ITP001 Axioms: ITP106_7.ax
%------------------------------------------------------------------------------
% File : ITP106_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 : DeepSyntax.ax [Gau19]
% : HL4106_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 199 ( 47 unt; 109 typ; 0 def)
% Number of atoms : 453 ( 228 equ)
% Maximal formula atoms : 44 ( 2 avg)
% Number of connectives : 397 ( 34 ~; 33 |; 221 &)
% ( 61 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Maximal term depth : 20 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 89 ( 50 >; 39 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 104 ( 104 usr; 35 con; 0-10 aty)
% Number of variables : 699 ( 564 !; 90 ?; 699 :)
% ( 45 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2EDeepSyntax_2Edeep__form,type,
tyop_2EDeepSyntax_2Edeep__form: $tType ).
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $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_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $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_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2EDeepSyntax_2EAset_2E0,type,
c_2EDeepSyntax_2EAset_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))) ).
tff(c_2EDeepSyntax_2EAset_2E2,type,
c_2EDeepSyntax_2EAset_2E2: ( tyop_2Emin_2Ebool * tyop_2EDeepSyntax_2Edeep__form ) > tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2EDeepSyntax_2EBset_2E0,type,
c_2EDeepSyntax_2EBset_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))) ).
tff(c_2EDeepSyntax_2EBset_2E2,type,
c_2EDeepSyntax_2EBset_2E2: ( tyop_2Emin_2Ebool * tyop_2EDeepSyntax_2Edeep__form ) > tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool) ).
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_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_2EDeepSyntax_2EConjn_2E0,type,
c_2EDeepSyntax_2EConjn_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)) ).
tff(c_2EDeepSyntax_2EConjn_2E2,type,
c_2EDeepSyntax_2EConjn_2E2: ( tyop_2EDeepSyntax_2Edeep__form * tyop_2EDeepSyntax_2Edeep__form ) > tyop_2EDeepSyntax_2Edeep__form ).
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_2EDeepSyntax_2EDisjn_2E0,type,
c_2EDeepSyntax_2EDisjn_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)) ).
tff(c_2EDeepSyntax_2EDisjn_2E2,type,
c_2EDeepSyntax_2EDisjn_2E2: ( tyop_2EDeepSyntax_2Edeep__form * tyop_2EDeepSyntax_2Edeep__form ) > tyop_2EDeepSyntax_2Edeep__form ).
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_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_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_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E2,type,
c_2Ecombin_2EK_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
tff(c_2EDeepSyntax_2ELTx_2E0,type,
c_2EDeepSyntax_2ELTx_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2ELTx_2E1,type,
c_2EDeepSyntax_2ELTx_2E1: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
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_2EDeepSyntax_2ENegn_2E0,type,
c_2EDeepSyntax_2ENegn_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2ENegn_2E1,type,
c_2EDeepSyntax_2ENegn_2E1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
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_2EDeepSyntax_2EUnrelatedBool_2E0,type,
c_2EDeepSyntax_2EUnrelatedBool_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2EUnrelatedBool_2E1,type,
c_2EDeepSyntax_2EUnrelatedBool_2E1: tyop_2Emin_2Ebool > tyop_2EDeepSyntax_2Edeep__form ).
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_2EDeepSyntax_2Ealldivide_2E0,type,
c_2EDeepSyntax_2Ealldivide_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2EDeepSyntax_2Ealldivide_2E2,type,
c_2EDeepSyntax_2Ealldivide_2E2: ( tyop_2EDeepSyntax_2Edeep__form * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2EbasicSize_2Ebool__size_2E0,type,
c_2EbasicSize_2Ebool__size_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Enum_2Enum) ).
tff(c_2EbasicSize_2Ebool__size_2E1,type,
c_2EbasicSize_2Ebool__size_2E1: tyop_2Emin_2Ebool > tyop_2Enum_2Enum ).
tff(c_2EDeepSyntax_2Edeep__form__CASE_2E0,type,
c_2EDeepSyntax_2Edeep__form__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a))))))))) ).
tff(c_2EDeepSyntax_2Edeep__form__CASE_2E9,type,
c_2EDeepSyntax_2Edeep__form__CASE_2E9:
!>[A_27a: $tType] : ( ( tyop_2EDeepSyntax_2Edeep__form * tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)) * tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)) * tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a) * tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a) * tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a) * tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a) * tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a) * tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)) ) > A_27a ) ).
tff(c_2EDeepSyntax_2Edeep__form__size_2E0,type,
c_2EDeepSyntax_2Edeep__form__size_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Enum_2Enum) ).
tff(c_2EDeepSyntax_2Edeep__form__size_2E1,type,
c_2EDeepSyntax_2Edeep__form__size_2E1: tyop_2EDeepSyntax_2Edeep__form > tyop_2Enum_2Enum ).
tff(c_2EDeepSyntax_2Eeval__form_2E0,type,
c_2EDeepSyntax_2Eeval__form_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2EDeepSyntax_2Eeval__form_2E2,type,
c_2EDeepSyntax_2Eeval__form_2E2: ( tyop_2EDeepSyntax_2Edeep__form * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__add_2E0,type,
c_2Einteger_2Eint__add_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__add_2E2,type,
c_2Einteger_2Eint__add_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__divides_2E0,type,
c_2Einteger_2Eint__divides_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__divides_2E2,type,
c_2Einteger_2Eint__divides_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__le_2E0,type,
c_2Einteger_2Eint__le_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__le_2E2,type,
c_2Einteger_2Eint__le_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__lt_2E0,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__lt_2E2,type,
c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__mul_2E0,type,
c_2Einteger_2Eint__mul_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__mul_2E2,type,
c_2Einteger_2Eint__mul_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__neg_2E0,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__neg_2E1,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__of__num_2E0,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__of__num_2E1,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
tff(c_2EDeepSyntax_2Eneginf_2E0,type,
c_2EDeepSyntax_2Eneginf_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2Eneginf_2E1,type,
c_2EDeepSyntax_2Eneginf_2E1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
tff(c_2EDeepSyntax_2Eposinf_2E0,type,
c_2EDeepSyntax_2Eposinf_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2Eposinf_2E1,type,
c_2EDeepSyntax_2Eposinf_2E1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
tff(c_2EDeepSyntax_2ExDivided_2E0,type,
c_2EDeepSyntax_2ExDivided_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)) ).
tff(c_2EDeepSyntax_2ExDivided_2E2,type,
c_2EDeepSyntax_2ExDivided_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2EDeepSyntax_2Edeep__form ).
tff(c_2EDeepSyntax_2ExEQ_2E0,type,
c_2EDeepSyntax_2ExEQ_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2ExEQ_2E1,type,
c_2EDeepSyntax_2ExEQ_2E1: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
tff(c_2EDeepSyntax_2ExLT_2E0,type,
c_2EDeepSyntax_2ExLT_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form) ).
tff(c_2EDeepSyntax_2ExLT_2E1,type,
c_2EDeepSyntax_2ExLT_2E1: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
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_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Epair_2E_2C_2E0(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),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(arityeq2_2Ec_2EDeepSyntax_2EAset_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EAset_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),c_2EDeepSyntax_2EAset_2E0,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(arityeq2_2Ec_2EDeepSyntax_2EBset_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EBset_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),c_2EDeepSyntax_2EBset_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))] : ( c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))),c_2Eind__type_2ECONSTR_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2EDeepSyntax_2EConjn_2E2,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form,X1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EConjn_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2EConjn_2E0,X0_2E0),X1_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_2EDeepSyntax_2EDisjn_2E2,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form,X1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EDisjn_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2EDisjn_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,axiom,
! [X0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Ecombin_2EK_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2ELTx_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ELTx_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ELTx_2E0,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(arityeq1_2Ec_2EDeepSyntax_2ENegn_2E1,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(X0_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ENegn_2E0,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_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29_20mono_2Etyop_2EDeepSyntax_2Edeep__form,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2EDeepSyntax_2Edeep__form,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2EDeepSyntax_2Edeep__form),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2EUnrelatedBool_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EUnrelatedBool_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EUnrelatedBool_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2EDeepSyntax_2Ealldivide_2E2,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form,X1_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2EDeepSyntax_2Ealldivide_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EbasicSize_2Ebool__size_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2EbasicSize_2Ebool__size_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E0,X0_2E0) ) ).
