%------------------------------------------------------------------------------
% File     : ITP098^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : enumeral.ax [Gau19]
%          : HL4098^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  479 ( 143 unt; 248 typ;   0 def)
%            Number of atoms       :  577 ( 332 equ;   5 cnn)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives : 18184 (   5   ~;  12   |; 132   &;17896   @)
%                                         (  42 <=>;  97  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   9 avg;17896 nst)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  338 ( 338   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  245 ( 243 usr; 113 con; 0-5 aty)
%            Number of variables   : 1170 (   0   ^1144   !;  26   ?;1170   :)
% 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_2EternaryComparisons_2Eordering,type,
    mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).

thf(tyop_2Eenumeral_2Ebl,type,
    tyop_2Eenumeral_2Ebl: d > d ).

thf(tyop_2Eenumeral_2Ebt,type,
    tyop_2Eenumeral_2Ebt: d > d ).

thf(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

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_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

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

thf(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: d ).

thf(tyop_2Etoto_2Etoto,type,
    tyop_2Etoto_2Etoto: 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_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_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_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_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

thf(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: du > du > u ).

thf(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: 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_2Eenumeral_2EBL__ACCUM_2E0,type,
    c_2Eenumeral_2EBL__ACCUM_2E0: u ).

thf(c_2Eenumeral_2EBL__ACCUM_2E3,type,
    c_2Eenumeral_2EBL__ACCUM_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EBL__CONS_2E0,type,
    c_2Eenumeral_2EBL__CONS_2E0: u ).

thf(c_2Eenumeral_2EBL__CONS_2E2,type,
    c_2Eenumeral_2EBL__CONS_2E2: du > du > u ).

thf(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: 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_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

thf(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: du > du > du > u ).

thf(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

thf(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

thf(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

thf(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: du > du > u ).

thf(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

thf(c_2Eenumeral_2EENUMERAL_2E0,type,
    c_2Eenumeral_2EENUMERAL_2E0: u ).

thf(c_2Eenumeral_2EENUMERAL_2E2,type,
    c_2Eenumeral_2EENUMERAL_2E2: du > du > u ).

thf(c_2EternaryComparisons_2EEQUAL_2E0,type,
    c_2EternaryComparisons_2EEQUAL_2E0: u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: du > du > u ).

thf(c_2EternaryComparisons_2EGREATER_2E0,type,
    c_2EternaryComparisons_2EGREATER_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_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

thf(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

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

thf(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

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

thf(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: u ).

thf(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: du > du > u ).

thf(c_2Eenumeral_2EK2_2E0,type,
    c_2Eenumeral_2EK2_2E0: u ).

thf(c_2Eenumeral_2EK2_2E1,type,
    c_2Eenumeral_2EK2_2E1: du > u ).

thf(c_2EternaryComparisons_2ELESS_2E0,type,
    c_2EternaryComparisons_2ELESS_2E0: u ).

thf(c_2Eenumeral_2ELESS__ALL_2E0,type,
    c_2Eenumeral_2ELESS__ALL_2E0: u ).

thf(c_2Eenumeral_2ELESS__ALL_2E3,type,
    c_2Eenumeral_2ELESS__ALL_2E3: du > du > 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_2Eenumeral_2EOL_2E0,type,
    c_2Eenumeral_2EOL_2E0: u ).

thf(c_2Eenumeral_2EOL_2E2,type,
    c_2Eenumeral_2EOL_2E2: du > du > u ).

thf(c_2Eenumeral_2EOL__bt_2E0,type,
    c_2Eenumeral_2EOL__bt_2E0: u ).

thf(c_2Eenumeral_2EOL__bt_2E2,type,
    c_2Eenumeral_2EOL__bt_2E2: du > du > u ).

thf(c_2Eenumeral_2EOL__bt__lb_2E0,type,
    c_2Eenumeral_2EOL__bt__lb_2E0: u ).

thf(c_2Eenumeral_2EOL__bt__lb_2E3,type,
    c_2Eenumeral_2EOL__bt__lb_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EOL__bt__lb__ub_2E0,type,
    c_2Eenumeral_2EOL__bt__lb__ub_2E0: u ).

thf(c_2Eenumeral_2EOL__bt__lb__ub_2E4,type,
    c_2Eenumeral_2EOL__bt__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2EOL__bt__ub_2E0,type,
    c_2Eenumeral_2EOL__bt__ub_2E0: u ).

thf(c_2Eenumeral_2EOL__bt__ub_2E3,type,
    c_2Eenumeral_2EOL__bt__ub_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EOL__sublists_2E0,type,
    c_2Eenumeral_2EOL__sublists_2E0: u ).

thf(c_2Eenumeral_2EOL__sublists_2E2,type,
    c_2Eenumeral_2EOL__sublists_2E2: du > du > u ).

thf(c_2Eenumeral_2EOU_2E0,type,
    c_2Eenumeral_2EOU_2E0: u ).

thf(c_2Eenumeral_2EOU_2E3,type,
    c_2Eenumeral_2EOU_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EOWL_2E0,type,
    c_2Eenumeral_2EOWL_2E0: u ).

thf(c_2Eenumeral_2EOWL_2E3,type,
    c_2Eenumeral_2EOWL_2E3: du > du > 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_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

thf(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: du > du > u ).

thf(c_2Eenumeral_2EUO_2E0,type,
    c_2Eenumeral_2EUO_2E0: u ).

thf(c_2Eenumeral_2EUO_2E3,type,
    c_2Eenumeral_2EUO_2E3: du > du > du > u ).

thf(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

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

thf(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: u ).

