ITP001 Axioms: ITP098_7.ax
%------------------------------------------------------------------------------
% File : ITP098_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 : enumeral.ax [Gau19]
% : HL4098_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 413 ( 118 unt; 201 typ; 0 def)
% Number of atoms : 505 ( 308 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 300 ( 7 ~; 14 |; 133 &)
% ( 47 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 204 ( 96 >; 108 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 197 ( 197 usr; 16 con; 0-6 aty)
% Number of variables : 1328 (1118 !; 26 ?;1328 :)
% ( 184 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eenumeral_2Ebl,type,
tyop_2Eenumeral_2Ebl: $tType > $tType ).
tff(tyop_2Eenumeral_2Ebt,type,
tyop_2Eenumeral_2Ebt: $tType > $tType ).
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
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_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
tff(tyop_2Etoto_2Etoto,type,
tyop_2Etoto_2Etoto: $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_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_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_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_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
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_2Eenumeral_2EBL__ACCUM_2E0,type,
c_2Eenumeral_2EBL__ACCUM_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))) ).
tff(c_2Eenumeral_2EBL__ACCUM_2E3,type,
c_2Eenumeral_2EBL__ACCUM_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eenumeral_2EBL__CONS_2E0,type,
c_2Eenumeral_2EBL__CONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a))) ).
tff(c_2Eenumeral_2EBL__CONS_2E2,type,
c_2Eenumeral_2EBL__CONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
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_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_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_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
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_2Eenumeral_2EENUMERAL_2E0,type,
c_2Eenumeral_2EENUMERAL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2EENUMERAL_2E2,type,
c_2Eenumeral_2EENUMERAL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2EternaryComparisons_2EEQUAL_2E0,type,
c_2EternaryComparisons_2EEQUAL_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eind__type_2EFCONS_2E2,type,
c_2Eind__type_2EFCONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
tff(c_2EternaryComparisons_2EGREATER_2E0,type,
c_2EternaryComparisons_2EGREATER_2E0: tyop_2EternaryComparisons_2Eordering ).
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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
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_2Epred__set_2EINTER_2E0,type,
c_2Epred__set_2EINTER_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_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINTER_2E2,type,
c_2Epred__set_2EINTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2EK2_2E0,type,
c_2Eenumeral_2EK2_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) ).
tff(c_2Eenumeral_2EK2_2E1,type,
c_2Eenumeral_2EK2_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Enum_2Enum ) ).
tff(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Eenumeral_2ELESS__ALL_2E0,type,
c_2Eenumeral_2ELESS__ALL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2ELESS__ALL_2E3,type,
c_2Eenumeral_2ELESS__ALL_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
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_2Eenumeral_2EOL_2E0,type,
c_2Eenumeral_2EOL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eenumeral_2EOL_2E2,type,
c_2Eenumeral_2EOL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOL__bt_2E0,type,
c_2Eenumeral_2EOL__bt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Eenumeral_2EOL__bt_2E2,type,
c_2Eenumeral_2EOL__bt_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOL__bt__lb_2E0,type,
c_2Eenumeral_2EOL__bt__lb_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2EOL__bt__lb_2E3,type,
c_2Eenumeral_2EOL__bt__lb_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOL__bt__lb__ub_2E0,type,
c_2Eenumeral_2EOL__bt__lb__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eenumeral_2EOL__bt__lb__ub_2E4,type,
c_2Eenumeral_2EOL__bt__lb__ub_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOL__bt__ub_2E0,type,
c_2Eenumeral_2EOL__bt__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2EOL__bt__ub_2E3,type,
c_2Eenumeral_2EOL__bt__ub_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOL__sublists_2E0,type,
c_2Eenumeral_2EOL__sublists_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)) ).
tff(c_2Eenumeral_2EOL__sublists_2E2,type,
c_2Eenumeral_2EOL__sublists_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eenumeral_2EOU_2E0,type,
c_2Eenumeral_2EOU_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eenumeral_2EOU_2E3,type,
c_2Eenumeral_2EOU_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2EOWL_2E0,type,
c_2Eenumeral_2EOWL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2EOWL_2E3,type,
c_2Eenumeral_2EOWL_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
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_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_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_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2EUO_2E0,type,
c_2Eenumeral_2EUO_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eenumeral_2EUO_2E3,type,
c_2Eenumeral_2EUO_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > 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_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( 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(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
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_2Etoto_2Eapto_2E0,type,
c_2Etoto_2Eapto_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2Etoto_2Eapto_2E3,type,
c_2Etoto_2Eapto_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * A_27a ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Eenumeral_2Ebl__CASE_2E0,type,
c_2Eenumeral_2Ebl__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b)))) ).
tff(c_2Eenumeral_2Ebl__CASE_2E4,type,
c_2Eenumeral_2Ebl__CASE_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eenumeral_2Ebl(A_27a) * A_27b * tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))) ) > A_27b ) ).
tff(c_2Eenumeral_2Ebl__rev_2E0,type,
c_2Eenumeral_2Ebl__rev_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a))) ).
tff(c_2Eenumeral_2Ebl__rev_2E1,type,
c_2Eenumeral_2Ebl__rev_2E1:
!>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebt(A_27a) > tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a)) ) ).
tff(c_2Eenumeral_2Ebl__rev_2E2,type,
c_2Eenumeral_2Ebl__rev_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebt(A_27a) ) ).
tff(c_2Eenumeral_2Ebl__size_2E0,type,
c_2Eenumeral_2Ebl__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Eenumeral_2Ebl__size_2E2,type,
c_2Eenumeral_2Ebl__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Eenumeral_2Ebl__to__bt_2E0,type,
c_2Eenumeral_2Ebl__to__bt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a)) ).
tff(c_2Eenumeral_2Ebl__to__bt_2E1,type,
c_2Eenumeral_2Ebl__to__bt_2E1:
!>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebl(A_27a) > tyop_2Eenumeral_2Ebt(A_27a) ) ).
tff(c_2Eenumeral_2Ebl__to__set_2E0,type,
c_2Eenumeral_2Ebl__to__set_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Eenumeral_2Ebl__to__set_2E2,type,
c_2Eenumeral_2Ebl__to__set_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2Ebt__CASE_2E0,type,
c_2Eenumeral_2Ebt__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),A_27b))) ).
tff(c_2Eenumeral_2Ebt__CASE_2E3,type,
c_2Eenumeral_2Ebt__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * A_27b * tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))) ) > A_27b ) ).
tff(c_2Eenumeral_2Ebt__rev_2E0,type,
c_2Eenumeral_2Ebt__rev_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a))) ).
tff(c_2Eenumeral_2Ebt__rev_2E2,type,
c_2Eenumeral_2Ebt__rev_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__size_2E0,type,
c_2Eenumeral_2Ebt__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Eenumeral_2Ebt__size_2E2,type,
c_2Eenumeral_2Ebt__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Eenumeral_2Ebt__to__bl_2E0,type,
c_2Eenumeral_2Ebt__to__bl_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebl(A_27a)) ).
tff(c_2Eenumeral_2Ebt__to__bl_2E1,type,
c_2Eenumeral_2Ebt__to__bl_2E1:
!>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebt(A_27a) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__list_2E0,type,
c_2Eenumeral_2Ebt__to__list_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Eenumeral_2Ebt__to__list_2E1,type,
c_2Eenumeral_2Ebt__to__list_2E1:
!>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebt(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__list__ac_2E0,type,
c_2Eenumeral_2Ebt__to__list__ac_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Eenumeral_2Ebt__to__list__ac_2E2,type,
c_2Eenumeral_2Ebt__to__list__ac_2E2:
!>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol_2E0,type,
c_2Eenumeral_2Ebt__to__ol_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Eenumeral_2Ebt__to__ol_2E2,type,
c_2Eenumeral_2Ebt__to__ol_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__ac_2E0,type,
c_2Eenumeral_2Ebt__to__ol__ac_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Ebt__to__ol__ac_2E3,type,
c_2Eenumeral_2Ebt__to__ol__ac_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb_2E0,type,
c_2Eenumeral_2Ebt__to__ol__lb_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb_2E3,type,
c_2Eenumeral_2Ebt__to__ol__lb_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0,type,
c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4,type,
c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0,type,
c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4,type,
c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0,type,
c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))))) ).
tff(c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5,type,
c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) * A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__ub_2E0,type,
c_2Eenumeral_2Ebt__to__ol__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Ebt__to__ol__ub_2E3,type,
c_2Eenumeral_2Ebt__to__ol__ub_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0,type,
c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4,type,
c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) * A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ebt__to__set__lb_2E0,type,
c_2Eenumeral_2Ebt__to__set__lb_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eenumeral_2Ebt__to__set__lb_2E3,type,
c_2Eenumeral_2Ebt__to__set__lb_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2Ebt__to__set__lb__ub_2E0,type,
c_2Eenumeral_2Ebt__to__set__lb__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) ).
