ITP001 Axioms: ITP086_7.ax
%------------------------------------------------------------------------------
% File : ITP086_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ordinal.ax [Gau19]
% : HL4086_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 504 ( 175 unt; 174 typ; 0 def)
% Number of atoms : 692 ( 332 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 443 ( 81 ~; 15 |; 131 &)
% ( 72 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 128 ( 85 >; 43 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 170 ( 170 usr; 17 con; 0-5 aty)
% Number of variables : 1189 ( 995 !; 28 ?;1189 :)
% ( 166 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Eordinal_2Eordinal,type,
tyop_2Eordinal_2Eordinal: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).
tff(tyop_2Ewellorder_2Ewellorder,type,
tyop_2Ewellorder_2Ewellorder: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : 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))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Epred__set_2EBIGUNION_2E0,type,
c_2Epred__set_2EBIGUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EBIGUNION_2E1,type,
c_2Epred__set_2EBIGUNION_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EBIJ_2E0,type,
c_2Epred__set_2EBIJ_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EBIJ_2E3,type,
c_2Epred__set_2EBIJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epred__set_2EDELETE_2E0,type,
c_2Epred__set_2EDELETE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDELETE_2E2,type,
c_2Epred__set_2EDELETE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a) ).
tff(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > A_27a ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EPSUBSET_2E0,type,
c_2Epred__set_2EPSUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EPSUBSET_2E2,type,
c_2Epred__set_2EPSUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2EQUOTIENT_2E0,type,
c_2Equotient_2EQUOTIENT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Equotient_2EQUOTIENT_2E3,type,
c_2Equotient_2EQUOTIENT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Eordinal_2EallOrds_2E0,type,
c_2Eordinal_2EallOrds_2E0:
!>[A_27a: $tType] : tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Ecardinal_2Ecardeq_2E0,type,
c_2Ecardinal_2Ecardeq_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardeq_2E2,type,
c_2Ecardinal_2Ecardeq_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecardinal_2Ecardleq_2E0,type,
c_2Ecardinal_2Ecardleq_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardleq_2E2,type,
c_2Ecardinal_2Ecardleq_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Ecountable_2E0,type,
c_2Epred__set_2Ecountable_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2Ecountable_2E1,type,
c_2Epred__set_2Ecountable_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Eordinal_2Edclose_2E0,type,
c_2Eordinal_2Edclose_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eordinal_2Edclose_2E1,type,
c_2Eordinal_2Edclose_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Eordinal_2Edownward__closed_2E0,type,
c_2Eordinal_2Edownward__closed_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Eordinal_2Edownward__closed_2E1,type,
c_2Eordinal_2Edownward__closed_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2EelsOf_2E0,type,
c_2Ewellorder_2EelsOf_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2EelsOf_2E1,type,
c_2Ewellorder_2EelsOf_2E1:
!>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eordinal_2Eepsilon0_2E0,type,
c_2Eordinal_2Eepsilon0_2E0:
!>[A_27a: $tType] : tyop_2Eordinal_2Eordinal(A_27a) ).
tff(c_2Eordinal_2Eeval__poly_2E0,type,
c_2Eordinal_2Eeval__poly_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2Eeval__poly_2E2,type,
c_2Eordinal_2Eeval__poly_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EfromNat_2E0,type,
c_2Eordinal_2EfromNat_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2EfromNat_2E1,type,
c_2Eordinal_2EfromNat_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2Eis__polyform_2E0,type,
c_2Eordinal_2Eis__polyform_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool)) ).
tff(c_2Eordinal_2Eis__polyform_2E2,type,
c_2Eordinal_2Eis__polyform_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eset__relation_2Emaximal__elements_2E0,type,
c_2Eset__relation_2Emaximal__elements_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eset__relation_2Emaximal__elements_2E2,type,
c_2Eset__relation_2Emaximal__elements_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eordinal_2Eoleast_2E0,type,
c_2Eordinal_2Eoleast_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2Eoleast_2E1,type,
c_2Eordinal_2Eoleast_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2Eomax_2E0,type,
c_2Eordinal_2Eomax_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2Eomax_2E1,type,
c_2Eordinal_2Eomax_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(c_2Eordinal_2Eomega_2E0,type,
c_2Eordinal_2Eomega_2E0:
!>[A_27a: $tType] : tyop_2Eordinal_2Eordinal(A_27a) ).
tff(c_2Eordinal_2EordADD_2E0,type,
c_2Eordinal_2EordADD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2EordADD_2E1,type,
c_2Eordinal_2EordADD_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(c_2Eordinal_2EordADD_2E2,type,
c_2Eordinal_2EordADD_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EordDIV_2E0,type,
c_2Eordinal_2EordDIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2EordDIV_2E2,type,
c_2Eordinal_2EordDIV_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EordEXP_2E0,type,
c_2Eordinal_2EordEXP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2EordEXP_2E1,type,
c_2Eordinal_2EordEXP_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(c_2Eordinal_2EordEXP_2E2,type,
c_2Eordinal_2EordEXP_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EordMOD_2E0,type,
c_2Eordinal_2EordMOD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2EordMOD_2E2,type,
c_2Eordinal_2EordMOD_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EordMULT_2E0,type,
c_2Eordinal_2EordMULT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ).
tff(c_2Eordinal_2EordMULT_2E1,type,
c_2Eordinal_2EordMULT_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(c_2Eordinal_2EordMULT_2E2,type,
c_2Eordinal_2EordMULT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2EordSUC_2E0,type,
c_2Eordinal_2EordSUC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2EordSUC_2E1,type,
c_2Eordinal_2EordSUC_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Ewellorder_2Eorderiso_2E0,type,
c_2Ewellorder_2Eorderiso_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2Eorderiso_2E1,type,
c_2Ewellorder_2Eorderiso_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool) ) ).
tff(c_2Ewellorder_2Eorderiso_2E2,type,
c_2Ewellorder_2Eorderiso_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2Eorderlt_2E0,type,
c_2Ewellorder_2Eorderlt_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2Eorderlt_2E2,type,
c_2Ewellorder_2Eorderlt_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ewellorder_2Ewellorder(A_27a) * tyop_2Ewellorder_2Ewellorder(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eordinal_2Eordinal__ABS_2E0,type,
c_2Eordinal_2Eordinal__ABS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2Eordinal__ABS_2E1,type,
c_2Eordinal_2Eordinal__ABS_2E1:
!>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2Eordinal__ABS__CLASS_2E0,type,
c_2Eordinal_2Eordinal__ABS__CLASS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2Eordinal__ABS__CLASS_2E1,type,
c_2Eordinal_2Eordinal__ABS__CLASS_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Eordinal_2Eordinal__REP_2E0,type,
c_2Eordinal_2Eordinal__REP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eordinal_2Eordinal__REP_2E1,type,
c_2Eordinal_2Eordinal__REP_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)) ) ).
tff(c_2Eordinal_2Eordinal__REP__CLASS_2E0,type,
c_2Eordinal_2Eordinal__REP__CLASS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)) ).
tff(c_2Eordinal_2Eordinal__REP__CLASS_2E1,type,
c_2Eordinal_2Eordinal__REP__CLASS_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool) ) ).
tff(c_2Eordinal_2Eordlt_2E0,type,
c_2Eordinal_2Eordlt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eordinal_2Eordlt_2E2,type,
c_2Eordinal_2Eordlt_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eordinal_2Epolyform_2E0,type,
c_2Eordinal_2Epolyform_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))))) ).
tff(c_2Eordinal_2Epolyform_2E2,type,
c_2Eordinal_2Epolyform_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eordinal_2Eordinal(A_27a) * tyop_2Eordinal_2Eordinal(A_27a) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ) ).
tff(c_2Eordinal_2Epreds_2E0,type,
c_2Eordinal_2Epreds_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eordinal_2Epreds_2E1,type,
c_2Eordinal_2Epreds_2E1:
!>[A_27a: $tType] : ( tyop_2Eordinal_2Eordinal(A_27a) > tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Eoption_2Esome_2E0,type,
c_2Eoption_2Esome_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2Esome_2E1,type,
c_2Eoption_2Esome_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Eset__relation_2Estrict_2E0,type,
c_2Eset__relation_2Estrict_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eset__relation_2Estrict_2E1,type,
c_2Eset__relation_2Estrict_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Eordinal_2Esup_2E0,type,
c_2Eordinal_2Esup_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a)) ).