thf(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: du > du > u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

thf(c_2Etoto_2Eapto_2E0,type,
    c_2Etoto_2Eapto_2E0: u ).

thf(c_2Etoto_2Eapto_2E3,type,
    c_2Etoto_2Eapto_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebl__CASE_2E0,type,
    c_2Eenumeral_2Ebl__CASE_2E0: u ).

thf(c_2Eenumeral_2Ebl__CASE_2E4,type,
    c_2Eenumeral_2Ebl__CASE_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Ebl__rev_2E0,type,
    c_2Eenumeral_2Ebl__rev_2E0: u ).

thf(c_2Eenumeral_2Ebl__rev_2E1,type,
    c_2Eenumeral_2Ebl__rev_2E1: du > u ).

thf(c_2Eenumeral_2Ebl__rev_2E2,type,
    c_2Eenumeral_2Ebl__rev_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebl__size_2E0,type,
    c_2Eenumeral_2Ebl__size_2E0: u ).

thf(c_2Eenumeral_2Ebl__size_2E2,type,
    c_2Eenumeral_2Ebl__size_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebl__to__bt_2E0,type,
    c_2Eenumeral_2Ebl__to__bt_2E0: u ).

thf(c_2Eenumeral_2Ebl__to__bt_2E1,type,
    c_2Eenumeral_2Ebl__to__bt_2E1: du > u ).

thf(c_2Eenumeral_2Ebl__to__set_2E0,type,
    c_2Eenumeral_2Ebl__to__set_2E0: u ).

thf(c_2Eenumeral_2Ebl__to__set_2E2,type,
    c_2Eenumeral_2Ebl__to__set_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__CASE_2E0,type,
    c_2Eenumeral_2Ebt__CASE_2E0: u ).

thf(c_2Eenumeral_2Ebt__CASE_2E3,type,
    c_2Eenumeral_2Ebt__CASE_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__rev_2E0,type,
    c_2Eenumeral_2Ebt__rev_2E0: u ).

thf(c_2Eenumeral_2Ebt__rev_2E2,type,
    c_2Eenumeral_2Ebt__rev_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__size_2E0,type,
    c_2Eenumeral_2Ebt__size_2E0: u ).

thf(c_2Eenumeral_2Ebt__size_2E2,type,
    c_2Eenumeral_2Ebt__size_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__to__bl_2E0,type,
    c_2Eenumeral_2Ebt__to__bl_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__bl_2E1,type,
    c_2Eenumeral_2Ebt__to__bl_2E1: du > u ).

thf(c_2Eenumeral_2Ebt__to__list_2E0,type,
    c_2Eenumeral_2Ebt__to__list_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__list_2E1,type,
    c_2Eenumeral_2Ebt__to__list_2E1: du > u ).

thf(c_2Eenumeral_2Ebt__to__list__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__list__ac_2E2,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol_2E0,type,
    c_2Eenumeral_2Ebt__to__ol_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol_2E2,type,
    c_2Eenumeral_2Ebt__to__ol_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__ac_2E3,type,
    c_2Eenumeral_2Ebt__to__ol__ac_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__lb_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb_2E3,type,
    c_2Eenumeral_2Ebt__to__ol__lb_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5,type,
    c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5: du > du > du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__ub_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__ub_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__ub_2E3,type,
    c_2Eenumeral_2Ebt__to__ol__ub_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4,type,
    c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__set__lb_2E0,type,
    c_2Eenumeral_2Ebt__to__set__lb_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__set__lb_2E3,type,
    c_2Eenumeral_2Ebt__to__set__lb_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__set__lb__ub_2E0,type,
    c_2Eenumeral_2Ebt__to__set__lb__ub_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__set__lb__ub_2E4,type,
    c_2Eenumeral_2Ebt__to__set__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__set__ub_2E0,type,
    c_2Eenumeral_2Ebt__to__set__ub_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__set__ub_2E3,type,
    c_2Eenumeral_2Ebt__to__set__ub_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Eincr__sbuild_2E0,type,
    c_2Eenumeral_2Eincr__sbuild_2E0: u ).

thf(c_2Eenumeral_2Eincr__sbuild_2E2,type,
    c_2Eenumeral_2Eincr__sbuild_2E2: du > du > u ).

thf(c_2Eenumeral_2Eincr__smerge_2E0,type,
    c_2Eenumeral_2Eincr__smerge_2E0: u ).

thf(c_2Eenumeral_2Eincr__smerge_2E3,type,
    c_2Eenumeral_2Eincr__smerge_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Eincr__ssort_2E0,type,
    c_2Eenumeral_2Eincr__ssort_2E0: u ).

thf(c_2Eenumeral_2Eincr__ssort_2E2,type,
    c_2Eenumeral_2Eincr__ssort_2E2: du > du > u ).

thf(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

thf(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Elist__to__bl_2E0,type,
    c_2Eenumeral_2Elist__to__bl_2E0: u ).

thf(c_2Eenumeral_2Elist__to__bl_2E1,type,
    c_2Eenumeral_2Elist__to__bl_2E1: du > u ).

thf(c_2Eenumeral_2Elist__to__bt_2E0,type,
    c_2Eenumeral_2Elist__to__bt_2E0: u ).

thf(c_2Eenumeral_2Elist__to__bt_2E1,type,
    c_2Eenumeral_2Elist__to__bt_2E1: du > u ).

thf(c_2Eenumeral_2Elol__set_2E0,type,
    c_2Eenumeral_2Elol__set_2E0: u ).

thf(c_2Eenumeral_2Elol__set_2E1,type,
    c_2Eenumeral_2Elol__set_2E1: du > u ).

