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 : 95 ( 6 unt; 59 typ; 0 def)
% Number of atoms : 506 ( 162 equ; 30 cnn)
% Maximal formula atoms : 56 ( 5 avg)
% Number of connectives : 2150 ( 30 ~; 24 |; 211 &;1809 @)
% ( 48 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 14 avg;1809 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 284 ( 284 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 55 usr; 5 con; 0-10 aty)
% Number of variables : 553 ( 33 ^ 421 !; 79 ?; 553 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2EDeepSyntax_2Edeep__form,type,
tyop_2EDeepSyntax_2Edeep__form: $tType ).
thf(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2EARB,type,
c_2Ebool_2EARB:
!>[A_27a: $tType] : A_27a ).
thf(c_2EDeepSyntax_2EAset,type,
c_2EDeepSyntax_2EAset: $o > tyop_2EDeepSyntax_2Edeep__form > tyop_2Einteger_2Eint > $o ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Eind__type_2EBOTTOM,type,
c_2Eind__type_2EBOTTOM:
!>[A_27a: $tType] : ( tyop_2Eind__type_2Erecspace @ A_27a ) ).
thf(c_2EDeepSyntax_2EBset,type,
c_2EDeepSyntax_2EBset: $o > tyop_2EDeepSyntax_2Edeep__form > tyop_2Einteger_2Eint > $o ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Eind__type_2ECONSTR,type,
c_2Eind__type_2ECONSTR:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Enum_2Enum > ( tyop_2Eind__type_2Erecspace @ A_27a ) ) > ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ).
thf(c_2EDeepSyntax_2EConjn,type,
c_2EDeepSyntax_2EConjn: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Ebool_2EDATATYPE,type,
c_2Ebool_2EDATATYPE:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2EDeepSyntax_2EDisjn,type,
c_2EDeepSyntax_2EDisjn: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Epred__set_2EEMPTY,type,
c_2Epred__set_2EEMPTY:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Eind__type_2EFCONS,type,
c_2Eind__type_2EFCONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Enum_2Enum > A_27a ) > tyop_2Enum_2Enum > A_27a ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Epred__set_2EINSERT,type,
c_2Epred__set_2EINSERT:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Ecombin_2EK,type,
c_2Ecombin_2EK:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2EDeepSyntax_2ELTx,type,
c_2EDeepSyntax_2ELTx: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EDeepSyntax_2ENegn,type,
c_2EDeepSyntax_2ENegn: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2ETYPE__DEFINITION,type,
c_2Ebool_2ETYPE__DEFINITION:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).
thf(c_2Epred__set_2EUNION,type,
c_2Epred__set_2EUNION:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2EDeepSyntax_2EUnrelatedBool,type,
c_2EDeepSyntax_2EUnrelatedBool: $o > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2EDeepSyntax_2Ealldivide,type,
c_2EDeepSyntax_2Ealldivide: tyop_2EDeepSyntax_2Edeep__form > tyop_2Einteger_2Eint > $o ).
thf(c_2EbasicSize_2Ebool__size,type,
c_2EbasicSize_2Ebool__size: $o > tyop_2Enum_2Enum ).
thf(c_2EDeepSyntax_2Edeep__form__CASE,type,
c_2EDeepSyntax_2Edeep__form__CASE:
!>[A_27a: $tType] : ( tyop_2EDeepSyntax_2Edeep__form > ( tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a ) > ( tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a ) > ( tyop_2EDeepSyntax_2Edeep__form > A_27a ) > ( $o > A_27a ) > ( tyop_2Einteger_2Eint > A_27a ) > ( tyop_2Einteger_2Eint > A_27a ) > ( tyop_2Einteger_2Eint > A_27a ) > ( tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a ) > A_27a ) ).
thf(c_2EDeepSyntax_2Edeep__form__size,type,
c_2EDeepSyntax_2Edeep__form__size: tyop_2EDeepSyntax_2Edeep__form > tyop_2Enum_2Enum ).