tff(arityeq9_2Ec_2EDeepSyntax_2Edeep__form__CASE_2E9_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2EDeepSyntax_2Edeep__form,X1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),X2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),X3_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),X4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),X5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),X6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),X7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),X8_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0,X5_2E0,X6_2E0,X7_2E0,X8_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a))))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a)))))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a))))))),app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),A_27a)))))))),c_2EDeepSyntax_2Edeep__form__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0),X5_2E0),X6_2E0),X7_2E0),X8_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2Edeep__form__size_2E1,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(X0_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Enum_2Enum,c_2EDeepSyntax_2Edeep__form__size_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2EDeepSyntax_2Eeval__form_2E2,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form,X1_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2EDeepSyntax_2Eeval__form_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__add_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__divides_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__divides_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__le_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__le_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__lt_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Einteger_2Eint__mul_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Einteger_2Eint__neg_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2Eneginf_2E1,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eneginf_2E1(X0_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2Eneginf_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2Eposinf_2E1,axiom,
! [X0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eposinf_2E1(X0_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2Eposinf_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2EDeepSyntax_2ExDivided_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExDivided_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2ExDivided_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2ExEQ_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExEQ_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExEQ_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2EDeepSyntax_2ExLT_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExLT_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExLT_2E0,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_2EDeepSyntax_2Edeep__form__TY__DEF,axiom,
! [F8_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F7_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F6_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F5_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool)] :
( ! [V22n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F8_2E0,V22n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V19n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F7_2E0,V19n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V17n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F6_2E0,V17n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V15n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F5_2E0,V15n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V13n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F4_2E0,V13n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V11n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F3_2E0,V11n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V9n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F2_2E0,V9n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),F1_2E0,V6n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27deep__form_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))] :
( ( ? [V4a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V5a1_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V4a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V5a1_2E0,F1_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V4a0_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V5a1_2E0)) )
| ? [V7a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V8a1_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V7a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V8a1_2E0,F2_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V7a0_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V8a1_2E0)) )
| ? [V10a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),V10a_2E0,F3_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V10a_2E0)) )
| ? [V12a_2E0: tyop_2Emin_2Ebool] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0))),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),V12a_2E0,c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),F4_2E0) )
| ? [V14a_2E0: tyop_2Einteger_2Eint] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)))),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,V14a_2E0,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),F5_2E0) )
| ? [V16a_2E0: tyop_2Einteger_2Eint] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0))))),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,V16a_2E0,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),F6_2E0) )
| ? [V18a_2E0: tyop_2Einteger_2Eint] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)))))),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,V18a_2E0,c_2Ebool_2EARB_2E0(tyop_2Einteger_2Eint))),F7_2E0) )
| ? [V20a0_2E0: tyop_2Einteger_2Eint,V21a1_2E0: tyop_2Einteger_2Eint] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0))))))),c_2Epair_2E_2C_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,V20a0_2E0,V21a1_2E0)),F8_2E0) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2Emin_2Ebool,V2_27deep__form_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),tyop_2EDeepSyntax_2Edeep__form,F0_2E0,V0rep_2E0)) ) ) ) ) ) ) ) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__case__def,axiom,
! [A_27a: $tType] :
( ! [V0a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V2f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V3f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V4f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V5f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V6f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V7f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V8f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V9f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2EConjn_2E2(V0a0_2E0,V1a1_2E0),V2f_2E0,V3f1_2E0,V4f2_2E0,V5f3_2E0,V6f4_2E0,V7f5_2E0,V8f6_2E0,V9f7_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V2f_2E0,V0a0_2E0),V1a1_2E0) )
& ! [V10a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V11a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V12f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V13f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V14f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V15f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V16f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V17f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V18f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V19f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2EDisjn_2E2(V10a0_2E0,V11a1_2E0),V12f_2E0,V13f1_2E0,V14f2_2E0,V15f3_2E0,V16f4_2E0,V17f5_2E0,V18f6_2E0,V19f7_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V13f1_2E0,V10a0_2E0),V11a1_2E0) )
& ! [V20a_2E0: tyop_2EDeepSyntax_2Edeep__form,V21f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V22f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V23f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V24f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V25f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V26f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V27f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V28f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2ENegn_2E1(V20a_2E0),V21f_2E0,V22f1_2E0,V23f2_2E0,V24f3_2E0,V25f4_2E0,V26f5_2E0,V27f6_2E0,V28f7_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V23f2_2E0,V20a_2E0) )
& ! [V29a_2E0: tyop_2Emin_2Ebool,V30f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V31f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V32f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V33f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V34f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V35f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V36f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V37f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2EUnrelatedBool_2E1(V29a_2E0),V30f_2E0,V31f1_2E0,V32f2_2E0,V33f3_2E0,V34f4_2E0,V35f5_2E0,V36f6_2E0,V37f7_2E0) = app_2E2(tyop_2Emin_2Ebool,A_27a,V33f3_2E0,V29a_2E0) )
& ! [V38a_2E0: tyop_2Einteger_2Eint,V39f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V40f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V41f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V42f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V43f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V44f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V45f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V46f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2ExLT_2E1(V38a_2E0),V39f_2E0,V40f1_2E0,V41f2_2E0,V42f3_2E0,V43f4_2E0,V44f5_2E0,V45f6_2E0,V46f7_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V43f4_2E0,V38a_2E0) )
