ITP001 Axioms: ITP105^4.ax


%------------------------------------------------------------------------------
% File     : ITP105^4 : 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    : veblen.ax [Gau19]
%          : HL4105^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  180 (  60 unt; 101 typ;   0 def)
%            Number of atoms       :  171 (  67 equ;   6 cnn)
%            Maximal formula atoms :    9 (   0 avg)
%            Number of connectives : 2868 (   6   ~;   1   |;  12   &;2814   @)
%                                         (  13 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg;2814 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  127 ( 127   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   99 (  97 usr;  40 con; 0-3 aty)
%            Number of variables   :  213 (   0   ^ 211   !;   2   ?; 213   :)
% 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_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

thf(tyop_2Eordinal_2Eordinal,type,
    tyop_2Eordinal_2Eordinal: d > d ).

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

thf(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: 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_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

thf(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

thf(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

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

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

thf(c_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_2EBIGINTER_2E0,type,
    c_2Epred__set_2EBIGINTER_2E0: u ).

thf(c_2Epred__set_2EBIGINTER_2E1,type,
    c_2Epred__set_2EBIGINTER_2E1: du > 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_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

thf(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: du > 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_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_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

thf(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

thf(c_2Ecardinal_2Ecardleq_2E0,type,
    c_2Ecardinal_2Ecardleq_2E0: u ).

thf(c_2Ecardinal_2Ecardleq_2E2,type,
    c_2Ecardinal_2Ecardleq_2E2: du > du > u ).

thf(c_2Eveblen_2Eclosed_2E0,type,
    c_2Eveblen_2Eclosed_2E0: u ).

thf(c_2Eveblen_2Eclosed_2E1,type,
    c_2Eveblen_2Eclosed_2E1: du > u ).

thf(c_2Eveblen_2Eclub_2E0,type,
    c_2Eveblen_2Eclub_2E0: u ).

thf(c_2Eveblen_2Eclub_2E1,type,
    c_2Eveblen_2Eclub_2E1: du > u ).

thf(c_2Eveblen_2Econtinuous_2E0,type,
    c_2Eveblen_2Econtinuous_2E0: u ).

thf(c_2Eveblen_2Econtinuous_2E1,type,
    c_2Eveblen_2Econtinuous_2E1: du > u ).

thf(c_2Eordinal_2EfromNat_2E0,type,
    c_2Eordinal_2EfromNat_2E0: u ).

thf(c_2Eordinal_2EfromNat_2E1,type,
    c_2Eordinal_2EfromNat_2E1: du > u ).

thf(c_2Eordinal_2Eoleast_2E0,type,
    c_2Eordinal_2Eoleast_2E0: u ).

thf(c_2Eordinal_2Eoleast_2E1,type,
    c_2Eordinal_2Eoleast_2E1: du > u ).

thf(c_2Eordinal_2EordSUC_2E0,type,
    c_2Eordinal_2EordSUC_2E0: u ).

thf(c_2Eordinal_2EordSUC_2E1,type,
    c_2Eordinal_2EordSUC_2E1: du > u ).

thf(c_2Eordinal_2Eordlt_2E0,type,
    c_2Eordinal_2Eordlt_2E0: u ).

thf(c_2Eordinal_2Eordlt_2E2,type,
    c_2Eordinal_2Eordlt_2E2: du > du > u ).

thf(c_2Eordinal_2Epreds_2E0,type,
    c_2Eordinal_2Epreds_2E0: u ).

thf(c_2Eordinal_2Epreds_2E1,type,
    c_2Eordinal_2Epreds_2E1: du > u ).

thf(c_2Eveblen_2Estrict__mono_2E0,type,
    c_2Eveblen_2Estrict__mono_2E0: u ).

thf(c_2Eveblen_2Estrict__mono_2E1,type,
    c_2Eveblen_2Estrict__mono_2E1: du > u ).

thf(c_2Eordinal_2Esup_2E0,type,
    c_2Eordinal_2Esup_2E0: u ).

thf(c_2Eordinal_2Esup_2E1,type,
    c_2Eordinal_2Esup_2E1: du > u ).

thf(c_2Eveblen_2Eunbounded_2E0,type,
    c_2Eveblen_2Eunbounded_2E0: u ).

thf(c_2Eveblen_2Eunbounded_2E1,type,
    c_2Eveblen_2Eunbounded_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

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

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_3C_3D,type,
    mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

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

thf(mono_2Ec_2Enum_2ESUC,type,
    mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_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(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).