thf(c_2Eenumeral_2Enbl_2E0,type,
    c_2Eenumeral_2Enbl_2E0: u ).

thf(c_2Eenumeral_2Enode_2E0,type,
    c_2Eenumeral_2Enode_2E0: u ).

thf(c_2Eenumeral_2Enode_2E3,type,
    c_2Eenumeral_2Enode_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ent_2E0,type,
    c_2Eenumeral_2Ent_2E0: u ).

thf(c_2Eenumeral_2Eonebl_2E0,type,
    c_2Eenumeral_2Eonebl_2E0: u ).

thf(c_2Eenumeral_2Eonebl_2E3,type,
    c_2Eenumeral_2Eonebl_2E3: du > du > du > u ).

thf(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
    c_2EternaryComparisons_2Eordering__CASE_2E0: u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
    c_2EternaryComparisons_2Eordering__CASE_2E4: du > du > du > du > u ).

thf(c_2Eenumeral_2Esdiff_2E0,type,
    c_2Eenumeral_2Esdiff_2E0: u ).

thf(c_2Eenumeral_2Esdiff_2E3,type,
    c_2Eenumeral_2Esdiff_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Esinter_2E0,type,
    c_2Eenumeral_2Esinter_2E0: u ).

thf(c_2Eenumeral_2Esinter_2E3,type,
    c_2Eenumeral_2Esinter_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Esmerge_2E0,type,
    c_2Eenumeral_2Esmerge_2E0: u ).

thf(c_2Eenumeral_2Esmerge_2E3,type,
    c_2Eenumeral_2Esmerge_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Esmerge__out_2E0,type,
    c_2Eenumeral_2Esmerge__out_2E0: u ).

thf(c_2Eenumeral_2Esmerge__out_2E3,type,
    c_2Eenumeral_2Esmerge__out_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ezerbl_2E0,type,
    c_2Eenumeral_2Ezerbl_2E0: u ).

thf(c_2Eenumeral_2Ezerbl_2E1,type,
    c_2Eenumeral_2Ezerbl_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o > $o ) > $o > $o > $o > $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_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ) > mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

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_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_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_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).

thf(mono_2Ec_2EternaryComparisons_2EEQUAL,type,
    mono_2Ec_2EternaryComparisons_2EEQUAL: mono_2Etyop_2EternaryComparisons_2Eordering ).

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

thf(mono_2Ec_2EternaryComparisons_2EGREATER,type,
    mono_2Ec_2EternaryComparisons_2EGREATER: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2ELESS,type,
    mono_2Ec_2EternaryComparisons_2ELESS: mono_2Etyop_2EternaryComparisons_2Eordering ).

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_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_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

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

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

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

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( $o > $o > $o > $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_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ) > u ).

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

thf(i_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    i_mono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > u ).

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

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

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > $o > $o > $o > $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_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

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

thf(j_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    j_mono_2Etyop_2EternaryComparisons_2Eordering: du > mono_2Etyop_2EternaryComparisons_2Eordering ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ 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_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ 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_2EternaryComparisons_2Eordering,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ).

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

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

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

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: $o > $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_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_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_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_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ 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_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eenumeral_2Ebt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( ( s @ A_27a @ X0_2E0 )
        = ( s @ A_27a @ X1_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EBL__ACCUM_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ c_2Eenumeral_2EBL__ACCUM_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EBL__CONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__CONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) @ c_2Eenumeral_2EBL__CONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDIFF_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_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EENUMERAL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2EENUMERAL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_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 ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

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

thf(arityeq2_2Ec_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_2EINTER_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_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2EK2_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2EK2_2E1 @ ( s @ A_27a @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ c_2Eenumeral_2EK2_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2ELESS__ALL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2ELESS__ALL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EOL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2EOL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EOL__bt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2EOL__bt_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EOL__bt__lb_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2EOL__bt__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2EOL__bt__lb__ub_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eenumeral_2EOL__bt__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EOL__bt__ub_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2EOL__bt__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EOL__sublists_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2EOL__sublists_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EOU_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( 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 @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eenumeral_2EOU_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EOWL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2EOWL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Eenumeral_2Ebt_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_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29_29_20mono_2Etyop_2Eenumeral_2Ebl_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_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EUNION_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_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EUO_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EUO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( 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 @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eenumeral_2EUO_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_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_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ 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_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Erelation_2EWFREC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2Eapto_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2Ebl__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ X3_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) @ c_2Eenumeral_2Ebl__CASE_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ebl__rev_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Eenumeral_2Ebl__rev_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ c_2Eenumeral_2Ebl__rev_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebl__rev_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ c_2Eenumeral_2Ebl__rev_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebl__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Eenumeral_2Ebl__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ebl__to__bt_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( c_2Eenumeral_2Ebl__to__bt_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ ( tyop_2Eenumeral_2Ebt @ A_27c ) ) @ c_2Eenumeral_2Ebl__to__bt_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebl__to__set_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Eenumeral_2Ebl__to__set_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ X2_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) @ c_2Eenumeral_2Ebt__CASE_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebt__rev_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) @ c_2Eenumeral_2Ebt__rev_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebt__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Eenumeral_2Ebt__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ebt__to__bl_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__bl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ c_2Eenumeral_2Ebt__to__bl_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ebt__to__list_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eenumeral_2Ebt__to__list_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebt__to__list__ac_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Eenumeral_2Ebt__to__list__ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebt__to__ol_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Eenumeral_2Ebt__to__ol_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__ac_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__lb_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__lb__ac_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__lb__ub_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X4_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__ub_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__ub__ac_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__to__set__lb_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eenumeral_2Ebt__to__set__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Eenumeral_2Ebt__to__set__lb__ub_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Eenumeral_2Ebt__to__set__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Ebt__to__set__ub_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eenumeral_2Ebt__to__set__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Eincr__sbuild_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__sbuild_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eenumeral_2Eincr__sbuild_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Eincr__smerge_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ c_2Eenumeral_2Eincr__smerge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Eincr__ssort_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Eincr__ssort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Eenumeral_2Eincr__ssort_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( 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 @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Elist_2Elist__CASE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elist__to__bl_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ c_2Eenumeral_2Elist__to__bl_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elist__to__bl_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Eenumeral_2Ebl @ A_27c ) ) @ c_2Eenumeral_2Elist__to__bl_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ c_2Eenumeral_2Elist__to__bt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Eenumeral_2Ebt @ A_27c ) ) @ c_2Eenumeral_2Elist__to__bt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elol__set_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2Elol__set_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ c_2Eenumeral_2Enode_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ c_2Eenumeral_2Eonebl_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( 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 @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Esdiff_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Esdiff_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Esinter_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Esinter_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Esmerge_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Esmerge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Esmerge__out_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eenumeral_2Esmerge__out_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ c_2Eenumeral_2Ezerbl_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ X0_2E0 ) ) ) ) ).