tff(c_2Eenumeral_2Ebt__to__set__lb__ub_2E4,type,
c_2Eenumeral_2Ebt__to__set__lb__ub_2E4:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2Ebt__to__set__ub_2E0,type,
c_2Eenumeral_2Ebt__to__set__ub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Eenumeral_2Ebt__to__set__ub_2E3,type,
c_2Eenumeral_2Ebt__to__set__ub_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2Eincr__sbuild_2E0,type,
c_2Eenumeral_2Eincr__sbuild_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))) ).
tff(c_2Eenumeral_2Eincr__sbuild_2E2,type,
c_2Eenumeral_2Eincr__sbuild_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ) ).
tff(c_2Eenumeral_2Eincr__smerge_2E0,type,
c_2Eenumeral_2Eincr__smerge_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))) ).
tff(c_2Eenumeral_2Eincr__smerge_2E3,type,
c_2Eenumeral_2Eincr__smerge_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ) > tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ) ).
tff(c_2Eenumeral_2Eincr__ssort_2E0,type,
c_2Eenumeral_2Eincr__ssort_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Eenumeral_2Eincr__ssort_2E2,type,
c_2Eenumeral_2Eincr__ssort_2E2:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2Elist__CASE_2E0,type,
c_2Elist_2Elist__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).
tff(c_2Elist_2Elist__CASE_2E3,type,
c_2Elist_2Elist__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).
tff(c_2Eenumeral_2Elist__to__bl_2E0,type,
c_2Eenumeral_2Elist__to__bl_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eenumeral_2Ebl(A_27a)) ).
tff(c_2Eenumeral_2Elist__to__bl_2E1,type,
c_2Eenumeral_2Elist__to__bl_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eenumeral_2Elist__to__bt_2E0,type,
c_2Eenumeral_2Elist__to__bt_2E0:
!>[A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Eenumeral_2Ebt(A_27c)) ).
tff(c_2Eenumeral_2Elist__to__bt_2E1,type,
c_2Eenumeral_2Elist__to__bt_2E1:
!>[A_27c: $tType] : ( tyop_2Elist_2Elist(A_27c) > tyop_2Eenumeral_2Ebt(A_27c) ) ).
tff(c_2Eenumeral_2Elol__set_2E0,type,
c_2Eenumeral_2Elol__set_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Eenumeral_2Elol__set_2E1,type,
c_2Eenumeral_2Elol__set_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Eenumeral_2Enbl_2E0,type,
c_2Eenumeral_2Enbl_2E0:
!>[A_27a: $tType] : tyop_2Eenumeral_2Ebl(A_27a) ).
tff(c_2Eenumeral_2Enode_2E0,type,
c_2Eenumeral_2Enode_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))) ).
tff(c_2Eenumeral_2Enode_2E3,type,
c_2Eenumeral_2Enode_2E3:
!>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Eenumeral_2Ebt(A_27a) ) ).
tff(c_2Eenumeral_2Ent_2E0,type,
c_2Eenumeral_2Ent_2E0:
!>[A_27a: $tType] : tyop_2Eenumeral_2Ebt(A_27a) ).
tff(c_2Eenumeral_2Eonebl_2E0,type,
c_2Eenumeral_2Eonebl_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))) ).
tff(c_2Eenumeral_2Eonebl_2E3,type,
c_2Eenumeral_2Eonebl_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebl(A_27a) ) ).
tff(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
c_2EternaryComparisons_2Eordering__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))) ).
tff(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
c_2EternaryComparisons_2Eordering__CASE_2E4:
!>[A_27a: $tType] : ( ( tyop_2EternaryComparisons_2Eordering * A_27a * A_27a * A_27a ) > A_27a ) ).
tff(c_2Eenumeral_2Esdiff_2E0,type,
c_2Eenumeral_2Esdiff_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Esdiff_2E3,type,
c_2Eenumeral_2Esdiff_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Esinter_2E0,type,
c_2Eenumeral_2Esinter_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Esinter_2E3,type,
c_2Eenumeral_2Esinter_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Esmerge_2E0,type,
c_2Eenumeral_2Esmerge_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Esmerge_2E3,type,
c_2Eenumeral_2Esmerge_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Esmerge__out_2E0,type,
c_2Eenumeral_2Esmerge__out_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)))) ).
tff(c_2Eenumeral_2Esmerge__out_2E3,type,
c_2Eenumeral_2Esmerge__out_2E3:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eenumeral_2Ezerbl_2E0,type,
c_2Eenumeral_2Ezerbl_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)) ).
tff(c_2Eenumeral_2Ezerbl_2E1,type,
c_2Eenumeral_2Ezerbl_2E1:
!>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebl(A_27a) > tyop_2Eenumeral_2Ebl(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_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_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eenumeral_2Ebt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Eenumeral_2Ebt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),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_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_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_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_2Eenumeral_2EBL__ACCUM_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a))),c_2Eenumeral_2EBL__ACCUM_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2EBL__CONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2EBL__CONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),c_2Eenumeral_2EBL__CONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ECONS_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2ECONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))] : ( c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))),c_2Eind__type_2ECONSTR_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2EENUMERAL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EENUMERAL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eenumeral_2EENUMERAL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),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_2EINTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2EK2_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eenumeral_2EK2_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,c_2Eenumeral_2EK2_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2ELESS__ALL_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2ELESS__ALL_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eenumeral_2ELESS__ALL_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),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_2Eenumeral_2EOL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2EOL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Eenumeral_2EOL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2EOL__bt_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EOL__bt_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool),c_2Eenumeral_2EOL__bt_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2EOL__bt__lb_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EOL__bt__lb_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool)),c_2Eenumeral_2EOL__bt__lb_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2EOL__bt__lb__ub_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a),X3_2E0: A_27a] : ( c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2EOL__bt__lb__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2EOL__bt__ub_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: A_27a] : ( c_2Eenumeral_2EOL__bt__ub_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eenumeral_2EOL__bt__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2EOL__sublists_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2EOL__sublists_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),c_2Eenumeral_2EOL__sublists_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2EOU_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EOU_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2EOU_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2EOWL_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2EOWL_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Eenumeral_2EOWL_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(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_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Eenumeral_2Ebt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Eenumeral_2Ebt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eenumeral_2Ebt_28A_27a_29_29_29_20mono_2Etyop_2Eenumeral_2Ebl_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Eenumeral_2Ebl(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Eenumeral_2Ebl(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2EUO_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EUO_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2EUO_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EWFREC_2E0(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_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(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2Eapto_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2Ebl__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebl(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),X3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b)),app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b))),c_2Eenumeral_2Ebl__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Ebl__rev_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebl__rev_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),c_2Eenumeral_2Ebl__rev_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebl__rev_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__rev_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),c_2Eenumeral_2Ebl__rev_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebl__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Enum_2Enum),c_2Eenumeral_2Ebl__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Ebl__to__bt_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Eenumeral_2Ebl(A_27c)] : ( c_2Eenumeral_2Ebl__to__bt_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27c),tyop_2Eenumeral_2Ebt(A_27c),c_2Eenumeral_2Ebl__to__bt_2E0(A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebl__to__set_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__to__set_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eenumeral_2Ebl__to__set_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),A_27b)),c_2Eenumeral_2Ebt__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebt__rev_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebt__rev_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),c_2Eenumeral_2Ebt__rev_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebt__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Enum_2Enum),c_2Eenumeral_2Ebt__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Ebt__to__bl_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__bl_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Ebt__to__bl_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Ebt__to__list_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__list_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a),c_2Eenumeral_2Ebt__to__list_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebt__to__list__ac_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Eenumeral_2Ebt__to__list__ac_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Ebt__to__ol_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Eenumeral_2Ebt__to__ol_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__ac_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ac_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Ebt__to__ol__ac_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__lb_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Ebt__to__ol__lb_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__lb__ac_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Eenumeral_2Ebt__to__ol__lb__ac_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__lb__ub_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a),X3_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)))),c_2Eenumeral_2Ebt__to__ol__lb__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq5_2Ec_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a),X3_2E0: A_27a,X4_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__to__ol__ub_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Ebt__to__ol__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2Ebt__to__ol__ub__ac_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: A_27a,X3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Eenumeral_2Ebt__to__ol__ub__ac_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__to__set__lb_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__set__lb_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2Ebt__to__set__lb_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Eenumeral_2Ebt__to__set__lb__ub_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a),X3_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__set__lb__ub_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eenumeral_2Ebt__to__set__lb__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Ebt__to__set__ub_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__set__ub_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eenumeral_2Ebt__to__set__ub_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Eincr__sbuild_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Eincr__sbuild_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eenumeral_2Eincr__sbuild_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Eincr__smerge_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2Eincr__smerge_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),c_2Eenumeral_2Eincr__smerge_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Eenumeral_2Eincr__ssort_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Eincr__ssort_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Eenumeral_2Eincr__ssort_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Elist__to__bl_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Elist__to__bl_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Elist__to__bl_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Elist__to__bl_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Eenumeral_2Elist__to__bl_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Eenumeral_2Ebl(A_27c),c_2Eenumeral_2Elist__to__bl_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Elist__to__bt_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eenumeral_2Ebt(A_27a),c_2Eenumeral_2Elist__to__bt_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Eenumeral_2Elist__to__bt_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Eenumeral_2Ebt(A_27c),c_2Eenumeral_2Elist__to__bt_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Elol__set_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2Elol__set_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eenumeral_2Elol__set_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Enode_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a))),c_2Eenumeral_2Enode_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Eenumeral_2Ebt(A_27a),X2_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Eonebl_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a))),c_2Eenumeral_2Eonebl_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool,X3_2E0: tyop_2Emin_2Ebool] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Esdiff_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Esdiff_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Esdiff_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Esinter_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Esinter_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Esinter_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Esmerge_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Esmerge_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Esmerge_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eenumeral_2Esmerge__out_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2Esmerge__out_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Elist_2Elist(A_27a))),c_2Eenumeral_2Esmerge__out_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ezerbl_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Ezerbl_2E0(A_27a),X0_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_2Eenumeral_2Ebl__TY__DEF,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool)] :
( ! [V10n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),F3_2E0,V10n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))) )
=> ( ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),F2_2E0,V6n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27bl_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))] :
( ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Eenumeral_2Ebt(A_27a),c_2Ebool_2EARB_2E0(A_27a),c_2Ebool_2EARB_2E0(tyop_2Eenumeral_2Ebt(A_27a))),F1_2E0) )
| ? [V5a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),c_2Epair_2E_2C_2E2(A_27a,tyop_2Eenumeral_2Ebt(A_27a),c_2Ebool_2EARB_2E0(A_27a),c_2Ebool_2EARB_2E0(tyop_2Eenumeral_2Ebt(A_27a))),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),V5a_2E0,F2_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool,V2_27bl_27_2E0,V5a_2E0)) )
| ? [V7a0_2E0: A_27a,V8a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V9a2_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)))] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Epair_2E_2C_2E2(A_27a,tyop_2Eenumeral_2Ebt(A_27a),V7a0_2E0,V8a1_2E0),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),V9a2_2E0,F3_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool,V2_27bl_27_2E0,V9a2_2E0)) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool,V2_27bl_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Emin_2Ebool,V2_27bl_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Eenumeral_2Ebt(A_27a))),tyop_2Eenumeral_2Ebl(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ) ).