& ! [V47a_2E0: tyop_2Einteger_2Eint,V48f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V49f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V50f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V51f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V52f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V53f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V54f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V55f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2ELTx_2E1(V47a_2E0),V48f_2E0,V49f1_2E0,V50f2_2E0,V51f3_2E0,V52f4_2E0,V53f5_2E0,V54f6_2E0,V55f7_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V53f5_2E0,V47a_2E0) )
& ! [V56a_2E0: tyop_2Einteger_2Eint,V57f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V58f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V59f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V60f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V61f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V62f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V63f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V64f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2ExEQ_2E1(V56a_2E0),V57f_2E0,V58f1_2E0,V59f2_2E0,V60f3_2E0,V61f4_2E0,V62f5_2E0,V63f6_2E0,V64f7_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V63f6_2E0,V56a_2E0) )
& ! [V65a0_2E0: tyop_2Einteger_2Eint,V66a1_2E0: tyop_2Einteger_2Eint,V67f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V68f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V69f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V70f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V71f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V72f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V73f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V74f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] : ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,c_2EDeepSyntax_2ExDivided_2E2(V65a0_2E0,V66a1_2E0),V67f_2E0,V68f1_2E0,V69f2_2E0,V70f3_2E0,V71f4_2E0,V72f5_2E0,V73f6_2E0,V74f7_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V74f7_2E0,V65a0_2E0),V66a1_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__size__def,axiom,
( ! [V0a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2EConjn_2E2(V0a0_2E0,V1a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2EDeepSyntax_2Edeep__form__size_2E1(V0a0_2E0),c_2EDeepSyntax_2Edeep__form__size_2E1(V1a1_2E0))) )
& ! [V2a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V3a1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2EDisjn_2E2(V2a0_2E0,V3a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2EDeepSyntax_2Edeep__form__size_2E1(V2a0_2E0),c_2EDeepSyntax_2Edeep__form__size_2E1(V3a1_2E0))) )
& ! [V4a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2ENegn_2E1(V4a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2EDeepSyntax_2Edeep__form__size_2E1(V4a_2E0)) )
& ! [V5a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2EUnrelatedBool_2E1(V5a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2EbasicSize_2Ebool__size_2E1(V5a_2E0)) )
& ! [V6a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2ExLT_2E1(V6a_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V7a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2ELTx_2E1(V7a_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V8a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2ExEQ_2E1(V8a_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V9a0_2E0: tyop_2Einteger_2Eint,V10a1_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Edeep__form__size_2E1(c_2EDeepSyntax_2ExDivided_2E2(V9a0_2E0,V10a1_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2EDeepSyntax_2Eeval__form__def,axiom,
( ! [V0f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V1f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2EConjn_2E2(V0f1_2E0,V1f2_2E0),V2x_2E0))
<=> ( p(c_2EDeepSyntax_2Eeval__form_2E2(V0f1_2E0,V2x_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(V1f2_2E0,V2x_2E0)) ) )
& ! [V3f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V4f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V5x_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2EDisjn_2E2(V3f1_2E0,V4f2_2E0),V5x_2E0))
<=> ( p(c_2EDeepSyntax_2Eeval__form_2E2(V3f1_2E0,V5x_2E0))
| p(c_2EDeepSyntax_2Eeval__form_2E2(V4f2_2E0,V5x_2E0)) ) )
& ! [V6f_2E0: tyop_2EDeepSyntax_2Edeep__form,V7x_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2ENegn_2E1(V6f_2E0),V7x_2E0))
<=> ~ p(c_2EDeepSyntax_2Eeval__form_2E2(V6f_2E0,V7x_2E0)) )
& ! [V8b_2E0: tyop_2Emin_2Ebool,V9x_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2EUnrelatedBool_2E1(V8b_2E0),V9x_2E0) = V8b_2E0 )
& ! [V10i_2E0: tyop_2Einteger_2Eint,V11x_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2ExLT_2E1(V10i_2E0),V11x_2E0) = c_2Einteger_2Eint__lt_2E2(V11x_2E0,V10i_2E0) )
& ! [V12i_2E0: tyop_2Einteger_2Eint,V13x_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2ELTx_2E1(V12i_2E0),V13x_2E0) = c_2Einteger_2Eint__lt_2E2(V12i_2E0,V13x_2E0) )
& ! [V14i_2E0: tyop_2Einteger_2Eint,V15x_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2ExEQ_2E1(V14i_2E0),V15x_2E0))
<=> ( V15x_2E0 = V14i_2E0 ) )
& ! [V16i1_2E0: tyop_2Einteger_2Eint,V17i2_2E0: tyop_2Einteger_2Eint,V18x_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2ExDivided_2E2(V16i1_2E0,V17i2_2E0),V18x_2E0) = c_2Einteger_2Eint__divides_2E2(V16i1_2E0,c_2Einteger_2Eint__add_2E2(V18x_2E0,V17i2_2E0)) ) ) ).
tff(thm_2EDeepSyntax_2Eneginf__def,axiom,
( ! [V0f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V1f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2EConjn_2E2(V0f1_2E0,V1f2_2E0)) = c_2EDeepSyntax_2EConjn_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f1_2E0),c_2EDeepSyntax_2Eneginf_2E1(V1f2_2E0)) )
& ! [V2f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V3f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2EDisjn_2E2(V2f1_2E0,V3f2_2E0)) = c_2EDeepSyntax_2EDisjn_2E2(c_2EDeepSyntax_2Eneginf_2E1(V2f1_2E0),c_2EDeepSyntax_2Eneginf_2E1(V3f2_2E0)) )
& ! [V4f_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2ENegn_2E1(V4f_2E0)) = c_2EDeepSyntax_2ENegn_2E1(c_2EDeepSyntax_2Eneginf_2E1(V4f_2E0)) )
& ! [V5b_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2EUnrelatedBool_2E1(V5b_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(V5b_2E0) )
& ! [V6i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2ExLT_2E1(V6i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2ET_2E0) )
& ! [V7i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2ELTx_2E1(V7i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2EF_2E0) )
& ! [V8i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2ExEQ_2E1(V8i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2EF_2E0) )
& ! [V9i1_2E0: tyop_2Einteger_2Eint,V10i2_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eneginf_2E1(c_2EDeepSyntax_2ExDivided_2E2(V9i1_2E0,V10i2_2E0)) = c_2EDeepSyntax_2ExDivided_2E2(V9i1_2E0,V10i2_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Eposinf__def,axiom,
( ! [V0f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V1f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2EConjn_2E2(V0f1_2E0,V1f2_2E0)) = c_2EDeepSyntax_2EConjn_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f1_2E0),c_2EDeepSyntax_2Eposinf_2E1(V1f2_2E0)) )
& ! [V2f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V3f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2EDisjn_2E2(V2f1_2E0,V3f2_2E0)) = c_2EDeepSyntax_2EDisjn_2E2(c_2EDeepSyntax_2Eposinf_2E1(V2f1_2E0),c_2EDeepSyntax_2Eposinf_2E1(V3f2_2E0)) )
& ! [V4f_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2ENegn_2E1(V4f_2E0)) = c_2EDeepSyntax_2ENegn_2E1(c_2EDeepSyntax_2Eposinf_2E1(V4f_2E0)) )
& ! [V5b_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2EUnrelatedBool_2E1(V5b_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(V5b_2E0) )
& ! [V6i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2ExLT_2E1(V6i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2EF_2E0) )
& ! [V7i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2ELTx_2E1(V7i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2ET_2E0) )
& ! [V8i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2ExEQ_2E1(V8i_2E0)) = c_2EDeepSyntax_2EUnrelatedBool_2E1(c_2Ebool_2EF_2E0) )
& ! [V9i1_2E0: tyop_2Einteger_2Eint,V10i2_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eposinf_2E1(c_2EDeepSyntax_2ExDivided_2E2(V9i1_2E0,V10i2_2E0)) = c_2EDeepSyntax_2ExDivided_2E2(V9i1_2E0,V10i2_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Ealldivide__def,axiom,
( ! [V0f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V1f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V2d_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2EConjn_2E2(V0f1_2E0,V1f2_2E0),V2d_2E0))
<=> ( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f1_2E0,V2d_2E0))
& p(c_2EDeepSyntax_2Ealldivide_2E2(V1f2_2E0,V2d_2E0)) ) )
& ! [V3f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V4f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V5d_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2EDisjn_2E2(V3f1_2E0,V4f2_2E0),V5d_2E0))
<=> ( p(c_2EDeepSyntax_2Ealldivide_2E2(V3f1_2E0,V5d_2E0))
& p(c_2EDeepSyntax_2Ealldivide_2E2(V4f2_2E0,V5d_2E0)) ) )
& ! [V6f_2E0: tyop_2EDeepSyntax_2Edeep__form,V7d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2ENegn_2E1(V6f_2E0),V7d_2E0) = c_2EDeepSyntax_2Ealldivide_2E2(V6f_2E0,V7d_2E0) )
& ! [V8b_2E0: tyop_2Emin_2Ebool,V9d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2EUnrelatedBool_2E1(V8b_2E0),V9d_2E0) = c_2Ebool_2ET_2E0 )
& ! [V10i_2E0: tyop_2Einteger_2Eint,V11d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2ExLT_2E1(V10i_2E0),V11d_2E0) = c_2Ebool_2ET_2E0 )
& ! [V12i_2E0: tyop_2Einteger_2Eint,V13d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2ELTx_2E1(V12i_2E0),V13d_2E0) = c_2Ebool_2ET_2E0 )
& ! [V14i_2E0: tyop_2Einteger_2Eint,V15d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2ExEQ_2E1(V14i_2E0),V15d_2E0) = c_2Ebool_2ET_2E0 )
& ! [V16i1_2E0: tyop_2Einteger_2Eint,V17i2_2E0: tyop_2Einteger_2Eint,V18d_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Ealldivide_2E2(c_2EDeepSyntax_2ExDivided_2E2(V16i1_2E0,V17i2_2E0),V18d_2E0) = c_2Einteger_2Eint__divides_2E2(V16i1_2E0,V18d_2E0) ) ) ).