tff(c_2Eordinal_2Esup_2E1,type,
c_2Eordinal_2Esup_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool) > tyop_2Eordinal_2Eordinal(A_27a) ) ).
tff(c_2Ewellorder_2Ewellorder_2E0,type,
c_2Ewellorder_2Ewellorder_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ewellorder_2Ewellorder_2E1,type,
c_2Ewellorder_2Ewellorder_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewellorder_2Ewellorder__ABS_2E0,type,
c_2Ewellorder_2Ewellorder__ABS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(A_27a)) ).
tff(c_2Ewellorder_2Ewellorder__ABS_2E1,type,
c_2Ewellorder_2Ewellorder__ABS_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).
tff(c_2Ewellorder_2Ewellorder__REP_2E0,type,
c_2Ewellorder_2Ewellorder__REP_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewellorder_2Ewellorder__REP_2E1,type,
c_2Ewellorder_2Ewellorder__REP_2E1:
!>[A_27a: $tType] : ( tyop_2Ewellorder_2Ewellorder(A_27a) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Ewellorder_2Ewobound_2E0,type,
c_2Ewellorder_2Ewobound_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a))) ).
tff(c_2Ewellorder_2Ewobound_2E2,type,
c_2Ewellorder_2Ewobound_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Ewellorder_2Ewellorder(A_27a) ) > tyop_2Ewellorder_2Ewellorder(A_27a) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(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(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),c_2Epair_2E_2C_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27b),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27b),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),c_2Emin_2E_40_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Emin_2E_40_2E0(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : ( c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),c_2Elist_2EEL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : ( c_2Elist_2EHD_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Elist_2EHD_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eordinal_2Eordinal(A_27a),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(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(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPSUBSET_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPSUBSET_2E2(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPSUBSET_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))] : ( c_2Equotient_2EQUOTIENT_2E3(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))] : ( c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Eordinal_2Eordinal(A_27a),c_2Epair_2ESND_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))] : ( c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),tyop_2Eordinal_2Eordinal(A_27b),c_2Epair_2ESND_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eoption_2Eoption(tyop_2Eordinal_2Eordinal(A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ewellorder_2Ewellorder_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Edclose_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Edclose_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Edclose_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Edownward__closed_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Edownward__closed_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eordinal_2Edownward__closed_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2EelsOf_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a))] : ( c_2Ewellorder_2EelsOf_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2EelsOf_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Eeval__poly_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : ( c_2Eordinal_2Eeval__poly_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Eeval__poly_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2EfromNat_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EfromNat_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Eis__polyform_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : ( c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool),c_2Eordinal_2Eis__polyform_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Eis__polyform_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : ( c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),c_2Eordinal_2Eis__polyform_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eset__relation_2Emaximal__elements_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Emaximal__elements_2E2(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Emaximal__elements_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eoleast_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Eoleast_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Eoleast_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eomax_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Eomax_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Eomax_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2EordADD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordADD_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2EordADD_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordADD_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2EordDIV_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordDIV_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordDIV_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2EordEXP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordEXP_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2EordEXP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordEXP_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2EordMOD_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMOD_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordMOD_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2EordMULT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordMULT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2EordMULT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2EordMULT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2EordSUC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordSUC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordSUC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a))] : ( c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2Eorderiso_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Ewellorder_2Eorderiso_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderiso_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27b)] : ( c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Ewellorder_2Eorderlt_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),c_2Ewellorder_2Eorderlt_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eordinal__ABS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Eordinal_2Eordinal__ABS_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Eordinal__ABS_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eordinal__ABS__CLASS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Eordinal__ABS__CLASS_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eordinal__REP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordinal__REP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Eordinal_2Eordinal__REP_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Eordinal__REP__CLASS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),c_2Eordinal_2Eordinal__REP__CLASS_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Eordlt_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Eordlt_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Eordlt_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27b),X1_2E0: tyop_2Eordinal_2Eordinal(A_27b)] : ( c_2Eordinal_2Eordlt_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27b),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27b),tyop_2Emin_2Ebool),c_2Eordinal_2Eordlt_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eordinal_2Epolyform_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epolyform_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))),c_2Eordinal_2Epolyform_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Epreds_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epreds_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Epreds_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone)] : ( c_2Eordinal_2Epreds_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eoption_2Esome_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Eordinal_2Eordinal(A_27a)),c_2Eoption_2Esome_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Eset__relation_2Estrict_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eordinal_2Esup_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Esup_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Esup_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ewellorder_2Ewellorder_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__ABS_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ewellorder_2Ewellorder__ABS_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),c_2Ewellorder_2Ewellorder__ABS_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Ewellorder_2Ewellorder__REP_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewellorder_2Ewellorder__REP_2E1_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a))] : ( c_2Ewellorder_2Ewellorder__REP_2E1(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),c_2Ewellorder_2Ewellorder__REP_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] : ( c_2Ewellorder_2Ewobound_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Ewellorder_2Ewellorder(A_27a)),c_2Ewellorder_2Ewobound_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ewellorder_2Ewobound_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eordinal_2Eordinal(A_27a),X1_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a))] : ( c_2Ewellorder_2Ewobound_2E2(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Ewellorder_2Ewellorder(tyop_2Eordinal_2Eordinal(A_27a))),c_2Ewellorder_2Ewobound_2E0(tyop_2Eordinal_2Eordinal(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Eordinal_2EordADD__def,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordADD_2E2(A_27a,V0b_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = V0b_2E0 )
& ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E2(A_27a,V0b_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0)) = c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V0b_2E0,V1a_2E0)) )
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( c_2Eordinal_2EordADD_2E2(A_27a,V0b_2E0,V2a_2E0) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordADD_2E1(A_27a,V0b_2E0),c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0))) ) ) ) ).
tff(thm_2Eordinal_2Eomega__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0i_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,c_2Eordinal_2EfromNat_2E1(A_27a,V0i_2E0),c_2Ebool_2ET_2E0) )
=> ( c_2Eordinal_2Eomega_2E0(A_27a) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Enum_2Enum,F0_2E0)) ) ) ).
tff(thm_2Eordinal_2Edclose__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0),V1x_2E0))
<=> ? [V2y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2y_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,V2y_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V1x_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0s_2E0),V1x_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Edclose_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Eordinal__TY__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V1c_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V1c_2E0))
<=> ? [V2r_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] :
( p(c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0,V2r_2E0))
& ( V1c_2E0 = c_2Ewellorder_2Eorderiso_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0) ) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a),F0_2E0,V0rep_2E0)) ) ).
tff(thm_2Eordinal_2Eordinal__bijections,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1r_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] :
( ? [V2r_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] :
( p(c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0,V2r_2E0))
& ( V1r_2E0 = c_2Ewellorder_2Eorderiso_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0) ) )
<=> ( c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,V1r_2E0)) = V1r_2E0 ) ) ) ).
tff(thm_2Eordinal_2Eordinal__REP__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordinal__REP_2E1(A_27a,V0a_2E0) = c_2Emin_2E_40_2E1(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,V0a_2E0)) ) ).
tff(thm_2Eordinal_2Eordinal__ABS__def,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : ( c_2Eordinal_2Eordinal__ABS_2E1(A_27a,V0r_2E0) = c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,c_2Ewellorder_2Eorderiso_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0r_2E0)) ) ).
tff(thm_2Eordinal_2Eordlt__def,axiom,
! [A_27a: $tType,V0T1_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1T2_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,V0T1_2E0,V1T2_2E0) = c_2Ewellorder_2Eorderlt_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Eordinal_2Eordinal__REP_2E1(A_27a,V0T1_2E0),c_2Eordinal_2Eordinal__REP_2E1(A_27a,V1T2_2E0)) ) ).
