%------------------------------------------------------------------------------
% File     : ITP086^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ordinal.ax [Gau19]
%          : HL4086^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  612 ( 212 unt; 243 typ;   0 def)
%            Number of atoms       :  911 ( 376 equ;  79 cnn)
%            Maximal formula atoms :   17 (   1 avg)
%            Number of connectives : 16331 (  79   ~;  13   |; 130   &;15900   @)
%                                         (  67 <=>; 142  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   8 avg;15900 nst)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  351 ( 351   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  239 ( 237 usr;  94 con; 0-3 aty)
%            Number of variables   : 1069 (   0   ^1041   !;  28   ?;1069   :)
% 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(mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

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_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

thf(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > 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(tyop_2Ewellorder_2Ewellorder,type,
    tyop_2Ewellorder_2Ewellorder: 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_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: u ).

thf(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: du > du > u ).

thf(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

thf(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: du > du > u ).

thf(c_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_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

thf(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

thf(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

thf(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

thf(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: du > du > u ).

thf(c_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_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

thf(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_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_2EBIJ_2E0,type,
    c_2Epred__set_2EBIJ_2E0: u ).

thf(c_2Epred__set_2EBIJ_2E3,type,
    c_2Epred__set_2EBIJ_2E3: du > du > du > u ).

thf(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

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

thf(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

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

thf(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

thf(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

thf(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: du > du > u ).

thf(c_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: u ).

thf(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: du > du > u ).

thf(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

thf(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: du > du > u ).

thf(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

thf(c_2Earithmetic_2EEXP_2E0,type,
    c_2Earithmetic_2EEXP_2E0: u ).

thf(c_2Earithmetic_2EEXP_2E2,type,
    c_2Earithmetic_2EEXP_2E2: du > du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_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_2Elist_2EHD_2E0,type,
    c_2Elist_2EHD_2E0: u ).

thf(c_2Elist_2EHD_2E1,type,
    c_2Elist_2EHD_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_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_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

thf(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: du > u ).

thf(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

thf(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

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

thf(c_2Epred__set_2EPSUBSET_2E0,type,
    c_2Epred__set_2EPSUBSET_2E0: u ).

thf(c_2Epred__set_2EPSUBSET_2E2,type,
    c_2Epred__set_2EPSUBSET_2E2: du > du > u ).

thf(c_2Equotient_2EQUOTIENT_2E0,type,
    c_2Equotient_2EQUOTIENT_2E0: u ).

thf(c_2Equotient_2EQUOTIENT_2E3,type,
    c_2Equotient_2EQUOTIENT_2E3: du > du > du > u ).

thf(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

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

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 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_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).

thf(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

thf(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

thf(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_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_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

thf(c_2Eordinal_2EallOrds_2E0,type,
    c_2Eordinal_2EallOrds_2E0: u ).

thf(c_2Ecardinal_2Ecardeq_2E0,type,
    c_2Ecardinal_2Ecardeq_2E0: u ).

thf(c_2Ecardinal_2Ecardeq_2E2,type,
    c_2Ecardinal_2Ecardeq_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_2Epred__set_2Ecountable_2E0,type,
    c_2Epred__set_2Ecountable_2E0: u ).

thf(c_2Epred__set_2Ecountable_2E1,type,
    c_2Epred__set_2Ecountable_2E1: du > u ).

thf(c_2Eordinal_2Edclose_2E0,type,
    c_2Eordinal_2Edclose_2E0: u ).

thf(c_2Eordinal_2Edclose_2E1,type,
    c_2Eordinal_2Edclose_2E1: du > u ).

thf(c_2Eordinal_2Edownward__closed_2E0,type,
    c_2Eordinal_2Edownward__closed_2E0: u ).

thf(c_2Eordinal_2Edownward__closed_2E1,type,
    c_2Eordinal_2Edownward__closed_2E1: du > u ).

thf(c_2Ewellorder_2EelsOf_2E0,type,
    c_2Ewellorder_2EelsOf_2E0: u ).

thf(c_2Ewellorder_2EelsOf_2E1,type,
    c_2Ewellorder_2EelsOf_2E1: du > u ).

thf(c_2Eordinal_2Eepsilon0_2E0,type,
    c_2Eordinal_2Eepsilon0_2E0: u ).

thf(c_2Eordinal_2Eeval__poly_2E0,type,
    c_2Eordinal_2Eeval__poly_2E0: u ).

thf(c_2Eordinal_2Eeval__poly_2E2,type,
    c_2Eordinal_2Eeval__poly_2E2: du > 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_2Eis__polyform_2E0,type,
    c_2Eordinal_2Eis__polyform_2E0: u ).

thf(c_2Eordinal_2Eis__polyform_2E2,type,
    c_2Eordinal_2Eis__polyform_2E2: du > du > u ).

thf(c_2Eset__relation_2Emaximal__elements_2E0,type,
    c_2Eset__relation_2Emaximal__elements_2E0: u ).

thf(c_2Eset__relation_2Emaximal__elements_2E2,type,
    c_2Eset__relation_2Emaximal__elements_2E2: du > 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_2Eomax_2E0,type,
    c_2Eordinal_2Eomax_2E0: u ).

thf(c_2Eordinal_2Eomax_2E1,type,
    c_2Eordinal_2Eomax_2E1: du > u ).

thf(c_2Eordinal_2Eomega_2E0,type,
    c_2Eordinal_2Eomega_2E0: u ).

thf(c_2Eordinal_2EordADD_2E0,type,
    c_2Eordinal_2EordADD_2E0: u ).

thf(c_2Eordinal_2EordADD_2E1,type,
    c_2Eordinal_2EordADD_2E1: du > u ).