tff(thm_2EDeepSyntax_2EAset__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V6pos_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V6pos_2E0))
<=> ~ p(V6pos_2E0) )
=> ( ! [V0pos_2E0: tyop_2Emin_2Ebool,V1f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V2f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,c_2EDeepSyntax_2EConjn_2E2(V1f1_2E0,V2f2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Einteger_2Eint,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V1f1_2E0),c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V2f2_2E0)) )
& ! [V3pos_2E0: tyop_2Emin_2Ebool,V4f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V5f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EAset_2E2(V3pos_2E0,c_2EDeepSyntax_2EDisjn_2E2(V4f1_2E0,V5f2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Einteger_2Eint,c_2EDeepSyntax_2EAset_2E2(V3pos_2E0,V4f1_2E0),c_2EDeepSyntax_2EAset_2E2(V3pos_2E0,V5f2_2E0)) )
& ! [V6pos_2E0: tyop_2Emin_2Ebool,V7f_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EAset_2E2(V6pos_2E0,c_2EDeepSyntax_2ENegn_2E1(V7f_2E0)) = c_2EDeepSyntax_2EAset_2E2(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V6pos_2E0),V7f_2E0) )
& ! [V8pos_2E0: tyop_2Emin_2Ebool,V9b_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EAset_2E2(V8pos_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V9b_2E0)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint) )
& ! [V10pos_2E0: tyop_2Emin_2Ebool,V11i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EAset_2E2(V10pos_2E0,c_2EDeepSyntax_2ExLT_2E1(V11i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V10pos_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,V11i_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)) )
& ! [V12pos_2E0: tyop_2Emin_2Ebool,V13i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EAset_2E2(V12pos_2E0,c_2EDeepSyntax_2ELTx_2E1(V13i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V12pos_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint),c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(V13i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint))) )
& ! [V14pos_2E0: tyop_2Emin_2Ebool,V15i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EAset_2E2(V14pos_2E0,c_2EDeepSyntax_2ExEQ_2E1(V15i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V14pos_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(V15i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)),c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,V15i_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint))) )
& ! [V16pos_2E0: tyop_2Emin_2Ebool,V17i1_2E0: tyop_2Einteger_2Eint,V18i2_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EAset_2E2(V16pos_2E0,c_2EDeepSyntax_2ExDivided_2E2(V17i1_2E0,V18i2_2E0)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint) ) ) ) ).
tff(thm_2EDeepSyntax_2EBset__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V6pos_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V6pos_2E0))
<=> ~ p(V6pos_2E0) )
=> ( ! [V0pos_2E0: tyop_2Emin_2Ebool,V1f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V2f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,c_2EDeepSyntax_2EConjn_2E2(V1f1_2E0,V2f2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Einteger_2Eint,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V1f1_2E0),c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V2f2_2E0)) )
& ! [V3pos_2E0: tyop_2Emin_2Ebool,V4f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V5f2_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EBset_2E2(V3pos_2E0,c_2EDeepSyntax_2EDisjn_2E2(V4f1_2E0,V5f2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Einteger_2Eint,c_2EDeepSyntax_2EBset_2E2(V3pos_2E0,V4f1_2E0),c_2EDeepSyntax_2EBset_2E2(V3pos_2E0,V5f2_2E0)) )
& ! [V6pos_2E0: tyop_2Emin_2Ebool,V7f_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EBset_2E2(V6pos_2E0,c_2EDeepSyntax_2ENegn_2E1(V7f_2E0)) = c_2EDeepSyntax_2EBset_2E2(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V6pos_2E0),V7f_2E0) )
& ! [V8pos_2E0: tyop_2Emin_2Ebool,V9b_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EBset_2E2(V8pos_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V9b_2E0)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint) )
& ! [V10pos_2E0: tyop_2Emin_2Ebool,V11i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EBset_2E2(V10pos_2E0,c_2EDeepSyntax_2ExLT_2E1(V11i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V10pos_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint),c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(V11i_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint))) )
& ! [V12pos_2E0: tyop_2Emin_2Ebool,V13i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EBset_2E2(V12pos_2E0,c_2EDeepSyntax_2ELTx_2E1(V13i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V12pos_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,V13i_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)) )
& ! [V14pos_2E0: tyop_2Emin_2Ebool,V15i_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EBset_2E2(V14pos_2E0,c_2EDeepSyntax_2ExEQ_2E1(V15i_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),V14pos_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(V15i_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))),c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint)),c_2Epred__set_2EINSERT_2E2(tyop_2Einteger_2Eint,V15i_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint))) )
& ! [V16pos_2E0: tyop_2Emin_2Ebool,V17i1_2E0: tyop_2Einteger_2Eint,V18i2_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EBset_2E2(V16pos_2E0,c_2EDeepSyntax_2ExDivided_2E2(V17i1_2E0,V18i2_2E0)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Einteger_2Eint) ) ) ) ).
tff(thm_2EDeepSyntax_2Edatatype__deep__form,axiom,
! [V0deep__form_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool))))))))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool))))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool)))))),app_2E2(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),tyop_2Emin_2Ebool))))))),V0deep__form_2E0,c_2EDeepSyntax_2EConjn_2E0),c_2EDeepSyntax_2EDisjn_2E0),c_2EDeepSyntax_2ENegn_2E0),c_2EDeepSyntax_2EUnrelatedBool_2E0),c_2EDeepSyntax_2ExLT_2E0),c_2EDeepSyntax_2ELTx_2E0),c_2EDeepSyntax_2ExEQ_2E0),c_2EDeepSyntax_2ExDivided_2E0))) ).