tff(thm_2Eordinal_2EallOrds__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)))] :
( ! [V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0x_2E0),V1y_2E0))
<=> ( ( V0x_2E0 = V1y_2E0 )
| p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V1y_2E0)) ) )
=> ( ! [V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0x_2E0,V1y_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0x_2E0),V1y_2E0)) )
=> ( c_2Eordinal_2EallOrds_2E0(A_27a) = c_2Ewellorder_2Ewellorder__ABS_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2EUNCURRY_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),F0_2E0))) ) ) ) ).
tff(thm_2Eordinal_2Epreds__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)))] :
( ! [V0w_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0),V1w0_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V1w0_2E0,c_2Eordinal_2Eordlt_2E2(A_27a,V1w0_2E0,V0w_2E0)) )
=> ! [V0w_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epreds_2E1(A_27a,V0w_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0w_2E0)) ) ) ).
tff(thm_2Eordinal_2Edownward__closed__def,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Eordinal_2Edownward__closed_2E1(A_27a,V0s_2E0))
<=> ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V2b_2E0,V1a_2E0)) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0,V0s_2E0)) ) ) ).
tff(thm_2Eordinal_2Eoleast__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1x_2E0))
<=> ( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
& ! [V2y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2y_2E0,V1x_2E0))
=> ~ p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2y_2E0)) ) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Eoleast_2E1(A_27a,V0P_2E0) = c_2Emin_2E_40_2E1(tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0P_2E0)) ) ) ).
tff(thm_2Eordinal_2EordSUC__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),V1b_2E0) = c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,V1b_2E0) )
=> ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0) = c_2Eordinal_2Eoleast_2E1(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0a_2E0)) ) ) ).
tff(thm_2Eordinal_2EfromNat__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0a_2E0) = c_2Ebool_2ET_2E0 )
=> ( ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) = c_2Eordinal_2Eoleast_2E1(A_27a,F0_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2ESUC_2E1(V1n_2E0)) = c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V1n_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Esup__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0ordset_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0ordset_2E0),V1a_2E0))
<=> ~ p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,c_2Epred__set_2EBIGUNION_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E0(A_27a),V0ordset_2E0)))) )
=> ! [V0ordset_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Esup_2E1(A_27a,V0ordset_2E0) = c_2Eordinal_2Eoleast_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0ordset_2E0)) ) ) ).
tff(thm_2Eordinal_2Eomax__def,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V3y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F2_2E0,V3y_2E0),V2x_2E0))
<=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V3y_2E0,V2x_2E0)) )
=> ( ! [V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0,V3y_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F2_2E0,V3y_2E0),V2x_2E0)) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0s_2E0),V1a_2E0))
<=> ( c_2Eset__relation_2Emaximal__elements_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0s_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2EUNCURRY_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),F1_2E0))) = c_2Epred__set_2EINSERT_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a))) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Eomax_2E1(A_27a,V0s_2E0) = c_2Eoption_2Esome_2E1(tyop_2Eordinal_2Eordinal(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0s_2E0)) ) ) ) ) ).
tff(thm_2Eordinal_2EordMULT__def,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordMULT_2E2(A_27a,V0b_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
& ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V0b_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0)) = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V0b_2E0,V1a_2E0),V0b_2E0) )
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( c_2Eordinal_2EordMULT_2E2(A_27a,V0b_2E0,V2a_2E0) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordMULT_2E1(A_27a,V0b_2E0),c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0))) ) ) ) ).
tff(thm_2Eordinal_2EordDIVISION,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V1b_2E0))
=> ( ( V0a_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V1b_2E0,c_2Eordinal_2EordDIV_2E2(A_27a,V0a_2E0,V1b_2E0)),c_2Eordinal_2EordMOD_2E2(A_27a,V0a_2E0,V1b_2E0)) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMOD_2E2(A_27a,V0a_2E0,V1b_2E0),V1b_2E0)) ) ) ).
tff(thm_2Eordinal_2EordEXP__def,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
& ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_27_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,V1a_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V2a_27_2E0)) = c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V1a_2E0,V2a_27_2E0),V1a_2E0) )
& ! [V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V4a_27_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V4a_27_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V4a_27_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,V3a_2E0,V4a_27_2E0) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordEXP_2E1(A_27a,V3a_2E0),c_2Eordinal_2Epreds_2E1(A_27a,V4a_27_2E0))) ) ) ) ).
tff(thm_2Eordinal_2Eepsilon0__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ! [V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0x_2E0))
<=> ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0x_2E0) = V0x_2E0 ) )
=> ( c_2Eordinal_2Eepsilon0_2E0(A_27a) = c_2Eordinal_2Eoleast_2E1(A_27a,F0_2E0) ) ) ).
tff(thm_2Eordinal_2Epolyform__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0))
=> ( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,V0a_2E0,c_2Eordinal_2Epolyform_2E2(A_27a,V0a_2E0,V1b_2E0)))
& ( V1b_2E0 = c_2Eordinal_2Eeval__poly_2E2(A_27a,V0a_2E0,c_2Eordinal_2Epolyform_2E2(A_27a,V0a_2E0,V1b_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Elt__suppreds,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,c_2Eordinal_2Esup_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0))))
<=> ? [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2d_2E0,V0a_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2d_2E0)) ) ) ).
tff(thm_2Eordinal_2EordADD__fromNat__omega,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2Eomega_2E0(A_27a)) = c_2Eordinal_2Eomega_2E0(A_27a) ) ).
tff(thm_2Eordinal_2Eomega__islimit,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2Eomega_2E0(A_27a))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eomax__preds__omega,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2Eomega_2E0(A_27a))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2EordADD__fromNat,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2EfromNat_2E1(A_27a,V1m_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0)) ) ).
tff(thm_2Eordinal_2Eubsup__thm,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0,V0s_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V2a_2E0,V1b_2E0)) )
=> ! [V3c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V3c_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ? [V4d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V4d_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V3c_2E0,V4d_2E0)) ) ) ) ).
tff(thm_2Eordinal_2EordADD__0L,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0) = V0a_2E0 ) ).
tff(thm_2Eordinal_2Eord__RECURSION,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27b,V1sf_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),V2lf_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27b))] :
? [V3h_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),A_27b)] :
( ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,V3h_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = V0z_2E0 )
& ! [V4a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,V3h_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V4a_2E0)) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),V1sf_2E0,V4a_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,V3h_2E0,V4a_2E0)) )
& ! [V5a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V5a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V5a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,V3h_2E0,V5a_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27b,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27b),V2lf_2E0,V5a_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),A_27b,V3h_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V5a_2E0))) ) ) ) ).
tff(thm_2Eordinal_2EfromNat__eq__omega,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0) != c_2Eordinal_2Eomega_2E0(A_27a) ) ).
tff(thm_2Eordinal_2EfromNat__lt__omega,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2Eomega_2E0(A_27a))) ).
tff(thm_2Eordinal_2Elt__omega,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,c_2Eordinal_2Eomega_2E0(A_27a)))
<=> ? [V1m_2E0: tyop_2Enum_2Enum] : ( V0a_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,V1m_2E0) ) ) ).
tff(thm_2Eordinal_2EfromNat__ordlt,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2EfromNat_2E1(A_27a,V1m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0) ) ).
tff(thm_2Eordinal_2Eordlt__fromNat,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0)))
<=> ? [V2m_2E0: tyop_2Enum_2Enum] :
( ( V1x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,V2m_2E0) )
& p(c_2Eprim__rec_2E_3C_2E2(V2m_2E0,V0n_2E0)) ) ) ).
tff(thm_2Eordinal_2EfromNat__11,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
( ( c_2Eordinal_2EfromNat_2E1(A_27a,V0x_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,V1y_2E0) )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Eordinal_2Epreds__suple,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Edownward__closed_2E1(A_27a,V0s_2E0))
& ( V0s_2E0 != c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ! [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2d_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2d_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Epreds__lesup,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Eordinal_2Edownward__closed_2E1(A_27a,V0s_2E0))
& ( V0s_2E0 != c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ! [V1d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1d_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0),V1d_2E0)) ) ) ).