thf(c_2Eordinal_2EordADD_2E2,type,
    c_2Eordinal_2EordADD_2E2: du > du > u ).

thf(c_2Eordinal_2EordDIV_2E0,type,
    c_2Eordinal_2EordDIV_2E0: u ).

thf(c_2Eordinal_2EordDIV_2E2,type,
    c_2Eordinal_2EordDIV_2E2: du > du > u ).

thf(c_2Eordinal_2EordEXP_2E0,type,
    c_2Eordinal_2EordEXP_2E0: u ).

thf(c_2Eordinal_2EordEXP_2E1,type,
    c_2Eordinal_2EordEXP_2E1: du > u ).

thf(c_2Eordinal_2EordEXP_2E2,type,
    c_2Eordinal_2EordEXP_2E2: du > du > u ).

thf(c_2Eordinal_2EordMOD_2E0,type,
    c_2Eordinal_2EordMOD_2E0: u ).

thf(c_2Eordinal_2EordMOD_2E2,type,
    c_2Eordinal_2EordMOD_2E2: du > du > u ).

thf(c_2Eordinal_2EordMULT_2E0,type,
    c_2Eordinal_2EordMULT_2E0: u ).

thf(c_2Eordinal_2EordMULT_2E1,type,
    c_2Eordinal_2EordMULT_2E1: du > u ).

thf(c_2Eordinal_2EordMULT_2E2,type,
    c_2Eordinal_2EordMULT_2E2: du > 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_2Ewellorder_2Eorderiso_2E0,type,
    c_2Ewellorder_2Eorderiso_2E0: u ).

thf(c_2Ewellorder_2Eorderiso_2E1,type,
    c_2Ewellorder_2Eorderiso_2E1: du > u ).

thf(c_2Ewellorder_2Eorderiso_2E2,type,
    c_2Ewellorder_2Eorderiso_2E2: du > du > u ).

thf(c_2Ewellorder_2Eorderlt_2E0,type,
    c_2Ewellorder_2Eorderlt_2E0: u ).

thf(c_2Ewellorder_2Eorderlt_2E2,type,
    c_2Ewellorder_2Eorderlt_2E2: du > du > u ).

thf(c_2Eordinal_2Eordinal__ABS_2E0,type,
    c_2Eordinal_2Eordinal__ABS_2E0: u ).

thf(c_2Eordinal_2Eordinal__ABS_2E1,type,
    c_2Eordinal_2Eordinal__ABS_2E1: du > u ).

thf(c_2Eordinal_2Eordinal__ABS__CLASS_2E0,type,
    c_2Eordinal_2Eordinal__ABS__CLASS_2E0: u ).

thf(c_2Eordinal_2Eordinal__ABS__CLASS_2E1,type,
    c_2Eordinal_2Eordinal__ABS__CLASS_2E1: du > u ).

thf(c_2Eordinal_2Eordinal__REP_2E0,type,
    c_2Eordinal_2Eordinal__REP_2E0: u ).

thf(c_2Eordinal_2Eordinal__REP_2E1,type,
    c_2Eordinal_2Eordinal__REP_2E1: du > u ).

thf(c_2Eordinal_2Eordinal__REP__CLASS_2E0,type,
    c_2Eordinal_2Eordinal__REP__CLASS_2E0: u ).

thf(c_2Eordinal_2Eordinal__REP__CLASS_2E1,type,
    c_2Eordinal_2Eordinal__REP__CLASS_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_2Epolyform_2E0,type,
    c_2Eordinal_2Epolyform_2E0: u ).

thf(c_2Eordinal_2Epolyform_2E2,type,
    c_2Eordinal_2Epolyform_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_2Eoption_2Esome_2E0,type,
    c_2Eoption_2Esome_2E0: u ).

thf(c_2Eoption_2Esome_2E1,type,
    c_2Eoption_2Esome_2E1: du > u ).

thf(c_2Eset__relation_2Estrict_2E0,type,
    c_2Eset__relation_2Estrict_2E0: u ).

thf(c_2Eset__relation_2Estrict_2E1,type,
    c_2Eset__relation_2Estrict_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_2Ewellorder_2Ewellorder_2E0,type,
    c_2Ewellorder_2Ewellorder_2E0: u ).

thf(c_2Ewellorder_2Ewellorder_2E1,type,
    c_2Ewellorder_2Ewellorder_2E1: du > u ).

thf(c_2Ewellorder_2Ewellorder__ABS_2E0,type,
    c_2Ewellorder_2Ewellorder__ABS_2E0: u ).

thf(c_2Ewellorder_2Ewellorder__ABS_2E1,type,
    c_2Ewellorder_2Ewellorder__ABS_2E1: du > u ).

thf(c_2Ewellorder_2Ewellorder__REP_2E0,type,
    c_2Ewellorder_2Ewellorder__REP_2E0: u ).

thf(c_2Ewellorder_2Ewellorder__REP_2E1,type,
    c_2Ewellorder_2Ewellorder__REP_2E1: du > u ).

thf(c_2Ewellorder_2Ewobound_2E0,type,
    c_2Ewellorder_2Ewobound_2E0: u ).

thf(c_2Ewellorder_2Ewobound_2E2,type,
    c_2Ewellorder_2Ewobound_2E2: du > du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o ) > ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Eapp_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ).

thf(mono_2Ec_2Earithmetic_2E_2A,type,
    mono_2Ec_2Earithmetic_2E_2A: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_2B,type,
    mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_2D,type,
    mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Eprim__rec_2E_3C,type,
    mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

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

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

thf(mono_2Ec_2Earithmetic_2EEXP,type,
    mono_2Ec_2Earithmetic_2EEXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

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

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_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ).

thf(mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
    mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ).

thf(mono_2Ec_2Earithmetic_2EZERO,type,
    mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_2Ecardinal_2Ecardeq_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ecardinal_2Ecardeq_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o ).

thf(mono_2Ec_2Eordinal_2Epreds_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eordinal_2Epreds_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ).