tff(thm_2Eenumeral_2Ebl__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V2f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,c_2Eenumeral_2Enbl_2E0(A_27a),V0v_2E0,V1f_2E0,V2f1_2E0) = V0v_2E0 )
& ! [V3a_2E0: tyop_2Eenumeral_2Ebl(A_27a),V4v_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V6f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,c_2Eenumeral_2Ezerbl_2E1(A_27a,V3a_2E0),V4v_2E0,V5f_2E0,V6f1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V5f_2E0,V3a_2E0) )
& ! [V7a0_2E0: A_27a,V8a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V9a2_2E0: tyop_2Eenumeral_2Ebl(A_27a),V10v_2E0: A_27b,V11f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V12f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,c_2Eenumeral_2Eonebl_2E3(A_27a,V7a0_2E0,V8a1_2E0,V9a2_2E0),V10v_2E0,V11f_2E0,V12f1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),V12f1_2E0,V7a0_2E0),V8a1_2E0),V9a2_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebl__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Eenumeral_2Ebl__size_2E2(A_27a,V0f_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__size_2E2(A_27a,V1f_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V2a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eenumeral_2Ebl__size_2E2(A_27a,V1f_2E0,V2a_2E0)) )
& ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4a0_2E0: A_27a,V5a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6a2_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__size_2E2(A_27a,V3f_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V4a0_2E0,V5a1_2E0,V6a2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V3f_2E0,V4a0_2E0),c_2Earithmetic_2E_2B_2E2(c_2Eenumeral_2Ebt__size_2E2(A_27a,V3f_2E0,V5a1_2E0),c_2Eenumeral_2Ebl__size_2E2(A_27a,V3f_2E0,V6a2_2E0)))) ) ) ).
tff(thm_2Eenumeral_2Ebt__TY__DEF,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V8n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27bt_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(A_27a),F1_2E0) )
| ? [V5a0_2E0: tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0: A_27a,V7a2_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V6a1_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V5a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V7a2_2E0,F2_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bt_27_2E0,V5a0_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bt_27_2E0,V7a2_2E0)) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bt_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27bt_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Eenumeral_2Ebt(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Eenumeral_2Ebt__size_2E2(A_27a,V0f_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3a1_2E0: A_27a,V4a2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__size_2E2(A_27a,V1f_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2a0_2E0,V3a1_2E0,V4a2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2Eenumeral_2Ebt__size_2E2(A_27a,V1f_2E0,V2a0_2E0),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3a1_2E0),c_2Eenumeral_2Ebt__size_2E2(A_27a,V1f_2E0,V4a2_2E0)))) ) ) ).
tff(thm_2Eenumeral_2EBL__ACCUM,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a,V1ac_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,V0a_2E0,V1ac_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) = c_2Eenumeral_2Eonebl_2E3(A_27a,V0a_2E0,V1ac_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) )
& ! [V2a_2E0: A_27a,V3ac_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4bl_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,V2a_2E0,V3ac_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V4bl_2E0)) = c_2Eenumeral_2Eonebl_2E3(A_27a,V2a_2E0,V3ac_2E0,V4bl_2E0) )
& ! [V5a_2E0: A_27a,V6ac_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7r_2E0: A_27a,V8rft_2E0: tyop_2Eenumeral_2Ebt(A_27a),V9bl_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,V5a_2E0,V6ac_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V7r_2E0,V8rft_2E0,V9bl_2E0)) = c_2Eenumeral_2Ezerbl_2E1(A_27a,c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,V5a_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V6ac_2E0,V7r_2E0,V8rft_2E0),V9bl_2E0)) ) ) ).
tff(thm_2Eenumeral_2EBL__CONS,axiom,
! [A_27a: $tType,V0a_2E0: A_27a,V1bl_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2EBL__CONS_2E2(A_27a,V0a_2E0,V1bl_2E0) = c_2Eenumeral_2EBL__ACCUM_2E3(A_27a,V0a_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V1bl_2E0) ) ).
tff(thm_2Eenumeral_2Elist__to__bl,axiom,
! [A_27a: $tType] :
( ( c_2Eenumeral_2Elist__to__bl_2E1(A_27a,c_2Elist_2ENIL_2E0(A_27a)) = c_2Eenumeral_2Enbl_2E0(A_27a) )
& ! [V0a_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Elist__to__bl_2E1(A_27a,c_2Elist_2ECONS_2E2(A_27a,V0a_2E0,V1l_2E0)) = c_2Eenumeral_2EBL__CONS_2E2(A_27a,V0a_2E0,c_2Eenumeral_2Elist__to__bl_2E1(A_27a,V1l_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__list,axiom,
! [A_27a: $tType] :
( ( c_2Eenumeral_2Ebt__to__list_2E1(A_27a,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V0l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1x_2E0: A_27a,V2r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__list_2E1(A_27a,c_2Eenumeral_2Enode_2E3(A_27a,V0l_2E0,V1x_2E0,V2r_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Eenumeral_2Ebt__to__list_2E1(A_27a,V0l_2E0),c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Eenumeral_2Ebt__to__list_2E1(A_27a,V2r_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__list__ac,axiom,
! [A_27a: $tType] :
( ! [V0m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,c_2Eenumeral_2Ent_2E0(A_27a),V0m_2E0) = V0m_2E0 )
& ! [V1l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2x_2E0: A_27a,V3r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,c_2Eenumeral_2Enode_2E3(A_27a,V1l_2E0,V2x_2E0,V3r_2E0),V4m_2E0) = c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,V1l_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,V3r_2E0,V4m_2E0))) ) ) ).
tff(thm_2Eenumeral_2Ebt__rev,axiom,
! [A_27a: $tType] :
( ! [V0bl_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebt__rev_2E2(A_27a,c_2Eenumeral_2Ent_2E0(A_27a),V0bl_2E0) = V0bl_2E0 )
& ! [V1lft_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2r_2E0: A_27a,V3rft_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4bl_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebt__rev_2E2(A_27a,c_2Eenumeral_2Enode_2E3(A_27a,V1lft_2E0,V2r_2E0,V3rft_2E0),V4bl_2E0) = c_2Eenumeral_2Ebt__rev_2E2(A_27a,V1lft_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V2r_2E0,V3rft_2E0,V4bl_2E0)) ) ) ).
tff(thm_2Eenumeral_2EK2,axiom,
! [A_27a: $tType,V0a_2E0: A_27a] : ( c_2Eenumeral_2EK2_2E1(A_27a,V0a_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ) ).