tff(thm_2Eordinal_2Epreds__sup__thm,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Eordinal_2Edownward__closed_2E1(A_27a,V0s_2E0))
& ( V0s_2E0 != c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ! [V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ? [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2d_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2d_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Ecsup__suple,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),V0s_2E0))
=> ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ! [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2d_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2d_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Ecsup__lesup,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),V0s_2E0))
=> ! [V1d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1d_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0),V1d_2E0)) ) ) ).
tff(thm_2Eordinal_2Epreds__sup,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
=> ( c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)) = c_2Eordinal_2Edclose_2E1(A_27a,V0s_2E0) ) ) ).
tff(thm_2Eordinal_2Esup__preds__omax__NONE,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> ( c_2Eordinal_2Esup_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0)) = V0a_2E0 ) ) ).
tff(thm_2Eordinal_2Esimple__ord__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)))
& ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0))
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0))) )
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2a_2E0))
& ! [V3b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V3b_2E0,V2a_2E0))
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3b_2E0)) ) )
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2a_2E0)) ) )
=> ! [V4a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V4a_2E0)) ) ).
tff(thm_2Eordinal_2Eordinal__ABS__REP__CLASS,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,V0a_2E0)) = V0a_2E0 )
& ! [V1c_2E0: tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] :
( ? [V2r_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] :
( p(c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0,V2r_2E0))
& ( V1c_2E0 = c_2Ewellorder_2Eorderiso_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2r_2E0) ) )
<=> ( c_2Eordinal_2Eordinal__REP__CLASS_2E1(A_27a,c_2Eordinal_2Eordinal__ABS__CLASS_2E1(A_27a,V1c_2E0)) = V1c_2E0 ) ) ) ).
tff(thm_2Eordinal_2Eordinal__QUOTIENT,axiom,
! [A_27a: $tType] : p(c_2Equotient_2EQUOTIENT_2E3(tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),tyop_2Eordinal_2Eordinal(A_27a),c_2Ewellorder_2Eorderiso_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),c_2Eordinal_2Eordinal__ABS_2E0(A_27a),c_2Eordinal_2Eordinal__REP_2E0(A_27a))) ).
tff(thm_2Eordinal_2Eordlt__REFL,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0w_2E0,V0w_2E0)) ).
tff(thm_2Eordinal_2Eordlt__TRANS,axiom,
! [A_27a: $tType,V0w1_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2w3_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0w1_2E0,V1w2_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1w2_2E0,V2w3_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V0w1_2E0,V2w3_2E0)) ) ).
tff(thm_2Eordinal_2Eordlt__WF,axiom,
! [A_27a: $tType] : p(c_2Erelation_2EWF_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Eordlt_2E0(A_27a))) ).
tff(thm_2Eordinal_2Eordlt__trichotomy,axiom,
! [A_27a: $tType,V0w2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1w1_2E0,V0w2_2E0))
| ( V1w1_2E0 = V0w2_2E0 )
| p(c_2Eordinal_2Eordlt_2E2(A_27a,V0w2_2E0,V1w1_2E0)) ) ).
tff(thm_2Eordinal_2Ewellorder__allOrds,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)))] :
( ! [V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0x_2E0),V1y_2E0))
<=> ( ( V0x_2E0 = V1y_2E0 )
| p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V1y_2E0)) ) )
=> ( ! [V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0x_2E0,V1y_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F1_2E0,V0x_2E0),V1y_2E0)) )
=> p(c_2Ewellorder_2Ewellorder_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2EUNCURRY_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),tyop_2Emin_2Ebool),F0_2E0)))) ) ) ).
tff(thm_2Eordinal_2EWIN__allOrds,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0,V0y_2E0),c_2Eset__relation_2Estrict_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Ewellorder_2Ewellorder__REP_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EallOrds_2E0(A_27a)))) = c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,V0y_2E0) ) ).
tff(thm_2Eordinal_2EelsOf__allOrds,axiom,
! [A_27a: $tType] : ( c_2Ewellorder_2EelsOf_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EallOrds_2E0(A_27a)) = c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eordlt__mkOrdinal,axiom,
! [A_27a: $tType,V0o2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1o1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1o1_2E0,V0o2_2E0))
<=> ! [V2w1_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),V3w2_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] :
( ( ( c_2Eordinal_2Eordinal__ABS_2E1(A_27a,V2w1_2E0) = V1o1_2E0 )
& ( c_2Eordinal_2Eordinal__ABS_2E1(A_27a,V3w2_2E0) = V0o2_2E0 ) )
=> p(c_2Ewellorder_2Eorderlt_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2w1_2E0,V3w2_2E0)) ) ) ).
tff(thm_2Eordinal_2Eorderlt__iso__REFL,axiom,
! [A_27a: $tType,A_27b: $tType,V0w2_2E0: tyop_2Ewellorder_2Ewellorder(A_27b),V1w1_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0))
=> ~ p(c_2Ewellorder_2Eorderlt_2E2(A_27a,A_27b,V1w1_2E0,V0w2_2E0)) ) ).
tff(thm_2Eordinal_2Eorderiso__wobound2,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2w_2E0: tyop_2Ewellorder_2Ewellorder(A_27a)] :
( p(c_2Ewellorder_2Eorderiso_2E2(A_27a,A_27a,c_2Ewellorder_2Ewobound_2E2(A_27a,V1x_2E0,V2w_2E0),c_2Ewellorder_2Ewobound_2E2(A_27a,V0y_2E0,V2w_2E0)))
=> ~ p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1x_2E0,V0y_2E0),c_2Eset__relation_2Estrict_2E1(A_27a,c_2Ewellorder_2Ewellorder__REP_2E1(A_27a,V2w_2E0)))) ) ).
tff(thm_2Eordinal_2Ewellorder__ordinal__isomorphism,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Ewellorder_2Ewellorder(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))] : p(c_2Ewellorder_2Eorderiso_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0w_2E0,c_2Ewellorder_2Ewobound_2E2(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Eordinal__ABS_2E1(A_27a,V0w_2E0),c_2Eordinal_2EallOrds_2E0(A_27a)))) ).
tff(thm_2Eordinal_2EIN__preds,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0x_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V1w_2E0)) = c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V1w_2E0) ) ).
tff(thm_2Eordinal_2Epreds__11,axiom,
! [A_27a: $tType,V0w2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Epreds_2E1(A_27a,V1w1_2E0) = c_2Eordinal_2Epreds_2E1(A_27a,V0w2_2E0) )
<=> ( V1w1_2E0 = V0w2_2E0 ) ) ).
tff(thm_2Eordinal_2Epreds__downward__closed,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(c_2Eordinal_2Edownward__closed_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0w_2E0))) ).
tff(thm_2Eordinal_2Epreds__bij,axiom,
! [A_27a: $tType] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)),c_2Epred__set_2EDELETE_2E2(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Edownward__closed_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a))))) ).
tff(thm_2Eordinal_2Epreds__lt__PSUBSET,axiom,
! [A_27a: $tType,V0w2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1w1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,V1w1_2E0,V0w2_2E0) = c_2Epred__set_2EPSUBSET_2E2(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Epreds_2E1(A_27a,V1w1_2E0),c_2Eordinal_2Epreds_2E1(A_27a,V0w2_2E0)) ) ).
tff(thm_2Eordinal_2Epreds__wobound,axiom,
! [A_27a: $tType,V0ord_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epreds_2E1(A_27a,V0ord_2E0) = c_2Ewellorder_2EelsOf_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Ewellorder_2Ewobound_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0ord_2E0,c_2Eordinal_2EallOrds_2E0(A_27a))) ) ).
tff(thm_2Eordinal_2Epreds__inj__univ,axiom,
! [A_27a: $tType,V0ord_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Eordinal_2Epreds_2E1(A_27a,V0ord_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ).
tff(thm_2Eordinal_2Eunitinf__univnum,axiom,
p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone),tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Eone_2Eone)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).
tff(thm_2Eordinal_2Ecord__countable__preds,axiom,
! [V0ord_2E0: tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone)] : p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),c_2Eordinal_2Epreds_2E1(tyop_2Eone_2Eone,V0ord_2E0))) ).
tff(thm_2Eordinal_2Euniv__ord__greater__cardinal,axiom,
! [A_27a: $tType] : ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ).