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

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

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

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > u ).

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

thf(i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > u ).

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

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

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ).

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

thf(j_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

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

thf(ij_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).

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

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

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

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

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

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

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

thf(ji_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_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_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

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_2Epair_2E_2C_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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Emin_2E_40_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Emin_2E_40_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_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EBIGUNION_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_2EBIGUNION_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_2EBIGUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ 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_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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EBIJ_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( 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 ) @ X1_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_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( 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_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_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( 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 ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_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(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_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_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2EHD_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ 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 @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ 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_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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 ) ) )
      = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_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_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ 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_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_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_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ 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_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_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_2EINSERT_2E2 @ ( s @ ( 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_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_2EINSERT_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EPSUBSET_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_2EPSUBSET_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_2EPSUBSET_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(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X2_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_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Equotient_2EQUOTIENT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29_20mono_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_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( 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_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum > $o,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) @ ( 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_2Enum_2Enum @ 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_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) ) ) @ ( 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_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_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_2Epred__set_2Ecountable_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Edclose_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_2Edclose_2E1 @ ( 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 ) @ ( 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 ) ) @ c_2Eordinal_2Edclose_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Edownward__closed_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_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_2Eordinal_2Edownward__closed_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewellorder_2EelsOf_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_2Ewellorder_2EelsOf_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( 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_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2EelsOf_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2Eeval__poly_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2Eeval__poly_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_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(arityeq2_2Ec_2Eordinal_2Eis__polyform_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eis__polyform_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2Eis__polyform_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eis__polyform_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eset__relation_2Emaximal__elements_2E2_2Emono_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_2Eset__relation_2Emaximal__elements_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eset__relation_2Emaximal__elements_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

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_2Eomax_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2Eomax_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2EordADD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordADD_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordADD_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2EordADD_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordADD_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2EordDIV_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordDIV_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordDIV_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2EordEXP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordEXP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordEXP_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2EordEXP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordEXP_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2EordMOD_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMOD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordMOD_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2EordMULT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordMULT_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordMULT_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eordinal_2EordMULT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eordinal_2EordMULT_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_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_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_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_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewellorder_2Eorderiso_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Eorderiso_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_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_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderlt_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderlt_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_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_2Ewellorder_2Eorderlt_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderlt_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Eordinal__ABS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2Eordinal__ABS_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Eordinal__ABS__CLASS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2Eordinal__ABS__CLASS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Eordinal__REP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eordinal_2Eordinal__REP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Eordinal_2Eordinal__REP_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eordinal_2Eordinal__REP__CLASS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eordinal__REP__CLASS_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(arityeq2_2Ec_2Eordinal_2Epolyform_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) ) @ c_2Eordinal_2Epolyform_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ 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_2Eoption_2Esome_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2Esome_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Eoption_2Esome_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Estrict_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Estrict_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Estrict_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Estrict_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ 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_2Ewellorder_2Ewellorder_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Ewellorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ewellorder_2Ewellorder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ewellorder_2Ewellorder__ABS_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Ewellorder_2Ewellorder__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Ewellorder_2Ewellorder__ABS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Ewellorder__REP_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Ewellorder__REP_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Ewellorder__REP_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Ewellorder__REP_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) ) ) @ c_2Ewellorder_2Ewobound_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) ) @ c_2Ewellorder_2Ewobound_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

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

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o,V1: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

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

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ecardinal_2Ecardeq_2E0_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ecardinal_2Ecardeq_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ecardinal_2Ecardeq_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecardinal_2Ecardeq_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardeq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2Ecountable_2E0_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2Ecountable_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Eordinal_2Epreds_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Eordinal_2Epreds_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Epreds_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eordinal_2Epreds_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Eordinal_2Epreds_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).