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

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_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_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o,V2: $o,V3: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 @ V3 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V3 ) ) ) ) ) ).

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

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( 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_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Eenumeral_2Ebl__TY__DEF,axiom,
    ! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V10n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10n ) ) ) )
          = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
     => ( ! [V6n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) )
            = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
       => ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
              ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
              = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
         => ( ! [V1a0_27_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V1a0_27_2E0 ) ) ) )
              <=> ! [V2_27bl_27_2E0: u] :
                    ( ! [V3a0_27_2E0: u] :
                        ( ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V3a0_27_2E0 )
                            = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F1_2E0 ) ) ) )
                          | ? [V5a_2E0: u] :
                              ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V3a0_27_2E0 )
                                = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V5a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F2_2E0 ) ) ) ) ) )
                              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27bl_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V5a_2E0 ) ) ) ) )
                          | ? [V7a0_2E0: u,V8a1_2E0: u,V9a2_2E0: u] :
                              ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V3a0_27_2E0 )
                                = ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V9a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ F3_2E0 ) ) ) ) ) )
                              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27bl_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V9a2_2E0 ) ) ) ) ) )
                       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27bl_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V3a0_27_2E0 ) ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27bl_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ V1a0_27_2E0 ) ) ) ) ) )
           => ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0v_2E0: u,V1f_2E0: u,V2f1_2E0: u] :
          ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V2f1_2E0 ) ) )
          = ( s @ A_27b @ V0v_2E0 ) )
      & ! [V3a_2E0: u,V4v_2E0: u,V5f_2E0: u,V6f1_2E0: u] :
          ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V3a_2E0 ) ) ) @ ( s @ A_27b @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V5f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V6f1_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V5f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V3a_2E0 ) ) ) )
      & ! [V7a0_2E0: u,V8a1_2E0: u,V9a2_2E0: u,V10v_2E0: u,V11f_2E0: u,V12f1_2E0: u] :
          ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V7a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V9a2_2E0 ) ) ) @ ( s @ A_27b @ V10v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V11f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V12f1_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V12f1_2E0 ) @ ( s @ A_27a @ V7a0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V9a2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) )
          = mono_2Ec_2Enum_2E0 )
      & ! [V1f_2E0: u,V2a_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2a_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2a_2E0 ) ) ) ) ) )
      & ! [V3f_2E0: u,V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6a2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebl__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6a2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__TY__DEF,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V8n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) )
          = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
     => ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
            = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
       => ( ! [V1a0_27_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V1a0_27_2E0 ) ) ) )
            <=> ! [V2_27bt_27_2E0: u] :
                  ( ! [V3a0_27_2E0: u] :
                      ( ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                          = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F1_2E0 ) ) ) )
                        | ? [V5a0_2E0: u,V6a1_2E0: u,V7a2_2E0: u] :
                            ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                              = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ A_27a @ V6a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V5a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V7a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F2_2E0 ) ) ) ) ) ) ) )
                            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27bt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V5a0_2E0 ) ) ) )
                            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27bt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V7a2_2E0 ) ) ) ) ) )
                     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27bt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 ) ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27bt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V1a0_27_2E0 ) ) ) ) ) )
         => ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
          = mono_2Ec_2Enum_2E0 )
      & ! [V1f_2E0: u,V2a0_2E0: u,V3a1_2E0: u,V4a2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a0_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4a2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a0_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2Ebt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4a2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EBL__ACCUM,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1ac_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) )
      & ! [V2a_2E0: u,V3ac_2E0: u,V4bl_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4bl_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4bl_2E0 ) ) ) )
      & ! [V5a_2E0: u,V6ac_2E0: u,V7r_2E0: u,V8rft_2E0: u,V9bl_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V7r_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8rft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V9bl_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6ac_2E0 ) @ ( s @ A_27a @ V7r_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8rft_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V9bl_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EBL__CONS,axiom,
    ! [A_27a: d,V0a_2E0: u,V1bl_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__CONS_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1bl_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__ACCUM_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1bl_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2Elist__to__bl,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) )
      & ! [V0a_2E0: u,V1l_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2EBL__CONS_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__list,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V0l_2E0: u,V1x_2E0: u,V2r_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0l_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__list__ac,axiom,
    ! [A_27a: d] :
      ( ! [V0m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0m_2E0 ) )
      & ! [V1l_2E0: u,V2x_2E0: u,V3r_2E0: u,V4m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1l_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__rev,axiom,
    ! [A_27a: d] :
      ( ! [V0bl_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0bl_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0bl_2E0 ) )
      & ! [V1lft_2E0: u,V2r_2E0: u,V3rft_2E0: u,V4bl_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1lft_2E0 ) @ ( s @ A_27a @ V2r_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3rft_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4bl_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1lft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V2r_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3rft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4bl_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EK2,axiom,
    ! [A_27a: d,V0a_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Eenumeral_2EK2_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) )
      = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ).