tff(thm_2Eenumeral_2Ebl__rev,axiom,
! [A_27a: $tType] :
( ! [V0ft_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebl__rev_2E2(A_27a,V0ft_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) = V0ft_2E0 )
& ! [V1ft_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__rev_2E2(A_27a,V1ft_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V2b_2E0)) = c_2Eenumeral_2Ebl__rev_2E2(A_27a,V1ft_2E0,V2b_2E0) )
& ! [V3ft_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4a_2E0: A_27a,V5f_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__rev_2E2(A_27a,V3ft_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V4a_2E0,V5f_2E0,V6b_2E0)) = c_2Eenumeral_2Ebl__rev_2E2(A_27a,c_2Eenumeral_2Enode_2E3(A_27a,V3ft_2E0,V4a_2E0,V5f_2E0),V6b_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebl__to__bt,axiom,
! [A_27a: $tType] : ( c_2Eenumeral_2Ebl__to__bt_2E0(A_27a) = c_2Eenumeral_2Ebl__rev_2E1(A_27a,c_2Eenumeral_2Ent_2E0(A_27a)) ) ).
tff(thm_2Eenumeral_2Ebt__to__bl,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__bl_2E1(A_27a,V0t_2E0) = c_2Eenumeral_2Ebt__rev_2E2(A_27a,V0t_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) ) ).
tff(thm_2Eenumeral_2Elist__to__bt,axiom,
! [A_27c: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Eenumeral_2Elist__to__bt_2E1(A_27c,V0l_2E0) = c_2Eenumeral_2Ebl__to__bt_2E1(A_27c,c_2Eenumeral_2Elist__to__bl_2E1(A_27c,V0l_2E0)) ) ).
tff(thm_2Eenumeral_2EOL,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2a_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V1cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V2a_2E0,V3l_2E0)))
<=> ( p(c_2Eenumeral_2EOL_2E2(A_27a,V1cmp_2E0,V3l_2E0))
& ! [V4p_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4p_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3l_2E0)))
=> ( c_2Etoto_2Eapto_2E3(A_27a,V1cmp_2E0,V2a_2E0,V4p_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ) ).
tff(thm_2Eenumeral_2Elol__set__primitive,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V0R_2E0))
& ! [V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0R_2E0,V1lol_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V1lol_2E0)))
& ! [V2m_2E0: tyop_2Elist_2Elist(A_27a),V3lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0R_2E0,V3lol_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2m_2E0),V3lol_2E0))) ) )
=> ( ! [V4lol__set_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V7lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V8m_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V4lol__set_2E0),V7lol_2E0),V8m_2E0) = c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V8m_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4lol__set_2E0,V7lol_2E0))) )
=> ( ! [V4lol__set_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6v_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),V7lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V4lol__set_2E0),V6v_2E0),V7lol_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6v_2E0,c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4lol__set_2E0,V7lol_2E0)),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V4lol__set_2E0),V7lol_2E0)) )
=> ( ! [V4lol__set_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V4lol__set_2E0),V5a_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5a_2E0,c_2Ecombin_2EI_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V4lol__set_2E0)) )
=> ( c_2Eenumeral_2Elol__set_2E0(A_27a) = c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ).
tff(thm_2Eenumeral_2Eincr__sbuild,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Eincr__sbuild_2E2(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Eincr__sbuild_2E2(A_27a,V1cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,V3l_2E0)) = c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V1cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V2x_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Eenumeral_2Eincr__sbuild_2E2(A_27a,V1cmp_2E0,V3l_2E0)) ) ) ).
tff(thm_2Eenumeral_2Eincr__ssort,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Eincr__ssort_2E2(A_27a,V0cmp_2E0,V1l_2E0) = c_2Eenumeral_2Esmerge__out_2E3(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Eenumeral_2Eincr__sbuild_2E2(A_27a,V0cmp_2E0,V1l_2E0)) ) ).
tff(thm_2Eenumeral_2Ebt__to__set,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V6z_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V6z_2E0),V1cmp_2E0),V4r_2E0),V3x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V6z_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V1cmp_2E0,V4r_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V1cmp_2E0,V3x_2E0,V6z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V6z_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0,V1cmp_2E0),V4r_2E0),V3x_2E0),V6z_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V6z_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V6z_2E0),V1cmp_2E0),V4r_2E0),V3x_2E0)) )
=> ( ! [V5y_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V5y_2E0),V1cmp_2E0),V2l_2E0),V3x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V1cmp_2E0,V2l_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V1cmp_2E0,V5y_2E0,V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V5y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V1cmp_2E0),V2l_2E0),V3x_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0,V5y_2E0),V1cmp_2E0),V2l_2E0),V3x_2E0)) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EENUMERAL_2E2(A_27a,V1cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2l_2E0,V3x_2E0,V4r_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V1cmp_2E0),V2l_2E0),V3x_2E0)),c_2Epred__set_2EINSERT_2E2(A_27a,V3x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0,V1cmp_2E0),V4r_2E0),V3x_2E0))) ) ) ) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__set__lb,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V3x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1lb_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V0cmp_2E0),V2t_2E0),V1lb_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V2t_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1lb_2E0: A_27a,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V2t_2E0),V1lb_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V0cmp_2E0),V2t_2E0),V1lb_2E0)) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__set__lb_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V2t_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V2t_2E0),V1lb_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__set__ub,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V3x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2ub_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V0cmp_2E0),V1t_2E0),V2ub_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V1t_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V3x_2E0,V2ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2ub_2E0: A_27a,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V1t_2E0),V2ub_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V0cmp_2E0),V1t_2E0),V2ub_2E0)) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__set__ub_2E3(A_27a,V0cmp_2E0,V1t_2E0,V2ub_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V1t_2E0),V2ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__set__lb__ub,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))))] :
( ! [V4x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1lb_2E0: A_27a,V3ub_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0,V4x_2E0),V0cmp_2E0),V2t_2E0),V1lb_2E0),V3ub_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V2t_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
& ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V4x_2E0,V3ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1lb_2E0: A_27a,V3ub_2E0: A_27a,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F0_2E0,V0cmp_2E0),V2t_2E0),V1lb_2E0),V3ub_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F1_2E0,V4x_2E0),V0cmp_2E0),V2t_2E0),V1lb_2E0),V3ub_2E0)) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__set__lb__ub_2E4(A_27a,V0cmp_2E0,V1lb_2E0,V2t_2E0,V3ub_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F0_2E0,V0cmp_2E0),V2t_2E0),V1lb_2E0),V3ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__lb__ub,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V6x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V4lb_2E0),V6x_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V4lb_2E0,V6x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V2ub_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V5l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6x_2E0: A_27a,V7r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V8ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V5l_2E0,V6x_2E0,V7r_2E0),V8ub_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V4lb_2E0),V6x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V6x_2E0),V8ub_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,V5l_2E0,V6x_2E0),c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V3cmp_2E0,V6x_2E0,V7r_2E0,V8ub_2E0)),c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,V5l_2E0,V8ub_2E0)),c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,V7r_2E0,V8ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__lb,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3lb_2E0: A_27a,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2cmp_2E0),V3lb_2E0),V5x_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V3lb_2E0,V5x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3lb_2E0: A_27a,V4l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V5x_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V2cmp_2E0,V3lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V4l_2E0,V5x_2E0,V6r_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2cmp_2E0),V3lb_2E0),V5x_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V2cmp_2E0,V3lb_2E0,V4l_2E0,V5x_2E0),c_2Elist_2ECONS_2E2(A_27a,V5x_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V2cmp_2E0,V5x_2E0,V6r_2E0)),c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V2cmp_2E0,V3lb_2E0,V6r_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__ub,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V6ub_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2cmp_2E0),V4x_2E0),V6ub_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V4x_2E0,V6ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V1ub_2E0) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6ub_2E0: A_27a] : ( c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V2cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V3l_2E0,V4x_2E0,V5r_2E0),V6ub_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V2cmp_2E0),V4x_2E0),V6ub_2E0),c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V2cmp_2E0,V3l_2E0,V4x_2E0),c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V2cmp_2E0,V4x_2E0,V5r_2E0,V6ub_2E0)),c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V2cmp_2E0,V3l_2E0,V6ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V1cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2l_2E0,V3x_2E0,V4r_2E0)) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EAPPEND_2E2(A_27a,c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V1cmp_2E0,V2l_2E0,V3x_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,c_2Elist_2ENIL_2E0(A_27a))),c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V1cmp_2E0,V3x_2E0,V4r_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__lb__ub__ac,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V7x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V4cmp_2E0),V5lb_2E0),V7x_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2ub_2E0: A_27a,V3m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V2ub_2E0,V3m_2E0) = V3m_2E0 )
& ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7x_2E0: A_27a,V8r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V9ub_2E0: A_27a,V10m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V4cmp_2E0,V5lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V6l_2E0,V7x_2E0,V8r_2E0),V9ub_2E0,V10m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V4cmp_2E0),V5lb_2E0),V7x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V4cmp_2E0),V7x_2E0),V9ub_2E0),c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V4cmp_2E0,V5lb_2E0,V6l_2E0,V7x_2E0,c_2Elist_2ECONS_2E2(A_27a,V7x_2E0,c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V4cmp_2E0,V7x_2E0,V8r_2E0,V9ub_2E0,V10m_2E0))),c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V4cmp_2E0,V5lb_2E0,V6l_2E0,V9ub_2E0,V10m_2E0)),c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V4cmp_2E0,V5lb_2E0,V8r_2E0,V9ub_2E0,V10m_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__lb__ac,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V6x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V4lb_2E0),V6x_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V4lb_2E0,V6x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V2m_2E0) = V2m_2E0 )
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V5l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6x_2E0: A_27a,V7r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V8m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,V3cmp_2E0,V4lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V5l_2E0,V6x_2E0,V7r_2E0),V8m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V4lb_2E0),V6x_2E0),c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V3cmp_2E0,V4lb_2E0,V5l_2E0,V6x_2E0,c_2Elist_2ECONS_2E2(A_27a,V6x_2E0,c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,V3cmp_2E0,V6x_2E0,V7r_2E0,V8m_2E0))),c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,V3cmp_2E0,V4lb_2E0,V7r_2E0,V8m_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__ub__ac,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5x_2E0: A_27a,V7ub_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V5x_2E0),V7ub_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V5x_2E0,V7ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1ub_2E0: A_27a,V2m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V1ub_2E0,V2m_2E0) = V2m_2E0 )
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V5x_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7ub_2E0: A_27a,V8m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,V3cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V4l_2E0,V5x_2E0,V6r_2E0),V7ub_2E0,V8m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V3cmp_2E0),V5x_2E0),V7ub_2E0),c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,V3cmp_2E0,V4l_2E0,V5x_2E0,c_2Elist_2ECONS_2E2(A_27a,V5x_2E0,c_2Eenumeral_2Ebt__to__ol__lb__ub__ac_2E5(A_27a,V3cmp_2E0,V5x_2E0,V6r_2E0,V7ub_2E0,V8m_2E0))),c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,V3cmp_2E0,V4l_2E0,V7ub_2E0,V8m_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__ac,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ac_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V1m_2E0) = V1m_2E0 )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6m_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol__ac_2E3(A_27a,V2cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V3l_2E0,V4x_2E0,V5r_2E0),V6m_2E0) = c_2Eenumeral_2Ebt__to__ol__ub__ac_2E4(A_27a,V2cmp_2E0,V3l_2E0,V4x_2E0,c_2Elist_2ECONS_2E2(A_27a,V4x_2E0,c_2Eenumeral_2Ebt__to__ol__lb__ac_2E4(A_27a,V2cmp_2E0,V4x_2E0,V5r_2E0,V6m_2E0))) ) ) ).