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

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o ) > $o,V1: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Eordinal_2EordADD__def,axiom,
    ! [A_27a: d,V0b_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( 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 ) @ V0b_2E0 ) )
      & ! [V1a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( 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 ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_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 ) ) ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
         => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) )
            = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordADD_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomega__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0i: 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 ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 )
        = ( 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 ) ) @ F0_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Edclose__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0s_2E0: u,V1x_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 ) @ ( 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 ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) )
        <=> ? [V2y_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
              & ( 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 ) ) ) ) ) )
     => ( ! [V0s_2E0: u,V1x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( 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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( 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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) ) ) )
       => ! [V0s_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Edclose_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( 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_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordinal__TY__DEF,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1c_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1c_2E0 ) ) ) )
        <=> ? [V2r_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1c_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Eorderiso_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) ) ) )
     => ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ V0rep_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordinal__bijections,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) )
      & ! [V1r_2E0: u] :
          ( ? [V2r_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1r_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Eorderiso_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) ) )
        <=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordinal__REP__def,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eordinal_2Eordinal__REP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
      = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordinal__ABS__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Eorderiso_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__def,axiom,
    ! [A_27a: d,V0T1_2E0: u,V1T2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0T1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1T2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderlt_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eordinal_2Eordinal__REP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0T1_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eordinal_2Eordinal__REP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1T2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EallOrds__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1y_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
     => ( ! [V0x_2E0: u,V1y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) @ ( 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 ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
       => ( ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EallOrds_2E0 )
          = ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Ewellorder_2Ewellorder__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0w_2E0: u,V1w0_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w0_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) ) ) ) )
     => ! [V0w_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Edownward__closed__def,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_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 ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
         => ( 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 ) @ V0s_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eoleast__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V1x_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 ) @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_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 ) @ V1x_2E0 ) ) ) )
            & ! [V2y_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_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 ) @ V2y_2E0 ) ) ) ) ) ) ) )
     => ! [V0P_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Emin_2E_40_2E1 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordSUC__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0a_2E0: u,V1b_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) )
     => ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0a_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 ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
     => ( ( ( 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 ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) )
        & ! [V1n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0ordset_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 ) @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0ordset_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
        <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGUNION_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0ordset_2E0 ) ) ) ) ) ) ) ) ) )
     => ! [V0ordset_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0ordset_2E0 ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0ordset_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomax__def,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V3y_2E0: u,V2x_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) )
        <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) ) ) )
     => ( ! [V2x_2E0: u,V3y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) ) ) @ ( 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 ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) ) ) )
       => ( ! [V0s_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 ) @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
            <=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Emaximal__elements_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) ) ) ) ) ) )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) )
         => ! [V0s_2E0: u] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2Esome_2E1 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__def,axiom,
    ! [A_27a: d,V0b_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( 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 ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
      & ! [V1a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_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 ) ) ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
         => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) )
            = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordMULT_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordDIVISION,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_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 ) @ V1b_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordDIV_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMOD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMOD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__def,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( 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 ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
      & ! [V1a_2E0: u,V2a_27_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_27_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_27_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
      & ! [V3a_2E0: u,V4a_27_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 ) @ V4a_27_2E0 ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_27_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
         => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_27_2E0 ) ) )
            = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordEXP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_27_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eepsilon0__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_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 ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Epolyform__def,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) )
        & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Elt__suppreds,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_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 ) @ V0a_2E0 ) ) ) ) ) ) ) )
    <=> ? [V2d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__fromNat__omega,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ).

thf(thm_2Eordinal_2Eomega__islimit,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2Eomax__preds__omega,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2EordADD__fromNat,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eubsup__thm,axiom,
    ! [A_27a: d,V0s_2E0: u,V1b_2E0: u] :
      ( ! [V2a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) )
     => ! [V3c_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) )
        <=> ? [V4d_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__0L,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_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 ) @ V0a_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2Eord__RECURSION,axiom,
    ! [A_27a: d,A_27b: d,V0z_2E0: u,V1sf_2E0: u,V2lf_2E0: u] :
    ? [V3h_2E0: u] :
      ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ V3h_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
        = ( s @ A_27b @ V0z_2E0 ) )
      & ! [V4a_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ V3h_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V1sf_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ V3h_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) ) ) )
      & ! [V5a_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 ) @ V5a_2E0 ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
         => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ V3h_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) )
            = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ A_27b ) ) @ V2lf_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ A_27b ) @ V3h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__eq__omega,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] :
      ( (~)
      @ ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ).

thf(thm_2Eordinal_2EfromNat__lt__omega,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] : ( 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 @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Elt__omega,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) )
    <=> ? [V1m: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__ordlt,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
      ( ( 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 @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) ) ) )
      = ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) ) ).

thf(thm_2Eordinal_2Eordlt__fromNat,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1x_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 ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) )
    <=> ? [V2m: mono_2Etyop_2Enum_2Enum] :
          ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) ) ) )
          & ( mono_2Ec_2Eprim__rec_2E_3C @ V2m @ V0n ) ) ) ).

thf(thm_2Eordinal_2EfromNat__11,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1y ) ) ) ) )
    <=> ( V0x = V1y ) ) ).

thf(thm_2Eordinal_2Epreds__suple,axiom,
    ! [A_27a: d,V0s_2E0: u,V1b_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) )
      <=> ! [V2d_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
           => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__lesup,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ! [V1d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
         => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__sup__thm,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ! [V1b_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) )
        <=> ? [V2d_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Ecsup__suple,axiom,
    ! [A_27a: d,V0s_2E0: u,V1b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
     => ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) )
      <=> ! [V2d_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
           => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Ecsup__lesup,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
     => ! [V1d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
         => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__sup,axiom,
    ! [A_27a: d,V0s_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 ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Edclose_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__preds__omax__NONE,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_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 ) @ V0a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ).

thf(thm_2Eordinal_2Esimple__ord__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] :
            ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_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 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
              & ( 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 ) @ 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_2Eordinal_2Eordinal__ABS__REP__CLASS,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) )
      & ! [V1c_2E0: u] :
          ( ? [V2r_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1c_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Eorderiso_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2r_2E0 ) ) ) ) )
        <=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Eordinal__REP__CLASS_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1c_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1c_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordinal__QUOTIENT,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ewellorder_2Eorderiso_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2Eordinal__ABS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Eordinal_2Eordinal__REP_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__REFL,axiom,
    ! [A_27a: d,V0w_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__TRANS,axiom,
    ! [A_27a: d,V0w1_2E0: u,V1w2_2E0: u,V2w3_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2w3_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2w3_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__WF,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eordinal_2Eordlt_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__trichotomy,axiom,
    ! [A_27a: d,V0w2_2E0: u,V1w1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) ) ) )
      | ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Ewellorder__allOrds,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1y_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
     => ( ! [V0x_2E0: u,V1y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( 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_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) @ ( 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 ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Ewellorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EWIN__allOrds,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Estrict_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Ewellorder__REP_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EallOrds_2E0 ) ) ) ) ) ) ) )
      = ( 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 ) @ V0y_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EelsOf__allOrds,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2EelsOf_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EallOrds_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).