thf(thm_2Eenumeral_2Ebl__rev,axiom,
    ! [A_27a: d] :
      ( ! [V0ft_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0ft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0ft_2E0 ) )
      & ! [V1ft_2E0: u,V2b_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1ft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1ft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) )
      & ! [V3ft_2E0: u,V4a_2E0: u,V5f_2E0: u,V6b_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3ft_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6b_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Ebl__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3ft_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6b_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__to__bt,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ c_2Eenumeral_2Ebl__to__bt_2E0 )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( c_2Eenumeral_2Ebl__rev_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__bl,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__bl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0t_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ebt__rev_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2Elist__to__bt,axiom,
    ! [A_27c: d,V0l_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V0l_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27c ) @ ( c_2Eenumeral_2Ebl__to__bt_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27c ) @ ( c_2Eenumeral_2Elist__to__bl_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ V0l_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1cmp_2E0: u,V2a_2E0: u,V3l_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) )
            & ! [V4p_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) ) )
               => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ A_27a @ V4p_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ) ).

thf(thm_2Eenumeral_2Elol__set__primitive,axiom,
    ! [A_27a: d,F0_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V0R_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
            & ! [V1lol_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) ) ) )
            & ! [V2m_2E0: u,V3lol_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) ) ) ) ) )
     => ( ! [V4lol__set_2E0: u,V7lol_2E0: u,V8m_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V7lol_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V7lol_2E0 ) ) ) ) ) ) ) )
       => ( ! [V4lol__set_2E0: u,V6v_2E0: u,V7lol_2E0: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V6v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V7lol_2E0 ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V6v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V7lol_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V7lol_2E0 ) ) ) ) ) )
         => ( ! [V4lol__set_2E0: u,V5a_2E0: u] :
                ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V5a_2E0 ) ) )
                = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V5a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4lol__set_2E0 ) ) ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2Elol__set_2E0 )
              = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eincr__sbuild,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__sbuild_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1cmp_2E0: u,V2x_2E0: u,V3l_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__sbuild_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__sbuild_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eincr__ssort,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Eincr__ssort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__sbuild_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__set,axiom,
    ! [A_27a: d,F3_2E0: u,F1_2E0: u,F2_2E0: u,F0_2E0: u] :
      ( ! [V6z_2E0: u,V1cmp_2E0: u,V4r_2E0: u,V3x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V6z_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V6z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V6z_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V1cmp_2E0: u,V4r_2E0: u,V3x_2E0: u,V6z_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V6z_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6z_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V6z_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
       => ( ! [V5y_2E0: u,V1cmp_2E0: u,V2l_2E0: u,V3x_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) ) ) )
                & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
         => ( ! [V1cmp_2E0: u,V2l_2E0: u,V3x_2E0: u,V5y_2E0: u] :
                ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V5y_2E0 ) ) )
                = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
           => ( ! [V0cmp_2E0: u] :
                  ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
                  = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
              & ! [V1cmp_2E0: u,V2l_2E0: u,V3x_2E0: u,V4r_2E0: u] :
                  ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) )
                  = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__set__lb,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3x_2E0: u,V0cmp_2E0: u,V2t_2E0: u,V1lb_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) ) ) )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V0cmp_2E0: u,V2t_2E0: u,V1lb_2E0: u,V3x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1lb_2E0: u,V2t_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__set__ub,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3x_2E0: u,V0cmp_2E0: u,V1t_2E0: u,V2ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) ) ) )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V0cmp_2E0: u,V1t_2E0: u,V2ub_2E0: u,V3x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1t_2E0: u,V2ub_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__set__lb__ub,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V4x_2E0: u,V0cmp_2E0: u,V2t_2E0: u,V1lb_2E0: u,V3ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) ) ) )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V0cmp_2E0: u,V2t_2E0: u,V1lb_2E0: u,V3ub_2E0: u,V4x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1lb_2E0: u,V2t_2E0: u,V3ub_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebt__to__set__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) @ ( s @ A_27a @ V3ub_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__lb__ub,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V3cmp_2E0: u,V4lb_2E0: u,V6x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u,V2ub_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V3cmp_2E0: u,V4lb_2E0: u,V5l_2E0: u,V6x_2E0: u,V7r_2E0: u,V8ub_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__lb,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2cmp_2E0: u,V3lb_2E0: u,V5x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ A_27a @ V3lb_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V2cmp_2E0: u,V3lb_2E0: u,V4l_2E0: u,V5x_2E0: u,V6r_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ A_27a @ V3lb_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__ub,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2cmp_2E0: u,V4x_2E0: u,V6ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1ub_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V1ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5r_2E0: u,V6ub_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1cmp_2E0: u,V2l_2E0: u,V3x_2E0: u,V4r_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__lb__ub__ac,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V4cmp_2E0: u,V5lb_2E0: u,V7x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u,V2ub_2E0: u,V3m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3m_2E0 ) )
        & ! [V4cmp_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7x_2E0: u,V8r_2E0: u,V9ub_2E0: u,V10m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6l_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8r_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6l_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8r_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6l_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8r_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__lb__ac,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V3cmp_2E0: u,V4lb_2E0: u,V6x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u,V2m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) )
        & ! [V3cmp_2E0: u,V4lb_2E0: u,V5l_2E0: u,V6x_2E0: u,V7r_2E0: u,V8m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__ub__ac,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V3cmp_2E0: u,V5x_2E0: u,V7ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V7ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27a @ V7ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1ub_2E0: u,V2m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V1ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5x_2E0: u,V6r_2E0: u,V7ub_2E0: u,V8m_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) @ ( s @ A_27a @ V7ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V7ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) @ ( s @ A_27a @ V7ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V7ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__ac,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u,V1m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1m_2E0 ) )
      & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5r_2E0: u,V6m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOWL,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOU,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3x_2E0: u,V1t_2E0: u,V2u_2E0: u,V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) )
            & ! [V4z_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) )
               => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) )
     => ( ! [V1t_2E0: u,V2u_2E0: u,V0cmp_2E0: u,V3x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1t_2E0: u,V2u_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EUO,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3y_2E0: u,V2t_2E0: u,V1s_2E0: u,V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) ) )
            & ! [V4z_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) )
               => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) )
     => ( ! [V2t_2E0: u,V1s_2E0: u,V0cmp_2E0: u,V3y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1s_2E0: u,V2t_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EUO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2ELESS__ALL,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) )
    <=> ! [V3y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ).