tff(thm_2Eordinal_2Euniv__cord__uncountable,axiom,
~ p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone),c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(tyop_2Eone_2Eone)))) ).
tff(thm_2Eordinal_2Eordle__lteq,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,V1a_2E0))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0))
| ( V1a_2E0 = V0b_2E0 ) ) ) ).
tff(thm_2Eordinal_2Eordle__ANTISYM,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,V1a_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0)) )
=> ( V1a_2E0 = V0b_2E0 ) ) ).
tff(thm_2Eordinal_2Eordle__TRANS,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2z_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1y_2E0,V0x_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V2z_2E0,V1y_2E0)) )
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V2z_2E0,V0x_2E0)) ) ).
tff(thm_2Eordinal_2Eordlet__TRANS,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2z_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1y_2E0,V0x_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1y_2E0,V2z_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V2z_2E0)) ) ).
tff(thm_2Eordinal_2Eordlte__TRANS,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2z_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V1y_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V2z_2E0,V1y_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V2z_2E0)) ) ).
tff(thm_2Eordinal_2Eoleast__intro,axiom,
! [A_27a: $tType,V0Q_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( ? [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V1P_2E0,V2a_2E0))
& ! [V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ! [V4b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V4b_2E0,V3a_2E0))
=> ~ p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V1P_2E0,V4b_2E0)) )
& p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V1P_2E0,V3a_2E0)) )
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0Q_2E0,V3a_2E0)) ) )
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0Q_2E0,c_2Eordinal_2Eoleast_2E1(A_27a,V1P_2E0))) ) ).
tff(thm_2Eordinal_2EfromNat__def__compute,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,F0_2E0,V0a_2E0) = c_2Ebool_2ET_2E0 )
=> ( ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) = c_2Eordinal_2Eoleast_2E1(A_27a,F0_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0))) = c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
& ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0))) = c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)))) ) ) ) ).
tff(thm_2Eordinal_2EfromNat__SUC,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0)) ) ).
tff(thm_2Eordinal_2Eordlt__ZERO,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0))) ).
tff(thm_2Eordinal_2Epreds__surj,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Eordinal_2Edownward__closed_2E1(A_27a,V0x_2E0))
& ( V0x_2E0 != c_2Epred__set_2EUNIV_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ? [V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epreds_2E1(A_27a,V1y_2E0) = V0x_2E0 ) ) ).
tff(thm_2Eordinal_2Eno__maximal__ordinal,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
? [V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,V1b_2E0)) ).
tff(thm_2Eordinal_2Eordlt__SUC,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0))) ).
tff(thm_2Eordinal_2EordSUC__ZERO,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0) != c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ).
tff(thm_2Eordinal_2Eordlt__DISCRETE1,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
~ ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0))) ) ).
tff(thm_2Eordinal_2Eordlt__SUC__DISCRETE,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V0b_2E0)))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0))
| ( V1a_2E0 = V0b_2E0 ) ) ) ).
tff(thm_2Eordinal_2EordSUC__MONO,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0),c_2Eordinal_2EordSUC_2E1(A_27a,V0b_2E0)) = c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0) ) ).
tff(thm_2Eordinal_2EordSUC__11,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0) = c_2Eordinal_2EordSUC_2E1(A_27a,V0b_2E0) )
<=> ( V1a_2E0 = V0b_2E0 ) ) ).
tff(thm_2Eordinal_2Eord__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ! [V1min_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ! [V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2b_2E0,V1min_2E0))
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2b_2E0)) )
=> p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1min_2E0)) )
=> ! [V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3a_2E0)) ) ).
tff(thm_2Eordinal_2Esup__thm,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
=> ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ? [V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V2b_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Esuple__thm,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0b_2E0,V1s_2E0)) )
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,V1s_2E0),V0b_2E0)) ) ).
tff(thm_2Eordinal_2Esup__eq__sup,axiom,
! [A_27a: $tType,V0s2_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s1_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s2_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0,V1s1_2E0))
=> ? [V3b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V3b_2E0,V0s2_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V3b_2E0,V2a_2E0)) ) )
& ! [V4b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V4b_2E0,V0s2_2E0))
=> ? [V5a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V5a_2E0,V1s1_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V5a_2E0,V4b_2E0)) ) ) )
=> ( c_2Eordinal_2Esup_2E1(A_27a,V1s1_2E0) = c_2Eordinal_2Esup_2E1(A_27a,V0s2_2E0) ) ) ).
tff(thm_2Eordinal_2EUnum__cle__Uinf,axiom,
! [A_27a: $tType] : p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ).
tff(thm_2Eordinal_2Ecsup__thm,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),V0s_2E0))
=> ! [V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0)))
<=> ? [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2d_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2d_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Epredimage__sup__thm,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2b_2E0,c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)))))
<=> ? [V3d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V3d_2E0,V1a_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V2b_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V3d_2E0))) ) ) ).
tff(thm_2Eordinal_2Epredimage__suplt__ELIM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V2a_2E0))),V1b_2E0))
=> ! [V3d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V3d_2E0,V2a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V3d_2E0))) ) ) ).
tff(thm_2Eordinal_2Esuppred__suplt__ELIM,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)),V0b_2E0))
=> ! [V2d_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2d_2E0,V1a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,V2d_2E0)) ) ) ).
tff(thm_2Eordinal_2Esup__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a))) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ).
tff(thm_2Eordinal_2Esup__SING,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0a_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)))) = V0a_2E0 ) ).
tff(thm_2Eordinal_2Esup__preds__SUC,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Esup_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0))) = V0a_2E0 ) ).
tff(thm_2Eordinal_2Epreds__ordSUC,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Eordinal_2Eordinal(A_27a),V0a_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0)) ) ).
tff(thm_2Eordinal_2EcountableOrds__dclosed,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0))
& p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Epreds_2E1(A_27a,V0b_2E0))) )
=> p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0))) ) ).
tff(thm_2Eordinal_2Eomax__SOME,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,V0s_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0) )
<=> ( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,V0s_2E0))
& ! [V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V2b_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Eomax__NONE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,V0s_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,V0s_2E0))
=> ? [V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0,V0s_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V2b_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Eomax__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Epreds__0,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eordleq0,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0))
<=> ( V0x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Eordinal_2Epreds__EQ__EMPTY,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Epreds_2E1(A_27a,V0x_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> ( V0x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Eordinal_2Eomax__sup,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,V0s_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0) )
=> ( c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0) = V1a_2E0 ) ) ).
tff(thm_2Eordinal_2Epreds__omax__SOME__SUC,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Eordinal_2Eordinal(A_27a),V0b_2E0) )
<=> ( V1a_2E0 = c_2Eordinal_2EordSUC_2E1(A_27a,V0b_2E0) ) ) ).
tff(thm_2Eordinal_2Eomax__preds__SUC,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V0x_2E0))) = c_2Eoption_2ESOME_2E1(tyop_2Eordinal_2Eordinal(A_27a),V0x_2E0) ) ).
tff(thm_2Eordinal_2EORD__ONE,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Eordinal_2EordSUC__NUMERAL,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EordSUC_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(V0n_2E0))) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).
tff(thm_2Eordinal_2EordZERO__ltSUC,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),c_2Eordinal_2EordSUC_2E1(A_27a,V0x_2E0))) ).
tff(thm_2Eordinal_2Eordlt__CANCEL__ADDR,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0b_2E0)) = c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0b_2E0) ) ).
tff(thm_2Eordinal_2Eordlt__CANCEL__ADDL,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0b_2E0),V1a_2E0) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Eordinal_2EordADD__CANCEL1,axiom,
! [A_27a: $tType] :
( ! [V0c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( V1a_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0c_2E0) )
<=> ( V0c_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) )
& ! [V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordADD_2E2(A_27a,V3a_2E0,V2c_2E0) = V3a_2E0 )
<=> ( V2c_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eordinal_2EordADD__MONO,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V2c_2E0,V1a_2E0),c_2Eordinal_2EordADD_2E2(A_27a,V2c_2E0,V0b_2E0))) ) ).