thf(thm_2Eordinal_2Eordlt__mkOrdinal,axiom,
    ! [A_27a: d,V0o2_2E0: u,V1o1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1o1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0o2_2E0 ) ) ) )
    <=> ! [V2w1_2E0: u,V3w2_2E0: u] :
          ( ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2w1_2E0 ) ) )
              = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1o1_2E0 ) )
            & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V3w2_2E0 ) ) )
              = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0o2_2E0 ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderlt_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V2w1_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V3w2_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eorderlt__iso__REFL,axiom,
    ! [A_27a: d,A_27b: d,V0w2_2E0: u,V1w1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ V1w1_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ V0w2_2E0 ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderlt_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ V1w1_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27b ) @ V0w2_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eorderiso__wobound2,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2w_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ V2w_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ A_27a @ V0y_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ V2w_2E0 ) ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Estrict_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2Ewellorder__REP_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ A_27a ) @ V2w_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Ewellorder__ordinal__isomorphism,axiom,
    ! [A_27a: d,V0w_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ewellorder_2Eorderiso_2E2 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V0w_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eordinal__ABS_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) ) @ V0w_2E0 ) ) ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EallOrds_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EIN__preds,axiom,
    ! [A_27a: d,V0x_2E0: u,V1w_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__11,axiom,
    ! [A_27a: d,V0w2_2E0: u,V1w1_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) ) ) ).

thf(thm_2Eordinal_2Epreds__downward__closed,axiom,
    ! [A_27a: d,V0w_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__bij,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( 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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Eordinal_2Edownward__closed_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__lt__PSUBSET,axiom,
    ! [A_27a: d,V0w2_2E0: u,V1w1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EPSUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1w1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0w2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__wobound,axiom,
    ! [A_27a: d,V0ord_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0ord_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Ewellorder_2EelsOf_2E1 @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Ewellorder_2Ewobound_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0ord_2E0 ) @ ( s @ ( tyop_2Ewellorder_2Ewellorder @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eordinal_2EallOrds_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__inj__univ,axiom,
    ! [A_27a: d,V0ord_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 ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0ord_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eunitinf__univnum,axiom,
    mono_2Ec_2Ecardinal_2Ecardeq_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ).

thf(thm_2Eordinal_2Ecord__countable__preds,axiom,
    ! [V0ord: mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Eordinal_2Epreds_2Emono_2Etyop_2Eone_2Eone @ V0ord ) ) ).

thf(thm_2Eordinal_2Euniv__ord__greater__cardinal,axiom,
    ! [A_27a: d] : ( (~) @ ( 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 ) @ c_2Epred__set_2EUNIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Euniv__cord__uncountable,axiom,
    (~) @ ( mono_2Ec_2Epred__set_2Ecountable_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29 ) ).

thf(thm_2Eordinal_2Eordle__lteq,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) @ V0b_2E0 ) ) ) )
        | ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordle__ANTISYM,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) @ V0b_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ).

thf(thm_2Eordinal_2Eordle__TRANS,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u,V2z_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlet__TRANS,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u,V2z_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlte__TRANS,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u,V2z_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2z_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eoleast__intro,axiom,
    ! [A_27a: d,V0Q_2E0: u,V1P_2E0: u] :
      ( ( ? [V2a_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 ) @ V1P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
        & ! [V3a_2E0: u] :
            ( ( ! [V4b_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) )
                 => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) ) ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0Q_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0Q_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__def__compute,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0a_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 ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
     => ( ( ( 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 ) @ ( c_2Eordinal_2Eoleast_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) )
        & ! [V1n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
        & ! [V2n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__SUC,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V0n ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__ZERO,axiom,
    ! [A_27a: d,V0a_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__surj,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Edownward__closed_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0x_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0x_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ? [V1y_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0x_2E0 ) ) ) ).

thf(thm_2Eordinal_2Eno__maximal__ordinal,axiom,
    ! [A_27a: d,V0a_2E0: u] :
    ? [V1b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__SUC,axiom,
    ! [A_27a: d,V0a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordSUC__ZERO,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( (~)
      @ ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__DISCRETE1,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( (~)
      @ ( ( 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 ) @ V0b_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__SUC__DISCRETE,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( 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_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) @ V0b_2E0 ) ) ) )
        | ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordSUC__MONO,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) @ V0b_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordSUC__11,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ).

thf(thm_2Eordinal_2Eord__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1min_2E0: u] :
          ( ! [V2b_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1min_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 ) @ V2b_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 ) @ V1min_2E0 ) ) ) ) )
     => ! [V3a_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 ) @ V3a_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__thm,axiom,
    ! [A_27a: d,V0s_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 ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ! [V1a_2E0: u] :
          ( ( 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_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) )
        <=> ? [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 ) @ V0s_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_2Eordinal_2Esuple__thm,axiom,
    ! [A_27a: d,V0b_2E0: u,V1s_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 ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__eq__sup,axiom,
    ! [A_27a: d,V0s2_2E0: u,V1s1_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 ) @ V1s1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ( 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 ) @ V0s2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ! [V2a_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) )
           => ? [V3b_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) )
                & ( (~) @ ( 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 ) ) ) ) ) ) )
        & ! [V4b_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) )
           => ? [V5a_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) )
                & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EUnum__cle__Uinf,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Ecsup__thm,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
     => ! [V1b_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) )
        <=> ? [V2d_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epredimage__sup__thm,axiom,
    ! [A_27a: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( 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_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_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ) ) )
    <=> ? [V3d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3d_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 ) @ V2b_2E0 ) @ ( 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 ) @ V3d_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epredimage__suplt__ELIM,axiom,
    ! [A_27a: d,V0f_2E0: u,V1b_2E0: u,V2a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_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_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_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
     => ! [V3d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3d_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
         => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( 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 ) @ V3d_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Esuppred__suplt__ELIM,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( 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 ) @ V1a_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) )
     => ! [V2d_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_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 ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2d_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__EMPTY,axiom,
    ! [A_27a: d] :
      ( ( 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_2EEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__SING,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( 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_2EINSERT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2Esup__preds__SUC,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( 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 ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2Epreds__ordSUC,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EcountableOrds__dclosed,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( 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 ) @ V0b_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomax__SOME,axiom,
    ! [A_27a: d,V0s_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
        & ! [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 ) @ V0s_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_2Eordinal_2Eomax__NONE,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> ! [V1a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
         => ? [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 ) @ V0s_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_2Eordinal_2Eomax__EMPTY,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2Epreds__0,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( 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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).