tff(thm_2EDeepSyntax_2Edeep__form__11,axiom,
( ! [V0a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V2a0_27_2E0: tyop_2EDeepSyntax_2Edeep__form,V3a1_27_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EConjn_2E2(V0a0_2E0,V1a1_2E0) = c_2EDeepSyntax_2EConjn_2E2(V2a0_27_2E0,V3a1_27_2E0) )
<=> ( ( V0a0_2E0 = V2a0_27_2E0 )
& ( V1a1_2E0 = V3a1_27_2E0 ) ) )
& ! [V4a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V5a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V6a0_27_2E0: tyop_2EDeepSyntax_2Edeep__form,V7a1_27_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EDisjn_2E2(V4a0_2E0,V5a1_2E0) = c_2EDeepSyntax_2EDisjn_2E2(V6a0_27_2E0,V7a1_27_2E0) )
<=> ( ( V4a0_2E0 = V6a0_27_2E0 )
& ( V5a1_2E0 = V7a1_27_2E0 ) ) )
& ! [V8a_2E0: tyop_2EDeepSyntax_2Edeep__form,V9a_27_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2ENegn_2E1(V8a_2E0) = c_2EDeepSyntax_2ENegn_2E1(V9a_27_2E0) )
<=> ( V8a_2E0 = V9a_27_2E0 ) )
& ! [V10a_2E0: tyop_2Emin_2Ebool,V11a_27_2E0: tyop_2Emin_2Ebool] :
( ( c_2EDeepSyntax_2EUnrelatedBool_2E1(V10a_2E0) = c_2EDeepSyntax_2EUnrelatedBool_2E1(V11a_27_2E0) )
<=> ( V10a_2E0 = V11a_27_2E0 ) )
& ! [V12a_2E0: tyop_2Einteger_2Eint,V13a_27_2E0: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2ExLT_2E1(V12a_2E0) = c_2EDeepSyntax_2ExLT_2E1(V13a_27_2E0) )
<=> ( V12a_2E0 = V13a_27_2E0 ) )
& ! [V14a_2E0: tyop_2Einteger_2Eint,V15a_27_2E0: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2ELTx_2E1(V14a_2E0) = c_2EDeepSyntax_2ELTx_2E1(V15a_27_2E0) )
<=> ( V14a_2E0 = V15a_27_2E0 ) )
& ! [V16a_2E0: tyop_2Einteger_2Eint,V17a_27_2E0: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2ExEQ_2E1(V16a_2E0) = c_2EDeepSyntax_2ExEQ_2E1(V17a_27_2E0) )
<=> ( V16a_2E0 = V17a_27_2E0 ) )
& ! [V18a0_2E0: tyop_2Einteger_2Eint,V19a1_2E0: tyop_2Einteger_2Eint,V20a0_27_2E0: tyop_2Einteger_2Eint,V21a1_27_2E0: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2ExDivided_2E2(V18a0_2E0,V19a1_2E0) = c_2EDeepSyntax_2ExDivided_2E2(V20a0_27_2E0,V21a1_27_2E0) )
<=> ( ( V18a0_2E0 = V20a0_27_2E0 )
& ( V19a1_2E0 = V21a1_27_2E0 ) ) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__distinct,axiom,
( ! [V0a1_27_2E0: tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V2a0_27_2E0: tyop_2EDeepSyntax_2Edeep__form,V3a0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EConjn_2E2(V3a0_2E0,V1a1_2E0) != c_2EDeepSyntax_2EDisjn_2E2(V2a0_27_2E0,V0a1_27_2E0) )
& ! [V4a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V5a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V6a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EConjn_2E2(V5a0_2E0,V4a1_2E0) != c_2EDeepSyntax_2ENegn_2E1(V6a_2E0) )
& ! [V7a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V8a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V9a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EConjn_2E2(V8a0_2E0,V7a1_2E0) != c_2EDeepSyntax_2EUnrelatedBool_2E1(V9a_2E0) )
& ! [V10a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V11a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V12a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EConjn_2E2(V11a0_2E0,V10a1_2E0) != c_2EDeepSyntax_2ExLT_2E1(V12a_2E0) )
& ! [V13a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V14a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V15a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EConjn_2E2(V14a0_2E0,V13a1_2E0) != c_2EDeepSyntax_2ELTx_2E1(V15a_2E0) )
& ! [V16a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V17a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V18a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EConjn_2E2(V17a0_2E0,V16a1_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V18a_2E0) )
& ! [V19a1_27_2E0: tyop_2Einteger_2Eint,V20a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V21a0_27_2E0: tyop_2Einteger_2Eint,V22a0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EConjn_2E2(V22a0_2E0,V20a1_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V21a0_27_2E0,V19a1_27_2E0) )
& ! [V23a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V24a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V25a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EDisjn_2E2(V24a0_2E0,V23a1_2E0) != c_2EDeepSyntax_2ENegn_2E1(V25a_2E0) )
& ! [V26a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V27a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V28a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EDisjn_2E2(V27a0_2E0,V26a1_2E0) != c_2EDeepSyntax_2EUnrelatedBool_2E1(V28a_2E0) )
& ! [V29a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V30a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V31a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EDisjn_2E2(V30a0_2E0,V29a1_2E0) != c_2EDeepSyntax_2ExLT_2E1(V31a_2E0) )
& ! [V32a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V33a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V34a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EDisjn_2E2(V33a0_2E0,V32a1_2E0) != c_2EDeepSyntax_2ELTx_2E1(V34a_2E0) )
& ! [V35a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V36a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V37a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2EDisjn_2E2(V36a0_2E0,V35a1_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V37a_2E0) )
& ! [V38a1_27_2E0: tyop_2Einteger_2Eint,V39a1_2E0: tyop_2EDeepSyntax_2Edeep__form,V40a0_27_2E0: tyop_2Einteger_2Eint,V41a0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2EDisjn_2E2(V41a0_2E0,V39a1_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V40a0_27_2E0,V38a1_27_2E0) )
& ! [V42a_27_2E0: tyop_2Emin_2Ebool,V43a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(V43a_2E0) != c_2EDeepSyntax_2EUnrelatedBool_2E1(V42a_27_2E0) )
& ! [V44a_27_2E0: tyop_2Einteger_2Eint,V45a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(V45a_2E0) != c_2EDeepSyntax_2ExLT_2E1(V44a_27_2E0) )
& ! [V46a_27_2E0: tyop_2Einteger_2Eint,V47a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(V47a_2E0) != c_2EDeepSyntax_2ELTx_2E1(V46a_27_2E0) )
& ! [V48a_27_2E0: tyop_2Einteger_2Eint,V49a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(V49a_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V48a_27_2E0) )
& ! [V50a1_2E0: tyop_2Einteger_2Eint,V51a0_2E0: tyop_2Einteger_2Eint,V52a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( c_2EDeepSyntax_2ENegn_2E1(V52a_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V51a0_2E0,V50a1_2E0) )
& ! [V53a_27_2E0: tyop_2Einteger_2Eint,V54a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EUnrelatedBool_2E1(V54a_2E0) != c_2EDeepSyntax_2ExLT_2E1(V53a_27_2E0) )
& ! [V55a_27_2E0: tyop_2Einteger_2Eint,V56a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EUnrelatedBool_2E1(V56a_2E0) != c_2EDeepSyntax_2ELTx_2E1(V55a_27_2E0) )
& ! [V57a_27_2E0: tyop_2Einteger_2Eint,V58a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EUnrelatedBool_2E1(V58a_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V57a_27_2E0) )
& ! [V59a1_2E0: tyop_2Einteger_2Eint,V60a0_2E0: tyop_2Einteger_2Eint,V61a_2E0: tyop_2Emin_2Ebool] : ( c_2EDeepSyntax_2EUnrelatedBool_2E1(V61a_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V60a0_2E0,V59a1_2E0) )
& ! [V62a_27_2E0: tyop_2Einteger_2Eint,V63a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExLT_2E1(V63a_2E0) != c_2EDeepSyntax_2ELTx_2E1(V62a_27_2E0) )
& ! [V64a_27_2E0: tyop_2Einteger_2Eint,V65a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExLT_2E1(V65a_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V64a_27_2E0) )
& ! [V66a1_2E0: tyop_2Einteger_2Eint,V67a0_2E0: tyop_2Einteger_2Eint,V68a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExLT_2E1(V68a_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V67a0_2E0,V66a1_2E0) )
& ! [V69a_27_2E0: tyop_2Einteger_2Eint,V70a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ELTx_2E1(V70a_2E0) != c_2EDeepSyntax_2ExEQ_2E1(V69a_27_2E0) )
& ! [V71a1_2E0: tyop_2Einteger_2Eint,V72a0_2E0: tyop_2Einteger_2Eint,V73a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ELTx_2E1(V73a_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V72a0_2E0,V71a1_2E0) )
& ! [V74a1_2E0: tyop_2Einteger_2Eint,V75a0_2E0: tyop_2Einteger_2Eint,V76a_2E0: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2ExEQ_2E1(V76a_2E0) != c_2EDeepSyntax_2ExDivided_2E2(V75a0_2E0,V74a1_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__nchotomy,axiom,
