc_2E1: du > u ).

thf(c_2Ewot_2Esuccl_2E0,type,
    c_2Ewot_2Esuccl_2E0: u ).

thf(c_2Ewot_2Esuccl_2E1,type,
    c_2Ewot_2Esuccl_2E1: du > u ).

thf(c_2Ewot_2Etower_2E0,type,
    c_2Ewot_2Etower_2E0: u ).

thf(c_2Ewot_2Etower_2E1,type,
    c_2Ewot_2Etower_2E1: du > u ).

thf(c_2Ewot_2Euncl_2E0,type,
    c_2Ewot_2Euncl_2E0: u ).

thf(c_2Ewot_2Euncl_2E1,type,
    c_2Ewot_2Euncl_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_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_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $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(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(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(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(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_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27x: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

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(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGUNION_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EBIGUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ A_27x @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ A_27x @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ A_27x ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ECOMPL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27x @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27x @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27x @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) @ ( s @ A_27x @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ESTRORD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) ) @ c_2Erelation_2ESTRORD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EStrongLinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EStrongLinearOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2EStrongWellOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2EStrongWellOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2EStrongWellOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWeakOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWeakOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2EWeakWellOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2EWeakWellOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2EWeakWellOrder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Echain_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Echain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2Echain_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ewot_2Ecpl_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Ecpl_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Ecpl_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Emex_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ A_27x @ ( c_2Ewot_2Emex_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ A_27x @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ A_27x ) @ c_2Ewot_2Emex_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ewot_2Emex__less__eq_2E2_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Emex__less__eq_2E2 @ ( s @ A_27x @ X0_2E0 ) @ ( s @ A_27x @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Emex__less__eq_2E0 ) @ ( s @ A_27x @ X0_2E0 ) ) ) @ ( s @ A_27x @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Epreds_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds_2E1 @ ( s @ A_27x @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Epreds_2E0 ) @ ( s @ A_27x @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Epreds__image_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds__image_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Epreds__image_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Esetsuc_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Esetsuc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Esetsuc_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Esuccl_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Esuccl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2Esuccl_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Etower_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Etower_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2Etower_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewot_2Euncl_2E1_2Emono_2EA_27x,axiom,
    ! [A_27x: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Euncl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ewot_2Euncl_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ 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(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(thm_2Ewot_2Ecpl__def,axiom,
    ! [A_27x: d,V0A_2E0: u,V1B_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Ecpl_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1B_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1B_2E0 ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Echain__def,axiom,
    ! [A_27x: d,V0C_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Echain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0C_2E0 ) ) ) )
    <=> ! [V1a_2E0: u,V2b_2E0: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0C_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V2b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0C_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Ecpl_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V2b_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Emex__def,axiom,
    ! [A_27x: d,V0s_2E0: u] :
      ( ( s @ A_27x @ ( c_2Ewot_2Emex_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
      = ( s @ A_27x @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Esetsuc__def,axiom,
    ! [A_27x: d,V0s_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Esetsuc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27x @ ( c_2Ewot_2Emex_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ).

thf(thm_2Ewot_2Esuccl__def,axiom,
    ! [A_27x: d,V0c_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Esuccl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) )
    <=> ! [V1s_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Esetsuc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Euncl__def,axiom,
    ! [A_27x: d,V0c_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Euncl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) )
    <=> ! [V1w_2E0: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V1w_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Echain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V1w_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGUNION_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V1w_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0c_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Etower__def,axiom,
    ! [A_27x: d,V0A_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Etower_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Esuccl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Euncl_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2Emex__less__eq__def,axiom,
    ! [A_27x: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2Emex__less__eq_2E2 @ ( s @ A_27x @ V0a_2E0 ) @ ( s @ A_27x @ V1b_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds_2E1 @ ( s @ A_27x @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds_2E1 @ ( s @ A_27x @ V1b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ewot_2Emex__less__def,axiom,
    ! [A_27x: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Emex__less_2E0 )
      = ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ESTRORD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) ) @ c_2Ewot_2Emex__less__eq_2E0 ) ) ) ) ).

thf(thm_2Ewot_2EWeakWellOrder__def,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2EWeakWellOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWeakOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
        & ! [V1B_2E0: u] :
            ( ( (~)
              @ ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1B_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
           => ? [V2m_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1B_2E0 ) ) ) )
                & ! [V3b_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1B_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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3b_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ewot_2Epreds__image__def,axiom,
    ! [A_27x: d,F0_2E0: u] :
      ( ! [V0X_2E0: u,V1x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0X_2E0 ) ) ) @ ( s @ A_27x @ V1x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds_2E1 @ ( s @ A_27x @ V1x_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27x @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0X_2E0 ) ) ) ) ) )
     => ! [V0X_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewot_2Epreds__image_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0X_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27x @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27x @ tyop_2Emin_2Ebool ) @ V0X_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ewot_2EStrongWellOrder__def,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewot_2EStrongWellOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EStrongLinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) ) ) ).

thf(thm_2Ewot_2EStrongWellOrderExists,axiom,
    ! [A_27a: d] :
    ? [V0R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EStrongLinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) ) ).

%------------------------------------------------------------------------------