thf(thm_2Eordinal_2Eordleq0,axiom,
    ! [A_27a: d,V0x_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 ) @ V0x_2E0 ) ) ) ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epreds__EQ__EMPTY,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomax__sup,axiom,
    ! [A_27a: d,V0s_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ).

thf(thm_2Eordinal_2Epreds__omax__SOME__SUC,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomax__preds__SUC,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EORD__ONE,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( 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 ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordSUC__NUMERAL,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordZERO__ltSUC,axiom,
    ! [A_27a: d,V0x_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 ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__CANCEL__ADDR,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( 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_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) )
      = ( 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 ) @ V0b_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__CANCEL__ADDL,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
      = mono_2Ec_2Ebool_2EF ) ).

thf(thm_2Eordinal_2EordADD__CANCEL1,axiom,
    ! [A_27a: d] :
      ( ! [V0c_2E0: u,V1a_2E0: u] :
          ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
      & ! [V2c_2E0: u,V3a_2E0: u] :
          ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) )
        <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__MONO,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u,V2c_2E0: u] :
      ( ( 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 ) @ V0b_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__CANCEL,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u,V2c_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_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 ) @ V0b_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__RIGHT__CANCEL,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u,V2c_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ).

thf(thm_2Eordinal_2EleqLEFT__CANCEL,axiom,
    ! [A_27a: d,V0x_2E0: u,V1a_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordlt__EXISTS__ADD,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
    <=> ? [V2c_2E0: u] :
          ( ( (~)
            @ ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 )
              = ( 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 ) @ V1b_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordle__EXISTS__ADD,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
    <=> ? [V2c_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eordle__CANCEL__ADDR,axiom,
    ! [A_27a: d,V0x_2E0: u,V1a_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Edclose__BIGUNION,axiom,
    ! [A_27a: d,V0s_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Edclose_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EBIGUNION_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EcountableOrds__uncountable,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2Ecountable_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Edclose__cardleq__univinf,axiom,
    ! [A_27a: d,V0s_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 ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( 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 ) @ ( c_2Eordinal_2Edclose_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__lt__implies,axiom,
    ! [A_27a: d,V0s_2E0: u,V1b_2E0: u,V2a_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 ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__eq__max,axiom,
    ! [A_27a: d,V0s_2E0: u,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 ) @ V0s_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 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ).

thf(thm_2Eordinal_2Esup__eq__SUC,axiom,
    ! [A_27a: d,V0s_2E0: u,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 ) @ V0s_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_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Egeneric__continuity,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( ! [V1a_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 ) @ V1a_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
           => ( ( 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 ) @ V1a_2E0 ) ) )
              = ( 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_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_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ) )
        & ! [V2x_2E0: u,V3y_2E0: u] :
            ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_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 ) @ V3y_2E0 ) ) ) @ ( 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 ) @ V2x_2E0 ) ) ) ) ) ) ) ) )
     => ! [V4s_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 ) @ V4s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
            & ( (~)
              @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V4s_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
         => ( ( 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 ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V4s_2E0 ) ) ) ) )
            = ( 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_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 ) @ V4s_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eord__CASES,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
      | ? [V1a0_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a0_2E0 ) ) ) )
      | ( ( 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 ) @ V0a_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eislimit__0,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( 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_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2Eordinal__IVT,axiom,
    ! [A_27a: d,V0f_2E0: u,V1c_2E0: u,V2a2_2E0: u,V3a1_2E0: u] :
      ( ( ! [V4a_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 ) @ V4a_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
           => ( ( 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 ) @ V4a_2E0 ) ) )
              = ( 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_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_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) ) ) ) ) ) ) ) )
        & ! [V5x_2E0: u,V6y_2E0: u] :
            ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V6y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5x_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 ) @ V6y_2E0 ) ) ) @ ( 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 ) @ V5x_2E0 ) ) ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a2_2E0 ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 ) @ ( 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 ) @ V3a1_2E0 ) ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 ) @ ( 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 ) @ V2a2_2E0 ) ) ) ) ) ) )
     => ? [V7b_2E0: u] :
          ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V7b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a1_2E0 ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V7b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a2_2E0 ) ) ) )
          & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 ) @ ( 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 ) @ V7b_2E0 ) ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 ) @ ( 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 ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V7b_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__continuous,axiom,
    ! [A_27a: d,V0a_2E0: u,V1s_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 ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
        = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordADD_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__ASSOC,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EADD1R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__weak__MONO,axiom,
    ! [A_27a: d,V0c_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( 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 ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__0L,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_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 ) @ V0a_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__0R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( 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 ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__1L,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2EordMULT__1R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2EordMULT__2R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eislimit__SUC__lt,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_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 ) @ V0b_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__lt__MONO__R,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
        & ( 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 ) @ V2c_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__le__MONO__R,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__lt__MONO__R__EQN,axiom,
    ! [A_27a: d,V0c_2E0: u,V1b_2E0: u,V2a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
        & ( 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 ) @ V0c_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__le__MONO__L,axiom,
    ! [A_27a: d,V0z_2E0: u,V1y_2E0: u,V2x_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__le__MONO__L,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__CANCEL__R,axiom,
    ! [A_27a: d,V0z_2E0: u,V1y_2E0: u,V2x_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 )
          = ( 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 ) @ V2x_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__continuous,axiom,
    ! [A_27a: d,V0a_2E0: u,V1s_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 ) @ V1s_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_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
        = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordMULT_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__fromNat,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2A @ V0n @ V1m ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomega__MUL__fromNat,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ).