tff(thm_2Eenumeral_2EOWL,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V1s_2E0,V2l_2E0))
<=> ( ( V1s_2E0 = c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0) )
& p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2l_2E0)) ) ) ).
tff(thm_2Eenumeral_2EOU,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V3x_2E0: A_27a,V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( p(app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V1t_2E0),V2u_2E0),V0cmp_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1t_2E0))
& ! [V4z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4z_2E0,V2u_2E0))
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V3x_2E0,V4z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) )
=> ( ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V1t_2E0),V2u_2E0),V0cmp_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V3x_2E0),V1t_2E0),V2u_2E0),V0cmp_2E0)) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V1t_2E0,V2u_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V1t_2E0),V2u_2E0),V0cmp_2E0)),V2u_2E0) ) ) ) ).
tff(thm_2Eenumeral_2EUO,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V3y_2E0: A_27a,V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( p(app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V3y_2E0),V2t_2E0),V1s_2E0),V0cmp_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V2t_2E0))
& ! [V4z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4z_2E0,V1s_2E0))
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V4z_2E0,V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) )
=> ( ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2t_2E0),V1s_2E0),V0cmp_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3y_2E0,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Ebool))),F1_2E0,V3y_2E0),V2t_2E0),V1s_2E0),V0cmp_2E0)) )
=> ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EUO_2E3(A_27a,V0cmp_2E0,V1s_2E0,V2t_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2t_2E0),V1s_2E0),V0cmp_2E0))) ) ) ) ).
tff(thm_2Eenumeral_2ELESS__ALL,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1x_2E0,V2s_2E0))
<=> ! [V3y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V2s_2E0))
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1x_2E0,V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ).
tff(thm_2Eenumeral_2Ebl__to__set,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V7y_2E0: A_27a,V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V7y_2E0),V3cmp_2E0),V5t_2E0),V4x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V7y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V3cmp_2E0,V5t_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V4x_2E0,V7y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
=> ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a,V7y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V3cmp_2E0),V5t_2E0),V4x_2E0),V7y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V7y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V7y_2E0),V3cmp_2E0),V5t_2E0),V4x_2E0)) )
=> ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Ebl__to__set_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__to__set_2E2(A_27a,V1cmp_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V2b_2E0)) = c_2Eenumeral_2Ebl__to__set_2E2(A_27a,V1cmp_2E0,V2b_2E0) )
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V5t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ebl__to__set_2E2(A_27a,V3cmp_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V4x_2E0,V5t_2E0,V6b_2E0)) = c_2Eenumeral_2EOU_2E3(A_27a,V3cmp_2E0,c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V4x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V3cmp_2E0),V5t_2E0),V4x_2E0))),c_2Eenumeral_2Ebl__to__set_2E2(A_27a,V3cmp_2E0,V6b_2E0)) ) ) ) ) ).
tff(thm_2Eenumeral_2EOL__bt__lb__ub,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2ub_2E0: A_27a] :
( p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V2ub_2E0))
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V2ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V5l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6x_2E0: A_27a,V7r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V8ub_2E0: A_27a] :
( p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V5l_2E0,V6x_2E0,V7r_2E0),V8ub_2E0))
<=> ( p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V3cmp_2E0,V4lb_2E0,V5l_2E0,V6x_2E0))
& p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V3cmp_2E0,V6x_2E0,V7r_2E0,V8ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2EOL__bt__lb,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a] : ( c_2Eenumeral_2EOL__bt__lb_2E3(A_27a,V0cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3lb_2E0: A_27a,V4l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V5x_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( p(c_2Eenumeral_2EOL__bt__lb_2E3(A_27a,V2cmp_2E0,V3lb_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V4l_2E0,V5x_2E0,V6r_2E0)))
<=> ( p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V2cmp_2E0,V3lb_2E0,V4l_2E0,V5x_2E0))
& p(c_2Eenumeral_2EOL__bt__lb_2E3(A_27a,V2cmp_2E0,V5x_2E0,V6r_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2EOL__bt__ub,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1ub_2E0: A_27a] : ( c_2Eenumeral_2EOL__bt__ub_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a),V1ub_2E0) = c_2Ebool_2ET_2E0 )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6ub_2E0: A_27a] :
( p(c_2Eenumeral_2EOL__bt__ub_2E3(A_27a,V2cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V3l_2E0,V4x_2E0,V5r_2E0),V6ub_2E0))
<=> ( p(c_2Eenumeral_2EOL__bt__ub_2E3(A_27a,V2cmp_2E0,V3l_2E0,V4x_2E0))
& p(c_2Eenumeral_2EOL__bt__lb__ub_2E4(A_27a,V2cmp_2E0,V4x_2E0,V5r_2E0,V6ub_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2EOL__bt,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2EOL__bt_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( p(c_2Eenumeral_2EOL__bt_2E2(A_27a,V1cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2l_2E0,V3x_2E0,V4r_2E0)))
<=> ( p(c_2Eenumeral_2EOL__bt__ub_2E3(A_27a,V1cmp_2E0,V2l_2E0,V3x_2E0))
& p(c_2Eenumeral_2EOL__bt__lb_2E3(A_27a,V1cmp_2E0,V3x_2E0,V4r_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__distinct,axiom,
! [A_27a: $tType,V0a2_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1a1_2E0: A_27a,V2a0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ent_2E0(A_27a) != c_2Eenumeral_2Enode_2E3(A_27a,V2a0_2E0,V1a1_2E0,V0a2_2E0) ) ).
tff(thm_2Eenumeral_2Ebt__nchotomy,axiom,
! [A_27a: $tType,V0bb_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( ( V0bb_2E0 = c_2Eenumeral_2Ent_2E0(A_27a) )
| ? [V1b_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2a_2E0: A_27a,V3b0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( V0bb_2E0 = c_2Eenumeral_2Enode_2E3(A_27a,V1b_2E0,V2a_2E0,V3b0_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebt__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: A_27b,V1f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))))] :
? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)] :
( ( app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,V2fn_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = V0f0_2E0 )
& ! [V3a0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4a1_2E0: A_27a,V5a2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,V2fn_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V3a0_2E0,V4a1_2E0,V5a2_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V1f1_2E0,V4a1_2E0),V3a0_2E0),V5a2_2E0),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,V2fn_2E0,V3a0_2E0)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,V2fn_2E0,V5a2_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebt__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eenumeral_2Ent_2E0(A_27a)))
& ! [V1b_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2b0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( ( p(app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0))
& p(app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2b0_2E0)) )
=> ! [V3a_2E0: A_27a] : p(app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V1b_2E0,V3a_2E0,V2b0_2E0))) ) )
=> ! [V4b_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V4b_2E0)) ) ).