! [V0dd_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ? [V1d_2E0: tyop_2EDeepSyntax_2Edeep__form,V2d0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( V0dd_2E0 = c_2EDeepSyntax_2EConjn_2E2(V1d_2E0,V2d0_2E0) )
| ? [V3d_2E0: tyop_2EDeepSyntax_2Edeep__form,V4d0_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( V0dd_2E0 = c_2EDeepSyntax_2EDisjn_2E2(V3d_2E0,V4d0_2E0) )
| ? [V5d_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( V0dd_2E0 = c_2EDeepSyntax_2ENegn_2E1(V5d_2E0) )
| ? [V6b_2E0: tyop_2Emin_2Ebool] : ( V0dd_2E0 = c_2EDeepSyntax_2EUnrelatedBool_2E1(V6b_2E0) )
| ? [V7i_2E0: tyop_2Einteger_2Eint] : ( V0dd_2E0 = c_2EDeepSyntax_2ExLT_2E1(V7i_2E0) )
| ? [V8i_2E0: tyop_2Einteger_2Eint] : ( V0dd_2E0 = c_2EDeepSyntax_2ELTx_2E1(V8i_2E0) )
| ? [V9i_2E0: tyop_2Einteger_2Eint] : ( V0dd_2E0 = c_2EDeepSyntax_2ExEQ_2E1(V9i_2E0) )
| ? [V10i_2E0: tyop_2Einteger_2Eint,V11i0_2E0: tyop_2Einteger_2Eint] : ( V0dd_2E0 = c_2EDeepSyntax_2ExDivided_2E2(V10i_2E0,V11i0_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__Axiom,axiom,
! [A_27a: $tType,V0f0_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),V1f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),V2f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,A_27a)),V3f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V4f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V5f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V6f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V7f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] :
? [V8fn_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)] :
( ! [V9a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V10a1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2EConjn_2E2(V9a0_2E0,V10a1_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V0f0_2E0,V9a0_2E0),V10a1_2E0),app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,V9a0_2E0)),app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,V10a1_2E0)) )
& ! [V11a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V12a1_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2EDisjn_2E2(V11a0_2E0,V12a1_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V1f1_2E0,V11a0_2E0),V12a1_2E0),app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,V11a0_2E0)),app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,V12a1_2E0)) )
& ! [V13a_2E0: tyop_2EDeepSyntax_2Edeep__form] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2ENegn_2E1(V13a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(A_27a,A_27a),V2f2_2E0,V13a_2E0),app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,V13a_2E0)) )
& ! [V14a_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V14a_2E0)) = app_2E2(tyop_2Emin_2Ebool,A_27a,V3f3_2E0,V14a_2E0) )
& ! [V15a_2E0: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2ExLT_2E1(V15a_2E0)) = app_2E2(tyop_2Einteger_2Eint,A_27a,V4f4_2E0,V15a_2E0) )
& ! [V16a_2E0: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2ELTx_2E1(V16a_2E0)) = app_2E2(tyop_2Einteger_2Eint,A_27a,V5f5_2E0,V16a_2E0) )
& ! [V17a_2E0: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2ExEQ_2E1(V17a_2E0)) = app_2E2(tyop_2Einteger_2Eint,A_27a,V6f6_2E0,V17a_2E0) )
& ! [V18a0_2E0: tyop_2Einteger_2Eint,V19a1_2E0: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V8fn_2E0,c_2EDeepSyntax_2ExDivided_2E2(V18a0_2E0,V19a1_2E0)) = app_2E2(tyop_2Einteger_2Eint,A_27a,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V7f7_2E0,V18a0_2E0),V19a1_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool)] :
( ( ! [V1d_2E0: tyop_2EDeepSyntax_2Edeep__form,V2d0_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V1d_2E0))
& p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V2d0_2E0)) )
=> p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2EConjn_2E2(V1d_2E0,V2d0_2E0))) )
& ! [V3d_2E0: tyop_2EDeepSyntax_2Edeep__form,V4d0_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V3d_2E0))
& p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V4d0_2E0)) )
=> p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2EDisjn_2E2(V3d_2E0,V4d0_2E0))) )
& ! [V5d_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V5d_2E0))
=> p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2ENegn_2E1(V5d_2E0))) )
& ! [V6b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V6b_2E0)))
& ! [V7i_2E0: tyop_2Einteger_2Eint] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2ExLT_2E1(V7i_2E0)))
& ! [V8i_2E0: tyop_2Einteger_2Eint] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2ELTx_2E1(V8i_2E0)))
& ! [V9i_2E0: tyop_2Einteger_2Eint] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2ExEQ_2E1(V9i_2E0)))
& ! [V10i_2E0: tyop_2Einteger_2Eint,V11i0_2E0: tyop_2Einteger_2Eint] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,c_2EDeepSyntax_2ExDivided_2E2(V10i_2E0,V11i0_2E0))) )
=> ! [V12d_2E0: tyop_2EDeepSyntax_2Edeep__form] : p(app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool,V0P_2E0,V12d_2E0)) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__case__cong,axiom,
! [A_27a: $tType,V0f7_27_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),V1f6_27_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V2f5_27_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V3f4_27_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V4f3_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V5f2_27_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V6f1_27_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V7f_27_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V8M_2E0: tyop_2EDeepSyntax_2Edeep__form,V9M_27_2E0: tyop_2EDeepSyntax_2Edeep__form,V10f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V11f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V12f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V13f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V14f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V15f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V16f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V17f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a))] :
( ( ( V8M_2E0 = V9M_27_2E0 )
& ! [V18a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V19a1_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2EConjn_2E2(V18a0_2E0,V19a1_2E0) )
=> ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V10f_2E0,V18a0_2E0),V19a1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V7f_27_2E0,V18a0_2E0),V19a1_2E0) ) )
& ! [V20a0_2E0: tyop_2EDeepSyntax_2Edeep__form,V21a1_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2EDisjn_2E2(V20a0_2E0,V21a1_2E0) )
=> ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V11f1_2E0,V20a0_2E0),V21a1_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V6f1_27_2E0,V20a0_2E0),V21a1_2E0) ) )
& ! [V22a_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2ENegn_2E1(V22a_2E0) )
=> ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V12f2_2E0,V22a_2E0) = app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V5f2_27_2E0,V22a_2E0) ) )
& ! [V23a_2E0: tyop_2Emin_2Ebool] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2EUnrelatedBool_2E1(V23a_2E0) )
=> ( app_2E2(tyop_2Emin_2Ebool,A_27a,V13f3_2E0,V23a_2E0) = app_2E2(tyop_2Emin_2Ebool,A_27a,V4f3_27_2E0,V23a_2E0) ) )
& ! [V24a_2E0: tyop_2Einteger_2Eint] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2ExLT_2E1(V24a_2E0) )
=> ( app_2E2(tyop_2Einteger_2Eint,A_27a,V14f4_2E0,V24a_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V3f4_27_2E0,V24a_2E0) ) )
& ! [V25a_2E0: tyop_2Einteger_2Eint] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2ELTx_2E1(V25a_2E0) )
=> ( app_2E2(tyop_2Einteger_2Eint,A_27a,V15f5_2E0,V25a_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V2f5_27_2E0,V25a_2E0) ) )
& ! [V26a_2E0: tyop_2Einteger_2Eint] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2ExEQ_2E1(V26a_2E0) )
=> ( app_2E2(tyop_2Einteger_2Eint,A_27a,V16f6_2E0,V26a_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,V1f6_27_2E0,V26a_2E0) ) )
& ! [V27a0_2E0: tyop_2Einteger_2Eint,V28a1_2E0: tyop_2Einteger_2Eint] :
( ( V9M_27_2E0 = c_2EDeepSyntax_2ExDivided_2E2(V27a0_2E0,V28a1_2E0) )
=> ( app_2E2(tyop_2Einteger_2Eint,A_27a,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V17f7_2E0,V27a0_2E0),V28a1_2E0) = app_2E2(tyop_2Einteger_2Eint,A_27a,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V0f7_27_2E0,V27a0_2E0),V28a1_2E0) ) ) )
=> ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,V8M_2E0,V10f_2E0,V11f1_2E0,V12f2_2E0,V13f3_2E0,V14f4_2E0,V15f5_2E0,V16f6_2E0,V17f7_2E0) = c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,V9M_27_2E0,V7f_27_2E0,V6f1_27_2E0,V5f2_27_2E0,V4f3_27_2E0,V3f4_27_2E0,V2f5_27_2E0,V1f6_27_2E0,V0f7_27_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Edeep__form__case__eq,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2EDeepSyntax_2Edeep__form,V1v_2E0: A_27a,V2f7_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a)),V3f6_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V4f5_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V5f4_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V6f3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V7f2_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V8f1_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a)),V9f_2E0: tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a))] :
( ( c_2EDeepSyntax_2Edeep__form__CASE_2E9(A_27a,V0x_2E0,V9f_2E0,V8f1_2E0,V7f2_2E0,V6f3_2E0,V5f4_2E0,V4f5_2E0,V3f6_2E0,V2f7_2E0) = V1v_2E0 )
<=> ( ? [V10d_2E0: tyop_2EDeepSyntax_2Edeep__form,V11d0_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x_2E0 = c_2EDeepSyntax_2EConjn_2E2(V10d_2E0,V11d0_2E0) )
& ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V9f_2E0,V10d_2E0),V11d0_2E0) = V1v_2E0 ) )
| ? [V12d_2E0: tyop_2EDeepSyntax_2Edeep__form,V13d0_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x_2E0 = c_2EDeepSyntax_2EDisjn_2E2(V12d_2E0,V13d0_2E0) )
& ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,app_2E2(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,A_27a),V8f1_2E0,V12d_2E0),V13d0_2E0) = V1v_2E0 ) )
| ? [V14d_2E0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x_2E0 = c_2EDeepSyntax_2ENegn_2E1(V14d_2E0) )
& ( app_2E2(tyop_2EDeepSyntax_2Edeep__form,A_27a,V7f2_2E0,V14d_2E0) = V1v_2E0 ) )
| ? [V15b_2E0: tyop_2Emin_2Ebool] :
( ( V0x_2E0 = c_2EDeepSyntax_2EUnrelatedBool_2E1(V15b_2E0) )
& ( app_2E2(tyop_2Emin_2Ebool,A_27a,V6f3_2E0,V15b_2E0) = V1v_2E0 ) )
| ? [V16i_2E0: tyop_2Einteger_2Eint] :
( ( V0x_2E0 = c_2EDeepSyntax_2ExLT_2E1(V16i_2E0) )
& ( app_2E2(tyop_2Einteger_2Eint,A_27a,V5f4_2E0,V16i_2E0) = V1v_2E0 ) )
| ? [V17i_2E0: tyop_2Einteger_2Eint] :
( ( V0x_2E0 = c_2EDeepSyntax_2ELTx_2E1(V17i_2E0) )
& ( app_2E2(tyop_2Einteger_2Eint,A_27a,V4f5_2E0,V17i_2E0) = V1v_2E0 ) )
| ? [V18i_2E0: tyop_2Einteger_2Eint] :
( ( V0x_2E0 = c_2EDeepSyntax_2ExEQ_2E1(V18i_2E0) )
& ( app_2E2(tyop_2Einteger_2Eint,A_27a,V3f6_2E0,V18i_2E0) = V1v_2E0 ) )
| ? [V19i_2E0: tyop_2Einteger_2Eint,V20i0_2E0: tyop_2Einteger_2Eint] :
( ( V0x_2E0 = c_2EDeepSyntax_2ExDivided_2E2(V19i_2E0,V20i0_2E0) )
& ( app_2E2(tyop_2Einteger_2Eint,A_27a,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,A_27a),V2f7_2E0,V19i_2E0),V20i0_2E0) = V1v_2E0 ) ) ) ) ).
tff(thm_2EDeepSyntax_2Eneginf__ok,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form] :
? [V1y_2E0: tyop_2Einteger_2Eint] :
! [V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V2x_2E0,V1y_2E0))
=> ( c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0) = c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),V2x_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Eposinf__ok,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form] :
? [V1y_2E0: tyop_2Einteger_2Eint] :
! [V2x_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(V1y_2E0,V2x_2E0))
=> ( c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0) = c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),V2x_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Eadd__d__neginf,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1x_2E0: tyop_2Einteger_2Eint,V2y_2E0: tyop_2Einteger_2Eint,V3d_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V3d_2E0))
=> ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),V1x_2E0) = c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(V2y_2E0,V3d_2E0))) ) ) ).
tff(thm_2EDeepSyntax_2Eadd__d__posinf,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1x_2E0: tyop_2Einteger_2Eint,V2y_2E0: tyop_2Einteger_2Eint,V3d_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V3d_2E0))
=> ( c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),V1x_2E0) = c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),c_2Einteger_2Eint__add_2E2(V1x_2E0,c_2Einteger_2Eint__mul_2E2(V2y_2E0,V3d_2E0))) ) ) ).
tff(thm_2EDeepSyntax_2Eneginf__disj1__implies__exoriginal,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint,V2i_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
=> ( ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V2i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V2i_2E0,V1d_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),V2i_2E0)) )
=> ? [V3x_2E0: tyop_2Einteger_2Eint] : p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V3x_2E0)) ) ) ).
tff(thm_2EDeepSyntax_2Eposinf__disj1__implies__exoriginal,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint,V2i_2E0: tyop_2Einteger_2Eint] :
( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
=> ( ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V2i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V2i_2E0,V1d_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),V2i_2E0)) )
=> ? [V3x_2E0: tyop_2Einteger_2Eint] : p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V3x_2E0)) ) ) ).
tff(thm_2EDeepSyntax_2Eneginf__exoriginal__implies__rhs,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V1d_2E0)) )
=> ( p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0))
=> ( ? [V3i_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V3i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V3i_2E0,V1d_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),V3i_2E0)) )
| ? [V4j_2E0: tyop_2Einteger_2Eint,V5b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V4j_2E0))
& p(c_2Einteger_2Eint__le_2E2(V4j_2E0,V1d_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V5b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,V0f_2E0)))
& p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,c_2Einteger_2Eint__add_2E2(V5b_2E0,V4j_2E0))) ) ) ) ) ).
tff(thm_2EDeepSyntax_2Eposinf__exoriginal__implies__rhs,axiom,
! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint,V2x_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V1d_2E0)) )
=> ( p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0))
=> ( ? [V3i_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V3i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V3i_2E0,V1d_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),V3i_2E0)) )
| ? [V4j_2E0: tyop_2Einteger_2Eint,V5b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V4j_2E0))
& p(c_2Einteger_2Eint__le_2E2(V4j_2E0,V1d_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V5b_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,V0f_2E0)))
& p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,c_2Einteger_2Eint__add_2E2(V5b_2E0,c_2Einteger_2Eint__neg_2E1(V4j_2E0)))) ) ) ) ) ).
tff(thm_2EDeepSyntax_2Eneginf__exoriginal__eq__rhs,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))] :
( ! [V5j_2E0: tyop_2Einteger_2Eint,V1d_2E0: tyop_2Einteger_2Eint] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F1_2E0,V5j_2E0),V1d_2E0))
<=> ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V5j_2E0))
& p(c_2Einteger_2Eint__le_2E2(V5j_2E0,V1d_2E0)) ) )
=> ( ! [V3i_2E0: tyop_2Einteger_2Eint,V1d_2E0: tyop_2Einteger_2Eint] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V3i_2E0),V1d_2E0))
<=> ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V3i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V3i_2E0,V1d_2E0)) ) )
=> ! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V1d_2E0)) )
=> ( ? [V2x_2E0: tyop_2Einteger_2Eint] : p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0))
<=> ( ? [V3i_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ecombin_2EK_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V3i_2E0),V1d_2E0),V3i_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eneginf_2E1(V0f_2E0),V3i_2E0)) )
| ? [V4b_2E0: tyop_2Einteger_2Eint,V5j_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V4b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,V0f_2E0)))
& p(c_2Ecombin_2EK_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F1_2E0,V5j_2E0),V1d_2E0),V5j_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,c_2Einteger_2Eint__add_2E2(V4b_2E0,V5j_2E0))) ) ) ) ) ) ) ).