thf(thm_2Eordinal_2EordMULT__LDISTRIB,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__ASSOC,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2c_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordDIV__UNIQUE,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2q_2E0: u,V3r_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 ) @ V1b_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2q_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3r_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3r_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordDIV_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2q_2E0 ) ) ) ).

thf(thm_2Eordinal_2EordMOD__UNIQUE,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2q_2E0: u,V3r_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 ) @ V1b_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2q_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3r_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3r_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMOD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3r_2E0 ) ) ) ).

thf(thm_2Eordinal_2EordEXP__1R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ).

thf(thm_2Eordinal_2EordEXP__1L,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__2R,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__fromNat,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEXP @ V0x @ V1n ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__le__MONO__L,axiom,
    ! [A_27a: d,V0x_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_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 ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EIFF__ZERO__lt,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( ( (~)
          @ ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
      <=> ( 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 ) @ V0x_2E0 ) ) ) ) )
      & ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
      <=> ( 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 ) @ V0x_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eislimit__SUC,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordSUC_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> mono_2Ec_2Ebool_2EF ) ).

thf(thm_2Eordinal_2Eislimit__fromNat,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> ( V0x = mono_2Ec_2Enum_2E0 ) ) ).

thf(thm_2Eordinal_2EordEXP__ZERO__limit,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_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 ) @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__ZERO__nonlimit,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( (~)
        @ ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_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 ) @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Esup__EQ__0,axiom,
    ! [A_27a: d,V0s_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 ) @ V0s_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_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
          = ( 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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
          | ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_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_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__EQ__0,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) )
        = ( 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 ) @ V1x_2E0 )
          = ( 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 ) @ V0y_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EIMAGE__EQ__SING,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1s_2E0: u,V2f_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
    <=> ( ? [V3y_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
        & ! [V4y_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V4y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
           => ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) )
              = ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMULT__EQ__0,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) )
        = ( 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 ) @ V0x_2E0 )
          = ( 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 ) @ V1y_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__EQ__0,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) )
        = ( 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 ) @ V1x_2E0 )
          = ( 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_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EZERO__lt__ordEXP__I,axiom,
    ! [A_27a: d,V0a_2E0: u,V1x_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 ) @ V0a_2E0 ) ) ) )
     => ( 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 ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EZERO__lt__ordEXP,axiom,
    ! [A_27a: d,V0x_2E0: u,V1a_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 ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) )
    <=> ( ( 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 ) @ V1a_2E0 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__lt__MONO__R,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
        & ( 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 ) @ V0y_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__lt__IFF,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u,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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__le__MONO__R,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u,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 ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__continuous,axiom,
    ! [A_27a: d,V0a_2E0: u,V1s_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 ) @ V0a_2E0 ) ) ) )
        & ( 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 ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
        = ( 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_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2EordEXP_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__ADD,axiom,
    ! [A_27a: d,V0z_2E0: u,V1y_2E0: u,V2x_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 ) @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__MUL,axiom,
    ! [A_27a: d,V0z_2E0: u,V1y_2E0: u,V2x_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 ) @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0z_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Efixpoints__exist,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( ! [V1s_2E0: u] :
            ( ( ( (~)
                @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
                  = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
              & ( 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 ) @ V1s_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_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 ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
              = ( 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_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 ) @ V1s_2E0 ) ) ) ) ) ) )
        & ! [V2x_2E0: u] : ( (~) @ ( 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 ) @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2x_2E0 ) ) ) ) ) )
     => ! [V3a_2E0: u] :
        ? [V4b_2E0: u] :
          ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) ) )
          & ( ( 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 ) @ V4b_2E0 ) ) )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4b_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Ex__le__ordEXP__x,axiom,
    ! [A_27a: d,V0a_2E0: u,V1x_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
     => ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eepsilon0__fixpoint,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) )
      = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ).

thf(thm_2Eordinal_2Eepsilon0__least__fixpoint,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eomega__lt__epsilon0,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2EfromNat__lt__epsilon0,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum] : ( 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 @ V0n ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ).

thf(thm_2Eordinal_2Eadd__nat__islimit,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
      ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0n )
     => ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
      <=> mono_2Ec_2Ebool_2EF ) ) ).