thf(thm_2Eenumeral_2Ebl__to__set,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V7y_2E0: u,V3cmp_2E0: u,V5t_2E0: u,V4x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) ) ) ) ) )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V3cmp_2E0: u,V5t_2E0: u,V4x_2E0: u,V7y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V7y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) )
       => ( ! [V0cmp_2E0: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
          & ! [V1cmp_2E0: u,V2b_2E0: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) )
          & ! [V3cmp_2E0: u,V4x_2E0: u,V5t_2E0: u,V6b_2E0: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6b_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5t_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Ebl__to__set_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V6b_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__lb__ub,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u,V1lb_2E0: u,V2ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
      & ! [V3cmp_2E0: u,V4lb_2E0: u,V5l_2E0: u,V6x_2E0: u,V7r_2E0: u,V8ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5l_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7r_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__lb,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u,V1lb_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V2cmp_2E0: u,V3lb_2E0: u,V4l_2E0: u,V5x_2E0: u,V6r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__ub,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u,V1ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V1ub_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5r_2E0: u,V6ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1cmp_2E0: u,V2l_2E0: u,V3x_2E0: u,V4r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__distinct,axiom,
    ! [A_27a: d,V0a2_2E0: u,V1a1_2E0: u,V2a0_2E0: u] :
      ( (~)
      @ ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 )
        = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a0_2E0 ) @ ( s @ A_27a @ V1a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0a2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__nchotomy,axiom,
    ! [A_27a: d,V0bb_2E0: u] :
      ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0bb_2E0 )
        = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) )
      | ? [V1b_2E0: u,V2a_2E0: u,V3b0_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0bb_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1b_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3b0_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u] :
    ? [V2fn_2E0: u] :
      ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ V2fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
        = ( s @ A_27b @ V0f0_2E0 ) )
      & ! [V3a0_2E0: u,V4a1_2E0: u,V5a2_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ V2fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a0_2E0 ) @ ( s @ A_27a @ V4a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a2_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) ) @ V1f1_2E0 ) @ ( s @ A_27a @ V4a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a2_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ V2fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ V2fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V1b_2E0: u,V2b0_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1b_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2b0_2E0 ) ) ) ) )
           => ! [V3a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1b_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2b0_2E0 ) ) ) ) ) ) ) )
     => ! [V4b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4b_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f_27_2E0: u,V2M_2E0: u,V3M_27_2E0: u,V4v_2E0: u,V5f_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2M_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3M_27_2E0 ) )
        & ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3M_27_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) )
         => ( ( s @ A_27b @ V4v_2E0 )
            = ( s @ A_27b @ V0v_27_2E0 ) ) )
        & ! [V6a0_2E0: u,V7a1_2E0: u,V8a2_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3M_27_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a0_2E0 ) @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a2_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a0_2E0 ) ) ) @ ( s @ A_27a @ V7a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a2_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V1f_27_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a0_2E0 ) ) ) @ ( s @ A_27a @ V7a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V8a2_2E0 ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2M_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V5f_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3M_27_2E0 ) @ ( s @ A_27b @ V0v_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V1f_27_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f_2E0: u] :
      ( ( ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V3f_2E0 ) ) )
        = ( s @ A_27b @ V1v_27_2E0 ) )
    <=> ( ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0x_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) )
          & ( ( s @ A_27b @ V2v_2E0 )
            = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V4b_2E0: u,V5a_2E0: u,V6b0_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4b_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6b0_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4b_2E0 ) ) ) @ ( s @ A_27a @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6b0_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Edatatype__bl,axiom,
    ! [A_27a: d,V0bl_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0bl_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) @ c_2Eenumeral_2Ezerbl_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Eenumeral_2Ebl @ A_27a ) ) ) ) @ c_2Eenumeral_2Eonebl_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a_27_2E0: u] :
          ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0a_2E0 ) ) )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1a_27_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0a_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1a_27_2E0 ) ) )
      & ! [V2a0_2E0: u,V3a1_2E0: u,V4a2_2E0: u,V5a0_27_2E0: u,V6a1_27_2E0: u,V7a2_27_2E0: u] :
          ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a2_2E0 ) ) )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V5a0_27_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a1_27_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a2_27_2E0 ) ) ) )
        <=> ( ( ( s @ A_27a @ V2a0_2E0 )
              = ( s @ A_27a @ V5a0_27_2E0 ) )
            & ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a1_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a1_27_2E0 ) )
            & ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a2_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a2_27_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__distinct,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0a_2E0 ) ) ) ) )
      & ! [V1a2_2E0: u,V2a1_2E0: u,V3a0_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V3a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1a2_2E0 ) ) ) ) )
      & ! [V4a2_2E0: u,V5a1_2E0: u,V6a0_2E0: u,V7a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a_2E0 ) ) )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V6a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a2_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__nchotomy,axiom,
    ! [A_27a: d,V0bb_2E0: u] :
      ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0bb_2E0 )
        = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) )
      | ? [V1b_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0bb_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1b_2E0 ) ) ) )
      | ? [V2a_2E0: u,V3b0_2E0: u,V4b_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0bb_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3b0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4b_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
    ? [V3fn_2E0: u] :
      ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) )
        = ( s @ A_27b @ V0f0_2E0 ) )
      & ! [V4a_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4a_2E0 ) ) ) ) ) )
      & ! [V5a0_2E0: u,V6a1_2E0: u,V7a2_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V5a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a2_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V2f2_2E0 ) @ ( s @ A_27a @ V5a0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V6a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a2_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V7a2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) )
        & ! [V1b_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1b_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V1b_2E0 ) ) ) ) ) ) )
        & ! [V2b_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) )
           => ! [V3b0_2E0: u,V4a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3b0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V2b_2E0 ) ) ) ) ) ) ) )
     => ! [V5b_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V5b_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f1_27_2E0: u,V2f_27_2E0: u,V3M_2E0: u,V4M_27_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V3M_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4M_27_2E0 ) )
        & ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4M_27_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) )
         => ( ( s @ A_27b @ V5v_2E0 )
            = ( s @ A_27b @ V0v_27_2E0 ) ) )
        & ! [V8a_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4M_27_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V8a_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V8a_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V2f_27_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V8a_2E0 ) ) ) ) )
        & ! [V9a0_2E0: u,V10a1_2E0: u,V11a2_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4M_27_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V9a0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V10a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V11a2_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V7f1_2E0 ) @ ( s @ A_27a @ V9a0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V10a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V11a2_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V1f1_27_2E0 ) @ ( s @ A_27a @ V9a0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V10a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V11a2_2E0 ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V3M_2E0 ) @ ( s @ A_27b @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V7f1_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V4M_27_2E0 ) @ ( s @ A_27b @ V0v_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V2f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V1f1_27_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebl__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f1_2E0: u,V4f_2E0: u] :
      ( ( ( s @ A_27b @ ( c_2Eenumeral_2Ebl__CASE_2E4 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V3f1_2E0 ) ) )
        = ( s @ A_27b @ V1v_27_2E0 ) )
    <=> ( ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0x_2E0 )
            = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ c_2Eenumeral_2Enbl_2E0 ) )
          & ( ( s @ A_27b @ V2v_2E0 )
            = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V5b_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V5b_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V5b_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V6a_2E0: u,V7b0_2E0: u,V8b_2E0: u] :
            ( ( ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7b0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V8b_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ A_27b ) ) ) @ V3f1_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V7b0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ A_27a ) @ V8b_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__11,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a0_27_2E0: u,V4a1_27_2E0: u,V5a2_27_2E0: u] :
      ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0a0_2E0 ) @ ( s @ A_27a @ V1a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a2_2E0 ) ) )
        = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a0_27_2E0 ) @ ( s @ A_27a @ V4a1_27_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a2_27_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0a0_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3a0_27_2E0 ) )
        & ( ( s @ A_27a @ V1a1_2E0 )
          = ( s @ A_27a @ V4a1_27_2E0 ) )
        & ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a2_2E0 )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5a2_27_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2Edatatype__bt,axiom,
    ! [A_27a: d,V0bt_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0bt_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) ) @ c_2Eenumeral_2Enode_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0v_2E0: u,V1f_2E0: u] :
          ( ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V1f_2E0 ) ) )
          = ( s @ A_27b @ V0v_2E0 ) )
      & ! [V2a0_2E0: u,V3a1_2E0: u,V4a2_2E0: u,V5v_2E0: u,V6f_2E0: u] :
          ( ( s @ A_27b @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a0_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4a2_2E0 ) ) ) @ ( s @ A_27b @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V6f_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ A_27b ) ) ) @ V6f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2a0_2E0 ) ) ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4a2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__list__thm,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0t_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2Esmerge__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3x_2E0: u,V4l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V5cmp_2E0: u,V6y_2E0: u,V7m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7m_2E0 ) ) ) ) ) )
        & ! [V8cmp_2E0: u,V9x_2E0: u,V10l_2E0: u,V11y_2E0: u,V12m_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V15v2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esmerge,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1x_2E0: u,V2l_2E0: u,V3cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
      & ! [V4y_2E0: u,V5m_2E0: u,V6cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) )
      & ! [V7y_2E0: u,V8x_2E0: u,V9m_2E0: u,V10l_2E0: u,V11cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esmerge__nil,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) )
      & ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ).