tff(thm_2Eordinal_2Eordlt__CANCEL,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V2c_2E0,V1a_2E0),c_2Eordinal_2EordADD_2E2(A_27a,V2c_2E0,V0b_2E0)) = c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0) ) ).
tff(thm_2Eordinal_2EordADD__RIGHT__CANCEL,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0b_2E0) = c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V2c_2E0) )
<=> ( V0b_2E0 = V2c_2E0 ) ) ).
tff(thm_2Eordinal_2EleqLEFT__CANCEL,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0x_2E0),V0x_2E0)) ).
tff(thm_2Eordinal_2Eordlt__EXISTS__ADD,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,V1b_2E0))
<=> ? [V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( V2c_2E0 != c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
& ( V1b_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,V2c_2E0) ) ) ) ).
tff(thm_2Eordinal_2Eordle__EXISTS__ADD,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V0a_2E0))
<=> ? [V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( V1b_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,V2c_2E0) ) ) ).
tff(thm_2Eordinal_2Eordle__CANCEL__ADDR,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V0x_2E0,V1a_2E0),V0x_2E0)) ).
tff(thm_2Eordinal_2Edclose__BIGUNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] : ( c_2Eordinal_2Edclose_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EBIGUNION_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E0(A_27a),V0s_2E0)) ) ).
tff(thm_2Eordinal_2EcountableOrds__uncountable,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool,V0a_2E0,c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0))) )
=> ~ p(c_2Epred__set_2Ecountable_2E1(tyop_2Eordinal_2Eordinal(A_27a),c_2Epred__set_2EGSPEC_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),F0_2E0))) ) ).
tff(thm_2Eordinal_2Edclose__cardleq__univinf,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Eordinal_2Edclose_2E1(A_27a,V0s_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ) ).
tff(thm_2Eordinal_2Esup__lt__implies,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0),V2a_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0,V0s_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V2a_2E0)) ) ).
tff(thm_2Eordinal_2Esup__eq__max,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ! [V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0,V0s_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V2b_2E0)) )
& p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0,V0s_2E0)) )
=> ( c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0) = V1a_2E0 ) ) ).
tff(thm_2Eordinal_2Esup__eq__SUC,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ( c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0) = c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0) ) )
=> p(c_2Ebool_2EIN_2E2(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0),V0s_2E0)) ) ).
tff(thm_2Eordinal_2Egeneric__continuity,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))] :
( ( ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V1a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V1a_2E0) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0))) ) )
& ! [V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V3y_2E0,V2x_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V3y_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V2x_2E0))) ) )
=> ! [V4s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V4s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ( V4s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Esup_2E1(A_27a,V4s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V4s_2E0)) ) ) ) ).
tff(thm_2Eordinal_2Eord__CASES,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( V0a_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
| ? [V1a0_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( V0a_2E0 = c_2Eordinal_2EordSUC_2E1(A_27a,V1a0_2E0) )
| ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ) ).
tff(thm_2Eordinal_2Eislimit__0,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eordinal__IVT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),V1c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3a1_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ! [V4a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V4a_2E0))
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V4a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V4a_2E0) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Epreds_2E1(A_27a,V4a_2E0))) ) )
& ! [V5x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V6y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V6y_2E0,V5x_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V6y_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V5x_2E0))) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V3a1_2E0,V2a2_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1c_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V3a1_2E0)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1c_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V2a2_2E0))) )
=> ? [V7b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V7b_2E0,V3a1_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V7b_2E0,V2a2_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1c_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V7b_2E0)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1c_2E0,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2EordSUC_2E1(A_27a,V7b_2E0)))) ) ) ).
tff(thm_2Eordinal_2EordADD__continuous,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,c_2Eordinal_2Esup_2E1(A_27a,V1s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordADD_2E1(A_27a,V0a_2E0),V1s_2E0)) ) ) ).
tff(thm_2Eordinal_2EordADD__ASSOC,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,c_2Eordinal_2EordADD_2E2(A_27a,V1b_2E0,V2c_2E0)) = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,V1b_2E0),V2c_2E0) ) ).
tff(thm_2Eordinal_2EADD1R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eordinal_2EordSUC_2E1(A_27a,V0a_2E0) ) ).
tff(thm_2Eordinal_2EordADD__weak__MONO,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V2b_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V2b_2E0,V0c_2E0),c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0c_2E0))) ) ).
tff(thm_2Eordinal_2EordMULT__0L,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ).
tff(thm_2Eordinal_2EordMULT__0R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ).
tff(thm_2Eordinal_2EordMULT__1L,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0) = V0a_2E0 ) ).
tff(thm_2Eordinal_2EordMULT__1R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = V0a_2E0 ) ).
tff(thm_2Eordinal_2EordMULT__2R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,V0a_2E0) ) ).
tff(thm_2Eordinal_2Eislimit__SUC__lt,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0b_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,V0b_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V1a_2E0),V0b_2E0)) ) ).
tff(thm_2Eordinal_2EordMULT__lt__MONO__R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,V1b_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2c_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V0a_2E0),c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V1b_2E0))) ) ).
tff(thm_2Eordinal_2EordMULT__le__MONO__R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V0a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V1b_2E0),c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V0a_2E0))) ) ).
tff(thm_2Eordinal_2EordMULT__lt__MONO__R__EQN,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V0c_2E0,V2a_2E0),c_2Eordinal_2EordMULT_2E2(A_27a,V0c_2E0,V1b_2E0)))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V2a_2E0,V1b_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0c_2E0)) ) ) ).
tff(thm_2Eordinal_2EordADD__le__MONO__L,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1y_2E0,V2x_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1y_2E0,V0z_2E0),c_2Eordinal_2EordADD_2E2(A_27a,V2x_2E0,V0z_2E0))) ) ).
tff(thm_2Eordinal_2EordMULT__le__MONO__L,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1b_2E0,V0a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V1b_2E0,V2c_2E0),c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,V2c_2E0))) ) ).
tff(thm_2Eordinal_2EordMULT__CANCEL__R,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordMULT_2E2(A_27a,V0z_2E0,V2x_2E0) = c_2Eordinal_2EordMULT_2E2(A_27a,V0z_2E0,V1y_2E0) )
<=> ( ( V0z_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
| ( V2x_2E0 = V1y_2E0 ) ) ) ).
tff(thm_2Eordinal_2EordMULT__continuous,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
=> ( c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,c_2Eordinal_2Esup_2E1(A_27a,V1s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordMULT_2E1(A_27a,V0a_2E0),V1s_2E0)) ) ) ).
tff(thm_2Eordinal_2EordMULT__fromNat,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2EfromNat_2E1(A_27a,V1m_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2E_2A_2E2(V0n_2E0,V1m_2E0)) ) ).
tff(thm_2Eordinal_2Eomega__MUL__fromNat,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ( c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2Eomega_2E0(A_27a)) = c_2Eordinal_2Eomega_2E0(A_27a) ) ) ).
tff(thm_2Eordinal_2EordMULT__LDISTRIB,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,V1b_2E0)) = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V0a_2E0),c_2Eordinal_2EordMULT_2E2(A_27a,V2c_2E0,V1b_2E0)) ) ).
tff(thm_2Eordinal_2EordMULT__ASSOC,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,c_2Eordinal_2EordMULT_2E2(A_27a,V1b_2E0,V2c_2E0)) = c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,V1b_2E0),V2c_2E0) ) ).
tff(thm_2Eordinal_2EordDIV__UNIQUE,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2q_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3r_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V1b_2E0))
& ( V0a_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V1b_2E0,V2q_2E0),V3r_2E0) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V3r_2E0,V1b_2E0)) )
=> ( c_2Eordinal_2EordDIV_2E2(A_27a,V0a_2E0,V1b_2E0) = V2q_2E0 ) ) ).
tff(thm_2Eordinal_2EordMOD__UNIQUE,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2q_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3r_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V1b_2E0))
& ( V0a_2E0 = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V1b_2E0,V2q_2E0),V3r_2E0) )
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V3r_2E0,V1b_2E0)) )
=> ( c_2Eordinal_2EordMOD_2E2(A_27a,V0a_2E0,V1b_2E0) = V3r_2E0 ) ) ).
tff(thm_2Eordinal_2EordEXP__1R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = V0a_2E0 ) ).