thf(thm_2Eordinal_2Estrict__continuity__preserves__islimit,axiom,
    ! [A_27a: d,V0f_2E0: u,V1a_2E0: u] :
      ( ( ! [V2s_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 ) @ V2s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
              & ( (~)
                @ ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2s_2E0 )
                  = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
           => ( ( 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 ) @ ( c_2Eordinal_2Esup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) ) )
              = ( 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_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 ) @ V2s_2E0 ) ) ) ) ) ) )
        & ! [V3x_2E0: u,V4y_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4y_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 ) @ V3x_2E0 ) ) ) @ ( 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 ) @ V4y_2E0 ) ) ) ) ) ) )
        & ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
        & ( (~)
          @ ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 )
            = ( 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_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( 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 ) @ V1a_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Eordinal_2Eadd__omega__islimit,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2Eislimit__mul__R,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Eordinal_2Emul__omega__islimit,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Eordinal_2Eomega__exp__islimit,axiom,
    ! [A_27a: d,V0a_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 ) @ V0a_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Eordinal_2Eomax_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eordinal_2Epreds_2E1 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Eordinal_2Eexpbound__add,axiom,
    ! [A_27a: d,V0a_2E0: u,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 ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EaddL__fixpoint__iff,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) )
    <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordADD__under__epsilon0,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_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 ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordMUL__under__epsilon0,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_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 ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2EordEXP__under__epsilon0,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( 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_2Eepsilon0_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eepsilon0_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eeval__poly__ind,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_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2a_2E0: u,V3c_2E0: u,V4e_2E0: u,V5t_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V5t_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V5t_2E0 ) ) ) ) ) ) ) )
     => ! [V6v_2E0: u,V7v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V6v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V7v1_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eeval__poly__def,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
      & ! [V1t_2E0: u,V2e_2E0: u,V3c_2E0: u,V4a_2E0: u] :
          ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V1t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordADD_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2e_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V1t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eis__polyform__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2a_2E0: u,V3c_2E0: u,V4e_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V4e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) )
        & ! [V5a_2E0: u,V6c1_2E0: u,V7e1_2E0: u,V8c2_2E0: u,V9e2_2E0: u,V10t_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V8c2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V9e2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V10t_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V6c1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V7e1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V8c2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V9e2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V10t_2E0 ) ) ) ) ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V11v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V12v1_2E0 ) ) ) ) ) ).

thf(thm_2Eordinal_2Eis__polyform__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1e_2E0: u,V2c_2E0: u,V3a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V1e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) )
        <=> ( ( 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 ) @ V2c_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) ) ) )
      & ! [V4t_2E0: u,V5e2_2E0: u,V6e1_2E0: u,V7c2_2E0: u,V8c1_2E0: u,V9a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V9a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V8c1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V6e1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V7c2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V5e2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V4t_2E0 ) ) ) ) ) ) ) )
        <=> ( ( 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 ) @ V8c1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V8c1_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V9a_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V5e2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V6e1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V9a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V7c2_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V5e2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V4t_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eis__polyform__ELthm,axiom,
    ! [A_27a: d,A_27b: d,V0ces_2E0: u,V1a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0ces_2E0 ) ) ) )
    <=> ( ! [V2i: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum] :
            ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ V3j )
              & ( mono_2Ec_2Eprim__rec_2E_3C @ V3j @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0ces_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0ces_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0ces_2E0 ) ) ) ) ) ) ) ) )
        & ! [V4c_2E0: u,V5e_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V5e_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0ces_2E0 ) ) ) ) ) )
           => ( ( 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 ) @ V4c_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epolyform__exists,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
     => ? [V2ces_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V2ces_2E0 ) ) ) )
          & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 )
            = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V2ces_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2ECNF__thm,axiom,
    ! [A_27a: d,V0b_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 )
        = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epolyform__0,axiom,
    ! [A_27a: d,V0a_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( 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_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ).

thf(thm_2Eordinal_2Epolyform__EQ__NIL,axiom,
    ! [A_27a: d,V0x_2E0: u,V1a_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) )
      <=> ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eis__polyform__CONS__E,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1e_2E0: u,V2c_2E0: u,V3a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27b ) @ V1e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0t_2E0 ) ) ) ) ) )
     => ( ( 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 ) @ V2c_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27b ) ) ) @ V0t_2E0 ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eis__polyform__head__dominates__tail,axiom,
    ! [A_27a: d,V0t_2E0: u,V1e_2E0: u,V2c_2E0: u,V3a_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2c_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1e_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V0t_2E0 ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V0t_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V3a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1e_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Ecx__lt__x,axiom,
    ! [A_27a: d,V0x_2E0: u,V1c_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordMULT_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) )
    <=> ( ( 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 ) @ V0x_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1c_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Epolyform__UNIQUE,axiom,
    ! [A_27a: d,V0a_2E0: u,V1b_2E0: u,V2ces_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V2ces_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 )
          = ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V2ces_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V2ces_2E0 ) ) ) ).

thf(thm_2Eordinal_2Epolyform__eval__poly,axiom,
    ! [A_27a: d,V0b_2E0: u,V1a_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eis__polyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V0b_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2Eeval__poly_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V0b_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ V0b_2E0 ) ) ) ).

thf(thm_2Eordinal_2ECNF__nat,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V0n: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V0n )
        <=> ( V0n = mono_2Ec_2Enum_2E0 ) )
     => ! [V0n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0n ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EfromNat_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( 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_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2EordLOG__correct,axiom,
    ! [A_27a: d,V0x_2E0: u,V1b_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_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) ) ) )
        & ( 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 ) @ V0x_2E0 ) ) ) ) )
     => ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ) ) ) ) ) ) )
        & ! [V2a_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1b_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V2a_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eordinal_2Eolog__correct,axiom,
    ! [A_27a: d,V0x_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 ) @ V0x_2E0 ) ) ) )
     => ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ) ) ) ) ) ) )
        & ! [V1a_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eordinal_2Eordlt_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( tyop_2Eordinal_2Eordinal @ A_27a ) ) ) @ ( c_2Eordinal_2Epolyform_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V0x_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 ) @ V0x_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ ( c_2Eordinal_2EordEXP_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ c_2Eordinal_2Eomega_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A_27a ) @ V1a_2E0 ) ) ) ) ) ) ) ) ) ).

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