tff(thm_2Eenumeral_2Ebt__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f_27_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),V2M_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3M_27_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4v_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)))] :
( ( ( V2M_2E0 = V3M_27_2E0 )
& ( ( V3M_27_2E0 = c_2Eenumeral_2Ent_2E0(A_27a) )
=> ( V4v_2E0 = V0v_27_2E0 ) )
& ! [V6a0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7a1_2E0: A_27a,V8a2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( ( V3M_27_2E0 = c_2Eenumeral_2Enode_2E3(A_27a,V6a0_2E0,V7a1_2E0,V8a2_2E0) )
=> ( app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)),V5f_2E0,V6a0_2E0),V7a1_2E0),V8a2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)),V1f_27_2E0,V6a0_2E0),V7a1_2E0),V8a2_2E0) ) ) )
=> ( c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,V2M_2E0,V4v_2E0,V5f_2E0) = c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,V3M_27_2E0,V0v_27_2E0,V1f_27_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebt__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)))] :
( ( c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,V0x_2E0,V2v_2E0,V3f_2E0) = V1v_27_2E0 )
<=> ( ( ( V0x_2E0 = c_2Eenumeral_2Ent_2E0(A_27a) )
& ( V2v_2E0 = V1v_27_2E0 ) )
| ? [V4b_2E0: tyop_2Eenumeral_2Ebt(A_27a),V5a_2E0: A_27a,V6b0_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( ( V0x_2E0 = c_2Eenumeral_2Enode_2E3(A_27a,V4b_2E0,V5a_2E0,V6b0_2E0) )
& ( app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)),V3f_2E0,V4b_2E0),V5a_2E0),V6b0_2E0) = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Eenumeral_2Edatatype__bl,axiom,
! [A_27a: $tType,V0bl_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))),tyop_2Emin_2Ebool)))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))),tyop_2Emin_2Ebool)),V0bl_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)),c_2Eenumeral_2Ezerbl_2E0(A_27a)),c_2Eenumeral_2Eonebl_2E0(A_27a)))) ).
tff(thm_2Eenumeral_2Ebl__11,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eenumeral_2Ebl(A_27a),V1a_27_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( c_2Eenumeral_2Ezerbl_2E1(A_27a,V0a_2E0) = c_2Eenumeral_2Ezerbl_2E1(A_27a,V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a0_2E0: A_27a,V3a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4a2_2E0: tyop_2Eenumeral_2Ebl(A_27a),V5a0_27_2E0: A_27a,V6a1_27_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7a2_27_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( c_2Eenumeral_2Eonebl_2E3(A_27a,V2a0_2E0,V3a1_2E0,V4a2_2E0) = c_2Eenumeral_2Eonebl_2E3(A_27a,V5a0_27_2E0,V6a1_27_2E0,V7a2_27_2E0) )
<=> ( ( V2a0_2E0 = V5a0_27_2E0 )
& ( V3a1_2E0 = V6a1_27_2E0 )
& ( V4a2_2E0 = V7a2_27_2E0 ) ) ) ) ).
tff(thm_2Eenumeral_2Ebl__distinct,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Enbl_2E0(A_27a) != c_2Eenumeral_2Ezerbl_2E1(A_27a,V0a_2E0) )
& ! [V1a2_2E0: tyop_2Eenumeral_2Ebl(A_27a),V2a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3a0_2E0: A_27a] : ( c_2Eenumeral_2Enbl_2E0(A_27a) != c_2Eenumeral_2Eonebl_2E3(A_27a,V3a0_2E0,V2a1_2E0,V1a2_2E0) )
& ! [V4a2_2E0: tyop_2Eenumeral_2Ebl(A_27a),V5a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6a0_2E0: A_27a,V7a_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( c_2Eenumeral_2Ezerbl_2E1(A_27a,V7a_2E0) != c_2Eenumeral_2Eonebl_2E3(A_27a,V6a0_2E0,V5a1_2E0,V4a2_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebl__nchotomy,axiom,
! [A_27a: $tType,V0bb_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( V0bb_2E0 = c_2Eenumeral_2Enbl_2E0(A_27a) )
| ? [V1b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( V0bb_2E0 = c_2Eenumeral_2Ezerbl_2E1(A_27a,V1b_2E0) )
| ? [V2a_2E0: A_27a,V3b0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( V0bb_2E0 = c_2Eenumeral_2Eonebl_2E3(A_27a,V2a_2E0,V3b0_2E0,V4b_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebl__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: A_27b,V1f1_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),V2f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))))] :
? [V3fn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)] :
( ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V3fn_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)) = V0f0_2E0 )
& ! [V4a_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V3fn_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V4a_2E0)) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),V1f1_2E0,V4a_2E0),app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V3fn_2E0,V4a_2E0)) )
& ! [V5a0_2E0: A_27a,V6a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V7a2_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V3fn_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V5a0_2E0,V6a1_2E0,V7a2_2E0)) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0,V5a0_2E0),V6a1_2E0),V7a2_2E0),app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V3fn_2E0,V7a2_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebl__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eenumeral_2Enbl_2E0(A_27a)))
& ! [V1b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0))
=> p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eenumeral_2Ezerbl_2E1(A_27a,V1b_2E0))) )
& ! [V2b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2b_2E0))
=> ! [V3b0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4a_2E0: A_27a] : p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Eenumeral_2Eonebl_2E3(A_27a,V4a_2E0,V3b0_2E0,V2b_2E0))) ) )
=> ! [V5b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V5b_2E0)) ) ).
tff(thm_2Eenumeral_2Ebl__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f1_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V2f_27_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V3M_2E0: tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0: tyop_2Eenumeral_2Ebl(A_27a),V5v_2E0: A_27b,V6f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V7f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)))] :
( ( ( V3M_2E0 = V4M_27_2E0 )
& ( ( V4M_27_2E0 = c_2Eenumeral_2Enbl_2E0(A_27a) )
=> ( V5v_2E0 = V0v_27_2E0 ) )
& ! [V8a_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( V4M_27_2E0 = c_2Eenumeral_2Ezerbl_2E1(A_27a,V8a_2E0) )
=> ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V6f_2E0,V8a_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V2f_27_2E0,V8a_2E0) ) )
& ! [V9a0_2E0: A_27a,V10a1_2E0: tyop_2Eenumeral_2Ebt(A_27a),V11a2_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( V4M_27_2E0 = c_2Eenumeral_2Eonebl_2E3(A_27a,V9a0_2E0,V10a1_2E0,V11a2_2E0) )
=> ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),V7f1_2E0,V9a0_2E0),V10a1_2E0),V11a2_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),V1f1_27_2E0,V9a0_2E0),V10a1_2E0),V11a2_2E0) ) ) )
=> ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,V3M_2E0,V5v_2E0,V6f_2E0,V7f1_2E0) = c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,V4M_27_2E0,V0v_27_2E0,V2f_27_2E0,V1f1_27_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebl__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Eenumeral_2Ebl(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V4f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)] :
( ( c_2Eenumeral_2Ebl__CASE_2E4(A_27a,A_27b,V0x_2E0,V2v_2E0,V4f_2E0,V3f1_2E0) = V1v_27_2E0 )
<=> ( ( ( V0x_2E0 = c_2Eenumeral_2Enbl_2E0(A_27a) )
& ( V2v_2E0 = V1v_27_2E0 ) )
| ? [V5b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( V0x_2E0 = c_2Eenumeral_2Ezerbl_2E1(A_27a,V5b_2E0) )
& ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,V4f_2E0,V5b_2E0) = V1v_27_2E0 ) )
| ? [V6a_2E0: A_27a,V7b0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V8b_2E0: tyop_2Eenumeral_2Ebl(A_27a)] :
( ( V0x_2E0 = c_2Eenumeral_2Eonebl_2E3(A_27a,V6a_2E0,V7b0_2E0,V8b_2E0) )
& ( app_2E2(tyop_2Eenumeral_2Ebl(A_27a),A_27b,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),V3f1_2E0,V6a_2E0),V7b0_2E0),V8b_2E0) = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Eenumeral_2Ebt__11,axiom,
! [A_27a: $tType,V0a0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V1a1_2E0: A_27a,V2a2_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3a0_27_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4a1_27_2E0: A_27a,V5a2_27_2E0: tyop_2Eenumeral_2Ebt(A_27a)] :
( ( c_2Eenumeral_2Enode_2E3(A_27a,V0a0_2E0,V1a1_2E0,V2a2_2E0) = c_2Eenumeral_2Enode_2E3(A_27a,V3a0_27_2E0,V4a1_27_2E0,V5a2_27_2E0) )
<=> ( ( V0a0_2E0 = V3a0_27_2E0 )
& ( V1a1_2E0 = V4a1_27_2E0 )
& ( V2a2_2E0 = V5a2_27_2E0 ) ) ) ).
tff(thm_2Eenumeral_2Edatatype__bt,axiom,
! [A_27a: $tType,V0bt_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Ebool))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))),tyop_2Emin_2Ebool),V0bt_2E0,c_2Eenumeral_2Ent_2E0(A_27a)),c_2Eenumeral_2Enode_2E0(A_27a)))) ).