thf(thm_2Eenumeral_2Esmerge__OL,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u,V2m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__sublists__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) ) ) ) )
        & ! [V4cmp_2E0: u,V5m_2E0: u,V6lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__sublists,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1lol_2E0: u,V2cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) ) )
      & ! [V3m_2E0: u,V4lol_2E0: u,V5cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V4lol_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3m_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V4lol_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Elol__set__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V1lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) ) ) ) )
        & ! [V2m_2E0: u,V3lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V3lol_2E0 ) ) ) ) ) ) ) )
     => ! [V4v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V4v_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Elol__set,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
      & ! [V0lol_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V0lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V0lol_2E0 ) ) ) )
      & ! [V1m_2E0: u,V2lol_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1m_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2Elol__set_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eincr__smerge__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5lol_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V5lol_2E0 ) ) ) ) ) )
        & ! [V6cmp_2E0: u,V7l_2E0: u,V8m_2E0: u,V9lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V9lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V9lol_2E0 ) ) ) ) ) ) ) )
     => ! [V10v_2E0: u,V11v1_2E0: u,V12v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V10v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V11v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V12v2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eincr__smerge,axiom,
    ! [A_27a: d] :
      ( ! [V0l_2E0: u,V1cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
      & ! [V2lol_2E0: u,V3l_2E0: u,V4cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) )
      & ! [V5m_2E0: u,V6lol_2E0: u,V7l_2E0: u,V8cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eincr__smerge__OL,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1lol_2E0: u,V2l_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Eenumeral_2Eincr__smerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1lol_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esmerge__out__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V5lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V5lol_2E0 ) ) ) ) ) ) )
        & ! [V6cmp_2E0: u,V7l_2E0: u,V8m_2E0: u,V9lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V9lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V9lol_2E0 ) ) ) ) ) ) ) )
     => ! [V10v_2E0: u,V11v1_2E0: u,V12v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V10v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V11v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V12v2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esmerge__out,axiom,
    ! [A_27a: d] :
      ( ! [V0l_2E0: u,V1cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) )
      & ! [V2lol_2E0: u,V3l_2E0: u,V4cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V2lol_2E0 ) ) ) )
      & ! [V5m_2E0: u,V6lol_2E0: u,V7l_2E0: u,V8cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V6lol_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2EIN__bt__to__set,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u,V1y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF )
      & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5r_2E0: u,V6y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) ) ) ) ) ) ) )
        <=> ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V3l_2E0 ) ) ) ) ) )
              & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
                = mono_2Ec_2EternaryComparisons_2ELESS ) )
            | ( ( s @ A_27a @ V6y_2E0 )
              = ( s @ A_27a @ V4x_2E0 ) )
            | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
              & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) )
                = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ) ).