tff(thm_2Eordinal_2EordEXP__1L,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ).
tff(thm_2Eordinal_2EordEXP__2R,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Eordinal_2EordMULT_2E2(A_27a,V0a_2E0,V0a_2E0) ) ).
tff(thm_2Eordinal_2EordEXP__fromNat,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0x_2E0),c_2Eordinal_2EfromNat_2E1(A_27a,V1n_2E0)) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2EEXP_2E2(V0x_2E0,V1n_2E0)) ) ).
tff(thm_2Eordinal_2EordEXP__le__MONO__L,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V2b_2E0,V1a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2b_2E0,V0x_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V1a_2E0,V0x_2E0))) ) ).
tff(thm_2Eordinal_2EIFF__ZERO__lt,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ( V0x_2E0 != c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
<=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0)) )
& ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
<=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0)) ) ) ).
tff(thm_2Eordinal_2Eislimit__SUC,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordSUC_2E1(A_27a,V0x_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> p(c_2Ebool_2EF_2E0) ) ).
tff(thm_2Eordinal_2Eislimit__fromNat,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0x_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> ( V0x_2E0 = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Eordinal_2EordEXP__ZERO__limit,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0x_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eordinal_2EordEXP__ZERO__nonlimit,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0x_2E0)) != c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Eordinal_2Esup__EQ__0,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
=> ( ( c_2Eordinal_2Esup_2E1(A_27a,V0s_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
<=> ( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
| ( V0s_2E0 = c_2Epred__set_2EINSERT_2E2(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a))) ) ) ) ) ).
tff(thm_2Eordinal_2EordADD__EQ__0,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordADD_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
<=> ( ( V1x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
& ( V0y_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eordinal_2EIMAGE__EQ__SING,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V2f_2E0,V1s_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) )
<=> ( ? [V3y_2E0: A_27b] : p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1s_2E0))
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1s_2E0))
=> ( app_2E2(A_27b,A_27a,V2f_2E0,V4y_2E0) = V0x_2E0 ) ) ) ) ).
tff(thm_2Eordinal_2EordMULT__EQ__0,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordMULT_2E2(A_27a,V0x_2E0,V1y_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
<=> ( ( V0x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
| ( V1y_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eordinal_2EordEXP__EQ__0,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordEXP_2E2(A_27a,V1x_2E0,V0y_2E0) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
<=> ( ( V1x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0y_2E0)) != c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ) ).
tff(thm_2Eordinal_2EZERO__lt__ordEXP__I,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,V1x_2E0))) ) ).
tff(thm_2Eordinal_2EZERO__lt__ordEXP,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V1a_2E0,V0x_2E0)))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V1a_2E0))
| ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V0x_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ) ).
tff(thm_2Eordinal_2EordEXP__lt__MONO__R,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2a_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,V0y_2E0)) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V1x_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V0y_2E0))) ) ).
tff(thm_2Eordinal_2EordEXP__lt__IFF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2a_2E0))
=> ( c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V0x_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V1y_2E0)) = c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,V1y_2E0) ) ) ).
tff(thm_2Eordinal_2EordEXP__le__MONO__R,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2a_2E0))
& ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V1y_2E0,V0x_2E0)) )
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V1y_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V2a_2E0,V0x_2E0))) ) ).
tff(thm_2Eordinal_2EordEXP__continuous,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,c_2Eordinal_2Esup_2E1(A_27a,V1s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EordEXP_2E1(A_27a,V0a_2E0),V1s_2E0)) ) ) ).
tff(thm_2Eordinal_2EordEXP__ADD,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2x_2E0))
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,V2x_2E0,c_2Eordinal_2EordADD_2E2(A_27a,V1y_2E0,V0z_2E0)) = c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2x_2E0,V1y_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V2x_2E0,V0z_2E0)) ) ) ).
tff(thm_2Eordinal_2EordEXP__MUL,axiom,
! [A_27a: $tType,V0z_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2x_2E0))
=> ( c_2Eordinal_2EordEXP_2E2(A_27a,V2x_2E0,c_2Eordinal_2EordMULT_2E2(A_27a,V1y_2E0,V0z_2E0)) = c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V2x_2E0,V1y_2E0),V0z_2E0) ) ) ).
tff(thm_2Eordinal_2Efixpoints__exist,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))] :
( ( ! [V1s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
& p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V1s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Esup_2E1(A_27a,V1s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V1s_2E0)) ) )
& ! [V2x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V2x_2E0),V2x_2E0)) )
=> ! [V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
? [V4b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V4b_2E0,V3a_2E0))
& ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V4b_2E0) = V4b_2E0 ) ) ) ).
tff(thm_2Eordinal_2Ex__le__ordEXP__x,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0))
=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V0a_2E0,V1x_2E0),V1x_2E0)) ) ).
tff(thm_2Eordinal_2Eepsilon0__fixpoint,axiom,
! [A_27a: $tType] : ( c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Eordinal_2Eepsilon0_2E0(A_27a)) = c_2Eordinal_2Eepsilon0_2E0(A_27a) ) ).
tff(thm_2Eordinal_2Eepsilon0__least__fixpoint,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a)))
=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V0a_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ) ) ).
tff(thm_2Eordinal_2Eomega__lt__epsilon0,axiom,
! [A_27a: $tType] : p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ).
tff(thm_2Eordinal_2EfromNat__lt__epsilon0,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] : p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ).
tff(thm_2Eordinal_2Eadd__nat__islimit,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
=> ( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0)))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
<=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Eordinal_2Estrict__continuity__preserves__islimit,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( ! [V2s_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),V2s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a))))
& ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) )
=> ( app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,c_2Eordinal_2Esup_2E1(A_27a,V2s_2E0)) = c_2Eordinal_2Esup_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V2s_2E0)) ) )
& ! [V3x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V4y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,V3x_2E0,V4y_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V3x_2E0),app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V4y_2E0))) )
& ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
& ( V1a_2E0 != c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) )
=> ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V0f_2E0,V1a_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ).
tff(thm_2Eordinal_2Eadd__omega__islimit,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V0a_2E0,c_2Eordinal_2Eomega_2E0(A_27a)))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eislimit__mul__R,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,V1a_2E0)) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) )
=> ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V0b_2E0,V1a_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ).
tff(thm_2Eordinal_2Emul__omega__islimit,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ).
tff(thm_2Eordinal_2Eomega__exp__islimit,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0a_2E0))
=> ( c_2Eordinal_2Eomax_2E1(A_27a,c_2Eordinal_2Epreds_2E1(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0))) = c_2Eoption_2ENONE_2E0(tyop_2Eordinal_2Eordinal(A_27a)) ) ) ).
tff(thm_2Eordinal_2Eexpbound__add,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2y_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V2y_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1x_2E0,V2y_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0a_2E0))) ) ).
tff(thm_2Eordinal_2EaddL__fixpoint__iff,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( c_2Eordinal_2EordADD_2E2(A_27a,V1a_2E0,V0b_2E0) = V0b_2E0 )
<=> ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,c_2Eordinal_2EordMULT_2E2(A_27a,V1a_2E0,c_2Eordinal_2Eomega_2E0(A_27a)))) ) ).
tff(thm_2Eordinal_2EordADD__under__epsilon0,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V0y_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordADD_2E2(A_27a,V1x_2E0,V0y_2E0),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ) ).
tff(thm_2Eordinal_2EordMUL__under__epsilon0,axiom,
! [A_27a: $tType,V0y_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1x_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V0y_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V1x_2E0,V0y_2E0),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ) ).
tff(thm_2Eordinal_2EordEXP__under__epsilon0,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,V1a_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a)))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V0b_2E0,c_2Eordinal_2Eepsilon0_2E0(A_27a))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V1a_2E0,V0b_2E0),c_2Eordinal_2Eepsilon0_2E0(A_27a))) ) ).
tff(thm_2Eordinal_2Eeval__poly__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool))] :
( ( ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V1a_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))))
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V4e_2E0: tyop_2Eordinal_2Eordinal(A_27a),V5t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V2a_2E0),V5t_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V2a_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V3c_2E0,V4e_2E0),V5t_2E0))) ) )
=> ! [V6v_2E0: tyop_2Eordinal_2Eordinal(A_27a),V7v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V6v_2E0),V7v1_2E0)) ) ).