tff(thm_2Eenumeral_2Ebt__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,c_2Eenumeral_2Ent_2E0(A_27a),V0v_2E0,V1f_2E0) = V0v_2E0 )
& ! [V2a0_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3a1_2E0: A_27a,V4a2_2E0: tyop_2Eenumeral_2Ebt(A_27a),V5v_2E0: A_27b,V6f_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)))] : ( c_2Eenumeral_2Ebt__CASE_2E3(A_27a,A_27b,c_2Eenumeral_2Enode_2E3(A_27a,V2a0_2E0,V3a1_2E0,V4a2_2E0),V5v_2E0,V6f_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b)),V6f_2E0,V2a0_2E0),V3a1_2E0),V4a2_2E0) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__list__thm,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__list_2E1(A_27a,V0t_2E0) = c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,V0t_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ).
tff(thm_2Eenumeral_2Esmerge__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6y_2E0: A_27a,V7m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V5cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ECONS_2E2(A_27a,V6y_2E0,V7m_2E0)))
& ! [V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V9x_2E0: A_27a,V10l_2E0: tyop_2Elist_2Elist(A_27a),V11y_2E0: A_27a,V12m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> ! [V13v_2E0: tyop_2Etoto_2Etoto(A_27a),V14v1_2E0: tyop_2Elist_2Elist(A_27a),V15v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V13v_2E0),V14v1_2E0),V15v2_2E0)) ) ).
tff(thm_2Eenumeral_2Esmerge,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge_2E3(A_27a,V3cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0) )
& ! [V4y_2E0: A_27a,V5m_2E0: tyop_2Elist_2Elist(A_27a),V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge_2E3(A_27a,V6cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V4y_2E0,V5m_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V4y_2E0,V5m_2E0) )
& ! [V7y_2E0: A_27a,V8x_2E0: A_27a,V9m_2E0: tyop_2Elist_2Elist(A_27a),V10l_2E0: tyop_2Elist_2Elist(A_27a),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V8x_2E0,V7y_2E0),c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V11cmp_2E0,V10l_2E0,c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0))),c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V11cmp_2E0,V10l_2E0,V9m_2E0)),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),V9m_2E0))) ) ) ).
tff(thm_2Eenumeral_2Esmerge__nil,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,V1l_2E0,c_2Elist_2ENIL_2E0(A_27a)) = V1l_2E0 )
& ( c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),V1l_2E0) = V1l_2E0 ) ) ).
tff(thm_2Eenumeral_2Esmerge__OL,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a),V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
& p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0)) )
=> p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0))) ) ).
tff(thm_2Eenumeral_2EOL__sublists__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V3lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V3lol_2E0))) )
& ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5m_2E0: tyop_2Elist_2Elist(A_27a),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),V6lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V5m_2E0),V6lol_2E0))) ) )
=> ! [V7v_2E0: tyop_2Etoto_2Etoto(A_27a),V8v1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).
tff(thm_2Eenumeral_2EOL__sublists,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2EOL__sublists_2E2(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) = c_2Ebool_2ET_2E0 )
& ! [V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2EOL__sublists_2E2(A_27a,V2cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V1lol_2E0)) = c_2Eenumeral_2EOL__sublists_2E2(A_27a,V2cmp_2E0,V1lol_2E0) )
& ! [V3m_2E0: tyop_2Elist_2Elist(A_27a),V4lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
( p(c_2Eenumeral_2EOL__sublists_2E2(A_27a,V5cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3m_2E0),V4lol_2E0)))
<=> ( p(c_2Eenumeral_2EOL_2E2(A_27a,V5cmp_2E0,V3m_2E0))
& p(c_2Eenumeral_2EOL__sublists_2E2(A_27a,V5cmp_2E0,V4lol_2E0)) ) ) ) ).
tff(thm_2Eenumeral_2Elol__set__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))
& ! [V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,V1lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V1lol_2E0))) )
& ! [V2m_2E0: tyop_2Elist_2Elist(A_27a),V3lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,V3lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V2m_2E0),V3lol_2E0))) ) )
=> ! [V4v_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,V0P_2E0,V4v_2E0)) ) ).
tff(thm_2Eenumeral_2Elol__set,axiom,
! [A_27a: $tType] :
( ( c_2Eenumeral_2Elol__set_2E1(A_27a,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ! [V0lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2Elol__set_2E1(A_27a,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V0lol_2E0)) = c_2Eenumeral_2Elol__set_2E1(A_27a,V0lol_2E0) )
& ! [V1m_2E0: tyop_2Elist_2Elist(A_27a),V2lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : ( c_2Eenumeral_2Elol__set_2E1(A_27a,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V1m_2E0),V2lol_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1m_2E0),c_2Eenumeral_2Elol__set_2E1(A_27a,V2lol_2E0)) ) ) ).
tff(thm_2Eenumeral_2Eincr__smerge__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Elist_2Elist(A_27a),V5lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V5lol_2E0)))
& ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7l_2E0: tyop_2Elist_2Elist(A_27a),V8m_2E0: tyop_2Elist_2Elist(A_27a),V9lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Eenumeral_2Esmerge_2E3(A_27a,V6cmp_2E0,V7l_2E0,V8m_2E0)),V9lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V7l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V8m_2E0),V9lol_2E0))) ) )
=> ! [V10v_2E0: tyop_2Etoto_2Etoto(A_27a),V11v1_2E0: tyop_2Elist_2Elist(A_27a),V12v2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V10v_2E0),V11v1_2E0),V12v2_2E0)) ) ).
tff(thm_2Eenumeral_2Eincr__smerge,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V1cmp_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V0l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) )
& ! [V2lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V3l_2E0: tyop_2Elist_2Elist(A_27a),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V4cmp_2E0,V3l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V2lol_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3l_2E0),V2lol_2E0) )
& ! [V5m_2E0: tyop_2Elist_2Elist(A_27a),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V7l_2E0: tyop_2Elist_2Elist(A_27a),V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V8cmp_2E0,V7l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V5m_2E0),V6lol_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V8cmp_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V8cmp_2E0,V7l_2E0,V5m_2E0),V6lol_2E0)) ) ) ).
tff(thm_2Eenumeral_2Eincr__smerge__OL,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V2l_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eenumeral_2EOL__sublists_2E2(A_27a,V0cmp_2E0,V1lol_2E0))
& p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2l_2E0)) )
=> p(c_2Eenumeral_2EOL__sublists_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Eincr__smerge_2E3(A_27a,V0cmp_2E0,V2l_2E0,V1lol_2E0))) ) ).
tff(thm_2Eenumeral_2Esmerge__out__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))
& ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Elist_2Elist(A_27a),V5lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),V5lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V5lol_2E0))) )
& ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7l_2E0: tyop_2Elist_2Elist(A_27a),V8m_2E0: tyop_2Elist_2Elist(A_27a),V9lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Eenumeral_2Esmerge_2E3(A_27a,V6cmp_2E0,V7l_2E0,V8m_2E0)),V9lol_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V7l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V8m_2E0),V9lol_2E0))) ) )
=> ! [V10v_2E0: tyop_2Etoto_2Etoto(A_27a),V11v1_2E0: tyop_2Elist_2Elist(A_27a),V12v2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0P_2E0,V10v_2E0),V11v1_2E0),V12v2_2E0)) ) ).
tff(thm_2Eenumeral_2Esmerge__out,axiom,
! [A_27a: $tType] :
( ! [V0l_2E0: tyop_2Elist_2Elist(A_27a),V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge__out_2E3(A_27a,V1cmp_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) = V0l_2E0 )
& ! [V2lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V3l_2E0: tyop_2Elist_2Elist(A_27a),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge__out_2E3(A_27a,V4cmp_2E0,V3l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27a)),V2lol_2E0)) = c_2Eenumeral_2Esmerge__out_2E3(A_27a,V4cmp_2E0,V3l_2E0,V2lol_2E0) )
& ! [V5m_2E0: tyop_2Elist_2Elist(A_27a),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),V7l_2E0: tyop_2Elist_2Elist(A_27a),V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esmerge__out_2E3(A_27a,V8cmp_2E0,V7l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V5m_2E0),V6lol_2E0)) = c_2Eenumeral_2Esmerge__out_2E3(A_27a,V8cmp_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V8cmp_2E0,V7l_2E0,V5m_2E0),V6lol_2E0) ) ) ).
tff(thm_2Eenumeral_2EIN__bt__to__set,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1y_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a))) = c_2Ebool_2EF_2E0 )
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V4x_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(A_27a),V6y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V2cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V3l_2E0,V4x_2E0,V5r_2E0))))
<=> ( ( p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V2cmp_2E0,V3l_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V6y_2E0,V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
| ( V6y_2E0 = V4x_2E0 )
| ( p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V2cmp_2E0,V5r_2E0)))
& ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V4x_2E0,V6y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ) ).
tff(thm_2Eenumeral_2ENOT__IN__nt,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1y_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1y_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(A_27a))) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Eenumeral_2EIN__node,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3y_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2l_2E0,V3y_2E0,V4r_2E0))) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1x_2E0,V3y_2E0),c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V2l_2E0)),c_2Ebool_2ET_2E0,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V4r_2E0))) ) ).
tff(thm_2Eenumeral_2Eol__set,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V1t_2E0) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,V1t_2E0)) ) ).