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

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

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

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

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

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

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

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

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

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

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

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

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

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

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ 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_2EBIGINTER_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGINTER_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EBIGINTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ 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 @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: 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_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ 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 @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ 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 @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ecardinal_2Ecardleq_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ 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 @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ecardinal_2Ecardleq_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Eclosed_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclosed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ 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 @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Eclosed_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Eclub_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ 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 @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Eclub_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Econtinuous_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Econtinuous_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Econtinuous_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Econtinuous_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Econtinuous_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Econtinuous_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2EfromNat_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EfromNat_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Eoleast_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2Eoleast_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2EordSUC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EordSUC_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2Eordlt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eordlt_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2Eordlt_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eordlt_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Epreds_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Epreds_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Estrict__mono_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Estrict__mono_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Estrict__mono_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Estrict__mono_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Estrict__mono_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Estrict__mono_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Esup_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2Esup_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Esup_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ c_2Eordinal_2Esup_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eveblen_2Eunbounded_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eunbounded_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ 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 @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Eveblen_2Eunbounded_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

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

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

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

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

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

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

thf(thm_2Eveblen_2Eclosed__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1g_2E0: u,V3n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V1g_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
     => ! [V0A_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclosed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
        <=> ! [V1g_2E0: u] :
              ( ! [V2n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V1g_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Eunbounded__def,axiom,
    ! [A_27a: d,V0A_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eunbounded_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
    <=> ! [V1a_2E0: u] :
        ? [V2b_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Eclub__def,axiom,
    ! [A_27a: d,V0A_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclosed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eunbounded_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0A_2E0 ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Econtinuous__def,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Econtinuous_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) ) ) )
    <=> ! [V1A_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1A_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
         => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1A_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1A_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Estrict__mono__def,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Estrict__mono_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u,V2y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Ebetter__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
        & ! [V1a_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) )
        & ! [V2a_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
              & ! [V3b_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3b_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ) ) ) ) )
     => ! [V4a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) ) ) ).

thf(thm_2Eveblen_2Enrange__IN__Uinf,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
     => ! [V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) ).

thf(thm_2Eveblen_2Eincreasing,axiom,
    ! [A_27a: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Estrict__mono_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Econtinuous_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Eclubs__exist,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Estrict__mono_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Econtinuous_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Emono__natI,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) ) )
     => ! [V2m: mono_2Etyop_2Enum_2Enum,V3n: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2m @ V3n )
         => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Esup__mem__INTER,axiom,
    ! [A_27a: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0f_2E0: u,V7n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
     => ( ! [V1A_2E0: u,V8n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
       => ! [V0f_2E0: u,V1A_2E0: u] :
            ( ( ! [V2n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) )
              & ! [V3n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V3n ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) ) ) )
              & ! [V4n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) ) ) ) )
              & ! [V5m: mono_2Etyop_2Enum_2Enum,V6n: mono_2Etyop_2Enum_2Enum] :
                  ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V5m @ V6n )
                 => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ V0f_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGINTER_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V1A_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Eoleast__leq,axiom,
    ! [A_27a: d,V0P_2E0: u,V1a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eveblen_2Eclub__INTER,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0A_2E0: u,V3n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
     => ! [V0A_2E0: u] :
          ( ( ! [V1n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) )
            & ! [V2n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eveblen_2Eclub_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGINTER_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0A_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

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