tff(thm_2Eordinal_2Eeval__poly__def,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eeval__poly_2E2(A_27a,V0a_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))) = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) )
& ! [V1t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),V2e_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V4a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eeval__poly_2E2(A_27a,V4a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V3c_2E0,V2e_2E0),V1t_2E0)) = c_2Eordinal_2EordADD_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,c_2Eordinal_2EordEXP_2E2(A_27a,V4a_2E0,V2e_2E0),V3c_2E0),c_2Eordinal_2Eeval__poly_2E2(A_27a,V4a_2E0,V1t_2E0)) ) ) ).
tff(thm_2Eordinal_2Eis__polyform__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool))] :
( ( ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),V0P_2E0,V1a_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))))
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V4e_2E0: tyop_2Eordinal_2Eordinal(A_27b)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),V0P_2E0,V2a_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V3c_2E0,V4e_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))))))
& ! [V5a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V6c1_2E0: tyop_2Eordinal_2Eordinal(A_27a),V7e1_2E0: tyop_2Eordinal_2Eordinal(A_27b),V8c2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V9e2_2E0: tyop_2Eordinal_2Eordinal(A_27b),V10t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),V0P_2E0,V5a_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V8c2_2E0,V9e2_2E0),V10t_2E0)))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),V0P_2E0,V5a_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V6c1_2E0,V7e1_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V8c2_2E0,V9e2_2E0),V10t_2E0)))) ) )
=> ! [V11v_2E0: tyop_2Eordinal_2Eordinal(A_27a),V12v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),tyop_2Emin_2Ebool),V0P_2E0,V11v_2E0),V12v1_2E0)) ) ).
tff(thm_2Eordinal_2Eis__polyform__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] : ( c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V0a_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)))) = c_2Ebool_2ET_2E0 )
& ! [V1e_2E0: tyop_2Eordinal_2Eordinal(A_27b),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V3a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V2c_2E0,V1e_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))))))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2c_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V2c_2E0,V3a_2E0)) ) )
& ! [V4t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),V5e2_2E0: tyop_2Eordinal_2Eordinal(A_27b),V6e1_2E0: tyop_2Eordinal_2Eordinal(A_27b),V7c2_2E0: tyop_2Eordinal_2Eordinal(A_27a),V8c1_2E0: tyop_2Eordinal_2Eordinal(A_27a),V9a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V9a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V8c1_2E0,V6e1_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V7c2_2E0,V5e2_2E0),V4t_2E0))))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V8c1_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V8c1_2E0,V9a_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27b,V5e2_2E0,V6e1_2E0))
& p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V9a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V7c2_2E0,V5e2_2E0),V4t_2E0))) ) ) ) ).
tff(thm_2Eordinal_2Eis__polyform__ELthm,axiom,
! [A_27a: $tType,A_27b: $tType,V0ces_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V1a_2E0,V0ces_2E0))
<=> ( ! [V2i_2E0: tyop_2Enum_2Enum,V3j_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,V3j_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V3j_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),V0ces_2E0))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27b,c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),V3j_2E0,V0ces_2E0)),c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),c_2Elist_2EEL_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),V2i_2E0,V0ces_2E0)))) )
& ! [V4c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V5e_2E0: tyop_2Eordinal_2Eordinal(A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V4c_2E0,V5e_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),V0ces_2E0)))
=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V4c_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V4c_2E0,V1a_2E0)) ) ) ) ) ).
tff(thm_2Eordinal_2Epolyform__exists,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0))
=> ? [V2ces_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,V0a_2E0,V2ces_2E0))
& ( V1b_2E0 = c_2Eordinal_2Eeval__poly_2E2(A_27a,V0a_2E0,V2ces_2E0) ) ) ) ).
tff(thm_2Eordinal_2ECNF__thm,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Eordinal_2Epolyform_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0b_2E0)))
& ( V0b_2E0 = c_2Eordinal_2Eeval__poly_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Eordinal_2Epolyform_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0b_2E0)) ) ) ).
tff(thm_2Eordinal_2Epolyform__0,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0))
=> ( c_2Eordinal_2Epolyform_2E2(A_27a,V0a_2E0,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) ) ) ).
tff(thm_2Eordinal_2Epolyform__EQ__NIL,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1a_2E0))
=> ( ( c_2Eordinal_2Epolyform_2E2(A_27a,V1a_2E0,V0x_2E0) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))) )
<=> ( V0x_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eordinal_2Eis__polyform__CONS__E,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b))),V1e_2E0: tyop_2Eordinal_2Eordinal(A_27b),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V3a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27b),V2c_2E0,V1e_2E0),V0t_2E0)))
=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V2c_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,V2c_2E0,V3a_2E0))
& p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27b,V3a_2E0,V0t_2E0)) ) ) ).
tff(thm_2Eordinal_2Eis__polyform__head__dominates__tail,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),V1e_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0: tyop_2Eordinal_2Eordinal(A_27a),V3a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V3a_2E0))
& p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,V3a_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),V2c_2E0,V1e_2E0),V0t_2E0))) )
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2Eeval__poly_2E2(A_27a,V3a_2E0,V0t_2E0),c_2Eordinal_2EordEXP_2E2(A_27a,V3a_2E0,V1e_2E0))) ) ).
tff(thm_2Eordinal_2Ecx__lt__x,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1c_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EordMULT_2E2(A_27a,V0x_2E0,V1c_2E0),V0x_2E0))
<=> ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0))
& ( V1c_2E0 = c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eordinal_2Epolyform__UNIQUE,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a),V2ces_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)))] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0a_2E0))
& p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,V0a_2E0,V2ces_2E0))
& ( V1b_2E0 = c_2Eordinal_2Eeval__poly_2E2(A_27a,V0a_2E0,V2ces_2E0) ) )
=> ( c_2Eordinal_2Epolyform_2E2(A_27a,V0a_2E0,V1b_2E0) = V2ces_2E0 ) ) ).
tff(thm_2Eordinal_2Epolyform__eval__poly,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1a_2E0))
& p(c_2Eordinal_2Eis__polyform_2E2(A_27a,A_27a,V1a_2E0,V0b_2E0)) )
=> ( c_2Eordinal_2Epolyform_2E2(A_27a,V1a_2E0,c_2Eordinal_2Eeval__poly_2E2(A_27a,V1a_2E0,V0b_2E0)) = V0b_2E0 ) ) ).
tff(thm_2Eordinal_2ECNF__nat,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V0n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eordinal_2Epolyform_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Epair_2E_2C_2E2(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2EfromNat_2E1(A_27a,V0n_2E0),c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0)),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a))))) ) ) ).
tff(thm_2Eordinal_2EordLOG__correct,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a),V1b_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( ( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1b_2E0))
& p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0)) )
=> ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,V1b_2E0,c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Elist_2EHD_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Epolyform_2E2(A_27a,V1b_2E0,V0x_2E0))))))
& ! [V2a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Elist_2EHD_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Epolyform_2E2(A_27a,V1b_2E0,V0x_2E0))),V2a_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,V1b_2E0,V2a_2E0))) ) ) ) ).
tff(thm_2Eordinal_2Eolog__correct,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Eordinal_2EfromNat_2E1(A_27a,c_2Enum_2E0_2E0),V0x_2E0))
=> ( ~ p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Elist_2EHD_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Epolyform_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0x_2E0))))))
& ! [V1a_2E0: tyop_2Eordinal_2Eordinal(A_27a)] :
( p(c_2Eordinal_2Eordlt_2E2(A_27a,c_2Epair_2ESND_2E1(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a),c_2Elist_2EHD_2E1(tyop_2Epair_2Eprod(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Epolyform_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V0x_2E0))),V1a_2E0))
=> p(c_2Eordinal_2Eordlt_2E2(A_27a,V0x_2E0,c_2Eordinal_2EordEXP_2E2(A_27a,c_2Eordinal_2Eomega_2E0(A_27a),V1a_2E0))) ) ) ) ).
%------------------------------------------------------------------------------