tff(thm_2EDeepSyntax_2Eposinf__exoriginal__eq__rhs,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))] :
( ! [V5j_2E0: tyop_2Einteger_2Eint,V1d_2E0: tyop_2Einteger_2Eint] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F1_2E0,V5j_2E0),V1d_2E0))
<=> ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V5j_2E0))
& p(c_2Einteger_2Eint__le_2E2(V5j_2E0,V1d_2E0)) ) )
=> ( ! [V3i_2E0: tyop_2Einteger_2Eint,V1d_2E0: tyop_2Einteger_2Eint] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V3i_2E0),V1d_2E0))
<=> ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V3i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V3i_2E0,V1d_2E0)) ) )
=> ! [V0f_2E0: tyop_2EDeepSyntax_2Edeep__form,V1d_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2EDeepSyntax_2Ealldivide_2E2(V0f_2E0,V1d_2E0))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V1d_2E0)) )
=> ( ? [V2x_2E0: tyop_2Einteger_2Eint] : p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,V2x_2E0))
<=> ( ? [V3i_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ecombin_2EK_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V3i_2E0),V1d_2E0),V3i_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(c_2EDeepSyntax_2Eposinf_2E1(V0f_2E0),V3i_2E0)) )
| ? [V4b_2E0: tyop_2Einteger_2Eint,V5j_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V4b_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,V0f_2E0)))
& p(c_2Ecombin_2EK_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F1_2E0,V5j_2E0),V1d_2E0),V5j_2E0))
& p(c_2EDeepSyntax_2Eeval__form_2E2(V0f_2E0,c_2Einteger_2Eint__add_2E2(V4b_2E0,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V5j_2E0)))) ) ) ) ) ) ) ).
tff(thm_2EDeepSyntax_2Ein__bset,axiom,
! [V0pos_2E0: tyop_2Emin_2Ebool,V1i2_2E0: tyop_2Einteger_2Eint,V2i1_2E0: tyop_2Einteger_2Eint,V3i_2E0: tyop_2Einteger_2Eint,V4f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V5f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V6f_2E0: tyop_2EDeepSyntax_2Edeep__form,V7b0_2E0: tyop_2Emin_2Ebool,V8P_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] :
( ( ? [V9b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V9b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,c_2EDeepSyntax_2EConjn_2E2(V5f1_2E0,V4f2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V9b_2E0)) )
<=> ( ? [V10b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V10b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V5f1_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V10b_2E0)) )
| ? [V11b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V11b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V4f2_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V11b_2E0)) ) ) )
& ( ? [V12b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V12b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,c_2EDeepSyntax_2EDisjn_2E2(V5f1_2E0,V4f2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V12b_2E0)) )
<=> ( ? [V13b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V13b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V5f1_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V13b_2E0)) )
| ? [V14b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V14b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,V4f2_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V14b_2E0)) ) ) )
& ( ? [V15b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V15b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ENegn_2E1(V6f_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V15b_2E0)) )
<=> ? [V16b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V16b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2EF_2E0,V6f_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V16b_2E0)) ) )
& ( ? [V17b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V17b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ENegn_2E1(V6f_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V17b_2E0)) )
<=> ? [V18b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V18b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,V6f_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V18b_2E0)) ) )
& ( ? [V19b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V19b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V7b0_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V19b_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V20b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V20b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ExLT_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V20b_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V21b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V21b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ExLT_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V21b_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,c_2Einteger_2Eint__add_2E2(V3i_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
& ( ? [V22b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V22b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ELTx_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V22b_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V3i_2E0)) )
& ( ? [V23b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V23b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ELTx_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V23b_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V24b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V24b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ExEQ_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V24b_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,c_2Einteger_2Eint__add_2E2(V3i_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
& ( ? [V25b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V25b_2E0,c_2EDeepSyntax_2EBset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ExEQ_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V25b_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V3i_2E0)) )
& ( ? [V26b_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V26b_2E0,c_2EDeepSyntax_2EBset_2E2(V0pos_2E0,c_2EDeepSyntax_2ExDivided_2E2(V2i1_2E0,V1i2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V26b_2E0)) )
<=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2EDeepSyntax_2Ein__aset,axiom,
! [V0pos_2E0: tyop_2Emin_2Ebool,V1i2_2E0: tyop_2Einteger_2Eint,V2i1_2E0: tyop_2Einteger_2Eint,V3i_2E0: tyop_2Einteger_2Eint,V4f2_2E0: tyop_2EDeepSyntax_2Edeep__form,V5f1_2E0: tyop_2EDeepSyntax_2Edeep__form,V6f_2E0: tyop_2EDeepSyntax_2Edeep__form,V7a0_2E0: tyop_2Emin_2Ebool,V8P_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)] :
( ( ? [V9a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V9a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,c_2EDeepSyntax_2EConjn_2E2(V5f1_2E0,V4f2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V9a_2E0)) )
<=> ( ? [V10a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V10a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V5f1_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V10a_2E0)) )
| ? [V11a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V11a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V4f2_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V11a_2E0)) ) ) )
& ( ? [V12a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V12a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,c_2EDeepSyntax_2EDisjn_2E2(V5f1_2E0,V4f2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V12a_2E0)) )
<=> ( ? [V13a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V13a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V5f1_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V13a_2E0)) )
| ? [V14a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V14a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,V4f2_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V14a_2E0)) ) ) )
& ( ? [V15a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V15a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ENegn_2E1(V6f_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V15a_2E0)) )
<=> ? [V16a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V16a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2EF_2E0,V6f_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V16a_2E0)) ) )
& ( ? [V17a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V17a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ENegn_2E1(V6f_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V17a_2E0)) )
<=> ? [V18a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V18a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,V6f_2E0)))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V18a_2E0)) ) )
& ( ? [V19a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V19a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,c_2EDeepSyntax_2EUnrelatedBool_2E1(V7a0_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V19a_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V20a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V20a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ExLT_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V20a_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V3i_2E0)) )
& ( ? [V21a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V21a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ExLT_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V21a_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V22a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V22a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ELTx_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V22a_2E0)) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ? [V23a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V23a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ELTx_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V23a_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,c_2Einteger_2Eint__add_2E2(V3i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
& ( ? [V24a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V24a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2ET_2E0,c_2EDeepSyntax_2ExEQ_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V24a_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,c_2Einteger_2Eint__add_2E2(V3i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
& ( ? [V25a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V25a_2E0,c_2EDeepSyntax_2EAset_2E2(c_2Ebool_2EF_2E0,c_2EDeepSyntax_2ExEQ_2E1(V3i_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V25a_2E0)) )
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V3i_2E0)) )
& ( ? [V26a_2E0: tyop_2Einteger_2Eint] :
( p(c_2Ebool_2EIN_2E2(tyop_2Einteger_2Eint,V26a_2E0,c_2EDeepSyntax_2EAset_2E2(V0pos_2E0,c_2EDeepSyntax_2ExDivided_2E2(V2i1_2E0,V1i2_2E0))))
& p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,V8P_2E0,V26a_2E0)) )
<=> p(c_2Ebool_2EF_2E0) ) ) ).
%------------------------------------------------------------------------------