thf(thm_2Eenumeral_2ENOT__IN__nt,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1y_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) ) ) ) )
      = mono_2Ec_2Ebool_2EF ) ).

thf(thm_2Eenumeral_2EIN__node,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2l_2E0: u,V3y_2E0: u,V4r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) )
      = ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) ) ) ) @ mono_2Ec_2Ebool_2ET @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eol__set,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__to__ol__lb__ub,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u,V2lb_2E0: u,V3ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__to__ol__lb,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u,V2lb_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__to__ol__ub,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u,V2ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__bt__to__ol,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOWL__bt__to__ol,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EEMPTY__OU,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1sl_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1sl_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1sl_2E0 ) ) ).

thf(thm_2Eenumeral_2EOU__EMPTY,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ).

thf(thm_2Eenumeral_2ELESS__UO__LEM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2y_2E0: u,V3s_2E0: u] :
      ( ! [V4z_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EUO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3s_2E0 ) ) ) ) ) )
         => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
    <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
        = mono_2Ec_2EternaryComparisons_2ELESS ) ) ).

thf(thm_2Eenumeral_2ELESS__ALL__OU,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1x_2E0: u,V2u_2E0: u,V3v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3v_2E0 ) ) ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2u_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3v_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOU__ASSOC,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1a_2E0: u,V2b_2E0: u,V3c_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2b_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3c_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3c_2E0 ) ) ) ) ).

thf(thm_2Eenumeral_2ELESS__ALL__UO__LEM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1a_2E0: u,V2s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EUO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2ELESS__ALL__OU__UO__LEM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1a_2E0: u,V2s_2E0: u,V3t_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EUO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EOU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebt__to__ol__ID__IMP,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ).

thf(thm_2Eenumeral_2EOL__UNION__IMP,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esinter__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3x_2E0: u,V4l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V5cmp_2E0: u,V6y_2E0: u,V7m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7m_2E0 ) ) ) ) ) )
        & ! [V8cmp_2E0: u,V9x_2E0: u,V10l_2E0: u,V11y_2E0: u,V12m_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V15v2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esinter,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1x_2E0: u,V2l_2E0: u,V3cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V4y_2E0: u,V5m_2E0: u,V6cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V7y_2E0: u,V8x_2E0: u,V9m_2E0: u,V10l_2E0: u,V11cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__INTER__IMP,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esdiff__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3x_2E0: u,V4l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V5cmp_2E0: u,V6y_2E0: u,V7m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7m_2E0 ) ) ) ) ) )
        & ! [V8cmp_2E0: u,V9x_2E0: u,V10l_2E0: u,V11y_2E0: u,V12m_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ A_27a @ V11y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12m_2E0 ) ) ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V15v2_2E0 ) ) ) ) ) ).

thf(thm_2Eenumeral_2Esdiff,axiom,
    ! [A_27a: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1x_2E0: u,V2l_2E0: u,V3cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
      & ! [V4y_2E0: u,V5m_2E0: u,V6cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V7y_2E0: u,V8x_2E0: u,V9m_2E0: u,V10l_2E0: u,V11cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__DIFF__IMP,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EENUMERAL__set,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Eincr__ssort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOL__ENUMERAL,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOWL__UNION__THM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esmerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOWL__INTER__THM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esinter_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2EOWL__DIFF__THM,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Esdiff_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Ebetter__bt__to__ol,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1t_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Ebt__to__ol__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V1t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ).

thf(thm_2Eenumeral_2Eset__OWL__thm,axiom,
    ! [A_27a: d,V0cmp_2E0: u,V1l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eenumeral_2Eincr__ssort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ).

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