tff(thm_2Eenumeral_2EOL__bt__to__ol__lb__ub,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2lb_2E0: A_27a,V3ub_2E0: A_27a] : p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ebt__to__ol__lb__ub_2E4(A_27a,V0cmp_2E0,V2lb_2E0,V1t_2E0,V3ub_2E0))) ).
tff(thm_2Eenumeral_2EOL__bt__to__ol__lb,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2lb_2E0: A_27a] : p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ebt__to__ol__lb_2E3(A_27a,V0cmp_2E0,V2lb_2E0,V1t_2E0))) ).
tff(thm_2Eenumeral_2EOL__bt__to__ol__ub,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a),V2ub_2E0: A_27a] : p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ebt__to__ol__ub_2E3(A_27a,V0cmp_2E0,V1t_2E0,V2ub_2E0))) ).
tff(thm_2Eenumeral_2EOL__bt__to__ol,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,V1t_2E0))) ).
tff(thm_2Eenumeral_2EOWL__bt__to__ol,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,V1t_2E0),c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,V1t_2E0))) ).
tff(thm_2Eenumeral_2EEMPTY__OU,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1sl_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V1sl_2E0) = V1sl_2E0 ) ).
tff(thm_2Eenumeral_2EOU__EMPTY,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V1t_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = V1t_2E0 ) ).
tff(thm_2Eenumeral_2ELESS__UO__LEM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27a,V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V4z_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4z_2E0,c_2Eenumeral_2EUO_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V3s_2E0)))
=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2y_2E0,V4z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
<=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V2y_2E0,V1x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Eenumeral_2ELESS__ALL__OU,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1x_2E0,c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V2u_2E0,V3v_2E0)))
<=> ( p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1x_2E0,V2u_2E0))
& p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1x_2E0,V3v_2E0)) ) ) ).
tff(thm_2Eenumeral_2EOU__ASSOC,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V1a_2E0,c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V2b_2E0,V3c_2E0)) = c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V1a_2E0,V2b_2E0),V3c_2E0) ) ).
tff(thm_2Eenumeral_2ELESS__ALL__UO__LEM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1a_2E0,V2s_2E0))
=> ( c_2Eenumeral_2EUO_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V2s_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,V2s_2E0) ) ) ).
tff(thm_2Eenumeral_2ELESS__ALL__OU__UO__LEM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1a_2E0,V2s_2E0))
& p(c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V1a_2E0,V3t_2E0)) )
=> ( c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,c_2Eenumeral_2EUO_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V2s_2E0),V3t_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,c_2Eenumeral_2EOU_2E3(A_27a,V0cmp_2E0,V2s_2E0,V3t_2E0)) ) ) ).
tff(thm_2Eenumeral_2Ebt__to__ol__ID__IMP,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
=> ( c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(A_27a,V1l_2E0)) = V1l_2E0 ) ) ).
tff(thm_2Eenumeral_2EOL__UNION__IMP,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0))
=> ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)))
& ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2m_2E0)) ) ) ) ) ).
tff(thm_2Eenumeral_2Esinter__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6y_2E0: A_27a,V7m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V5cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ECONS_2E2(A_27a,V6y_2E0,V7m_2E0)))
& ! [V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V9x_2E0: A_27a,V10l_2E0: tyop_2Elist_2Elist(A_27a),V11y_2E0: A_27a,V12m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> ! [V13v_2E0: tyop_2Etoto_2Etoto(A_27a),V14v1_2E0: tyop_2Elist_2Elist(A_27a),V15v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V13v_2E0),V14v1_2E0),V15v2_2E0)) ) ).
tff(thm_2Eenumeral_2Esinter,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esinter_2E3(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esinter_2E3(A_27a,V3cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V4y_2E0: A_27a,V5m_2E0: tyop_2Elist_2Elist(A_27a),V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esinter_2E3(A_27a,V6cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V4y_2E0,V5m_2E0)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V7y_2E0: A_27a,V8x_2E0: A_27a,V9m_2E0: tyop_2Elist_2Elist(A_27a),V10l_2E0: tyop_2Elist_2Elist(A_27a),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esinter_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V8x_2E0,V7y_2E0),c_2Eenumeral_2Esinter_2E3(A_27a,V11cmp_2E0,V10l_2E0,c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0)),c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,c_2Eenumeral_2Esinter_2E3(A_27a,V11cmp_2E0,V10l_2E0,V9m_2E0)),c_2Eenumeral_2Esinter_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),V9m_2E0)) ) ) ).
tff(thm_2Eenumeral_2EOL__INTER__IMP,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0))
=> ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Esinter_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)))
& ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Eenumeral_2Esinter_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2m_2E0)) ) ) ) ) ).
tff(thm_2Eenumeral_2Esdiff__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V4l_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V3x_2E0,V4l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))
& ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6y_2E0: A_27a,V7m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V5cmp_2E0),c_2Elist_2ENIL_2E0(A_27a)),c_2Elist_2ECONS_2E2(A_27a,V6y_2E0,V7m_2E0)))
& ! [V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V9x_2E0: A_27a,V10l_2E0: tyop_2Elist_2Elist(A_27a),V11y_2E0: A_27a,V12m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),V12m_2E0)) )
& ( ( c_2Etoto_2Eapto_2E3(A_27a,V8cmp_2E0,V9x_2E0,V11y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V8cmp_2E0),c_2Elist_2ECONS_2E2(A_27a,V9x_2E0,V10l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V11y_2E0,V12m_2E0))) ) )
=> ! [V13v_2E0: tyop_2Etoto_2Etoto(A_27a),V14v1_2E0: tyop_2Elist_2Elist(A_27a),V15v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V13v_2E0),V14v1_2E0),V15v2_2E0)) ) ).
tff(thm_2Eenumeral_2Esdiff,axiom,
! [A_27a: $tType] :
( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esdiff_2E3(A_27a,V0cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V1x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(A_27a),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esdiff_2E3(A_27a,V3cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(A_27a,V1x_2E0,V2l_2E0) )
& ! [V4y_2E0: A_27a,V5m_2E0: tyop_2Elist_2Elist(A_27a),V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esdiff_2E3(A_27a,V6cmp_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ECONS_2E2(A_27a,V4y_2E0,V5m_2E0)) = c_2Elist_2ENIL_2E0(A_27a) )
& ! [V7y_2E0: A_27a,V8x_2E0: A_27a,V9m_2E0: tyop_2Elist_2Elist(A_27a),V10l_2E0: tyop_2Elist_2Elist(A_27a),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Eenumeral_2Esdiff_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(A_27a),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V8x_2E0,V7y_2E0),c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,c_2Eenumeral_2Esdiff_2E3(A_27a,V11cmp_2E0,V10l_2E0,c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V9m_2E0))),c_2Eenumeral_2Esdiff_2E3(A_27a,V11cmp_2E0,V10l_2E0,V9m_2E0),c_2Eenumeral_2Esdiff_2E3(A_27a,V11cmp_2E0,c_2Elist_2ECONS_2E2(A_27a,V8x_2E0,V10l_2E0),V9m_2E0)) ) ) ).
tff(thm_2Eenumeral_2EOL__DIFF__IMP,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
=> ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0))
=> ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Esdiff_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)))
& ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Eenumeral_2Esdiff_2E3(A_27a,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2m_2E0)) ) ) ) ) ).
tff(thm_2Eenumeral_2EENUMERAL__set,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0) = c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(A_27a,c_2Eenumeral_2Eincr__ssort_2E2(A_27a,V0cmp_2E0,V1l_2E0))) ) ).
tff(thm_2Eenumeral_2EOL__ENUMERAL,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V1l_2E0))
=> ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0) = c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(A_27a,V1l_2E0)) ) ) ).
tff(thm_2Eenumeral_2EOWL__UNION__THM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V1s_2E0,V2l_2E0))
& p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
=> p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V3t_2E0),c_2Eenumeral_2Esmerge_2E3(A_27a,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).
tff(thm_2Eenumeral_2EOWL__INTER__THM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V1s_2E0,V2l_2E0))
& p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
=> p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V3t_2E0),c_2Eenumeral_2Esinter_2E3(A_27a,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).
tff(thm_2Eenumeral_2EOWL__DIFF__THM,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V1s_2E0,V2l_2E0))
& p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
=> p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V3t_2E0),c_2Eenumeral_2Esdiff_2E3(A_27a,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).
tff(thm_2Eenumeral_2Ebetter__bt__to__ol,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Ebt__to__ol_2E2(A_27a,V0cmp_2E0,V1t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(A_27a),c_2Eenumeral_2EOL__bt_2E2(A_27a,V0cmp_2E0,V1t_2E0),c_2Eenumeral_2Ebt__to__list__ac_2E2(A_27a,V1t_2E0,c_2Elist_2ENIL_2E0(A_27a)),c_2Eenumeral_2Ebt__to__ol__ac_2E3(A_27a,V0cmp_2E0,V1t_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ).
tff(thm_2Eenumeral_2Eset__OWL__thm,axiom,
! [A_27a: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0),c_2Eenumeral_2Eincr__ssort_2E2(A_27a,V0cmp_2E0,V1l_2E0))) ).
%------------------------------------------------------------------------------