thf(c_2EDeepSyntax_2Eeval__form,type,
c_2EDeepSyntax_2Eeval__form: tyop_2EDeepSyntax_2Edeep__form > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__add,type,
c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__divides,type,
c_2Einteger_2Eint__divides: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__le,type,
c_2Einteger_2Eint__le: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__lt,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__mul,type,
c_2Einteger_2Eint__mul: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2EDeepSyntax_2Eneginf,type,
c_2EDeepSyntax_2Eneginf: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2EDeepSyntax_2Eposinf,type,
c_2EDeepSyntax_2Eposinf: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2EDeepSyntax_2ExDivided,type,
c_2EDeepSyntax_2ExDivided: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2EDeepSyntax_2ExEQ,type,
c_2EDeepSyntax_2ExEQ: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2EDeepSyntax_2ExLT,type,
c_2EDeepSyntax_2ExLT: tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__TY__DEF,axiom,
? [V0rep: tyop_2EDeepSyntax_2Edeep__form > ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )] :
( c_2Ebool_2ETYPE__DEFINITION @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ tyop_2EDeepSyntax_2Edeep__form
@ ^ [V1a0_27: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_21 @ ( ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) > $o )
@ ^ [V2_27deep__form_27: ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) > $o] :
( c_2Emin_2E_3D_3D_3E
@ ( c_2Ebool_2E_21 @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V3a0_27: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Emin_2E_3D_3D_3E
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V4a0: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_3F @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V5a1: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_2F_5C
@ ( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V6a0: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ),V7a1: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ( c_2Eind__type_2EFCONS @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V6a0
@ ( c_2Eind__type_2EFCONS @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V7a1
@ ^ [V8n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) ) ) )
@ V4a0
@ V5a1 ) )
@ ( c_2Ebool_2E_2F_5C @ ( V2_27deep__form_27 @ V4a0 ) @ ( V2_27deep__form_27 @ V5a1 ) ) ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V9a0: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_3F @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V10a1: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_2F_5C
@ ( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V11a0: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ),V12a1: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ( c_2Eind__type_2EFCONS @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V11a0
@ ( c_2Eind__type_2EFCONS @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V12a1
@ ^ [V13n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) ) ) )
@ V9a0
@ V10a1 ) )
@ ( c_2Ebool_2E_2F_5C @ ( V2_27deep__form_27 @ V9a0 ) @ ( V2_27deep__form_27 @ V10a1 ) ) ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) )
@ ^ [V14a: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Ebool_2E_2F_5C
@ ( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V15a: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) )] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ( c_2Eind__type_2EFCONS @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V15a
@ ^ [V16n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) ) )
@ V14a ) )
@ ( V2_27deep__form_27 @ V14a ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ $o
@ ^ [V17a: $o] :
( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V18a: $o] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V18a @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ^ [V19n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) )
@ V17a ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ tyop_2Einteger_2Eint
@ ^ [V20a: tyop_2Einteger_2Eint] :
( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V21a: tyop_2Einteger_2Eint] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ V21a @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ^ [V22n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) )
@ V20a ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ tyop_2Einteger_2Eint
@ ^ [V23a: tyop_2Einteger_2Eint] :
( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V24a: tyop_2Einteger_2Eint] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ) ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ V24a @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ^ [V25n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) )
@ V23a ) ) )
@ ( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_3F @ tyop_2Einteger_2Eint
@ ^ [V26a: tyop_2Einteger_2Eint] :
( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V27a: tyop_2Einteger_2Eint] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ) ) ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ V27a @ ( c_2Ebool_2EARB @ tyop_2Einteger_2Eint ) ) )
@ ^ [V28n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) )
@ V26a ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Einteger_2Eint
@ ^ [V29a0: tyop_2Einteger_2Eint] :
( c_2Ebool_2E_3F @ tyop_2Einteger_2Eint
@ ^ [V30a1: tyop_2Einteger_2Eint] :
( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V3a0_27
@ ( ^ [V31a0: tyop_2Einteger_2Eint,V32a1: tyop_2Einteger_2Eint] :
( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ) ) ) ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ $o ) @ ( c_2Epair_2E_2C @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint @ V31a0 @ V32a1 ) )
@ ^ [V33n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) )
@ V29a0
@ V30a1 ) ) ) ) ) ) ) ) ) ) )
@ ( V2_27deep__form_27 @ V3a0_27 ) ) )
@ ( V2_27deep__form_27 @ V1a0_27 ) ) )
@ V0rep ) ).
thf(thm_2EDeepSyntax_2Edeep__form__case__def,axiom,
! [A_27a: $tType] :
( ! [V0a0: tyop_2EDeepSyntax_2Edeep__form,V1a1: tyop_2EDeepSyntax_2Edeep__form,V2f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V3f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V4f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V5f3: $o > A_27a,V6f4: tyop_2Einteger_2Eint > A_27a,V7f5: tyop_2Einteger_2Eint > A_27a,V8f6: tyop_2Einteger_2Eint > A_27a,V9f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2EConjn @ V0a0 @ V1a1 ) @ V2f @ V3f1 @ V4f2 @ V5f3 @ V6f4 @ V7f5 @ V8f6 @ V9f7 )
= ( V2f @ V0a0 @ V1a1 ) )
& ! [V10a0: tyop_2EDeepSyntax_2Edeep__form,V11a1: tyop_2EDeepSyntax_2Edeep__form,V12f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V13f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V14f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V15f3: $o > A_27a,V16f4: tyop_2Einteger_2Eint > A_27a,V17f5: tyop_2Einteger_2Eint > A_27a,V18f6: tyop_2Einteger_2Eint > A_27a,V19f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2EDisjn @ V10a0 @ V11a1 ) @ V12f @ V13f1 @ V14f2 @ V15f3 @ V16f4 @ V17f5 @ V18f6 @ V19f7 )
= ( V13f1 @ V10a0 @ V11a1 ) )
& ! [V20a: tyop_2EDeepSyntax_2Edeep__form,V21f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V22f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V23f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V24f3: $o > A_27a,V25f4: tyop_2Einteger_2Eint > A_27a,V26f5: tyop_2Einteger_2Eint > A_27a,V27f6: tyop_2Einteger_2Eint > A_27a,V28f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2ENegn @ V20a ) @ V21f @ V22f1 @ V23f2 @ V24f3 @ V25f4 @ V26f5 @ V27f6 @ V28f7 )
= ( V23f2 @ V20a ) )
& ! [V29a: $o,V30f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V31f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V32f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V33f3: $o > A_27a,V34f4: tyop_2Einteger_2Eint > A_27a,V35f5: tyop_2Einteger_2Eint > A_27a,V36f6: tyop_2Einteger_2Eint > A_27a,V37f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2EUnrelatedBool @ V29a ) @ V30f @ V31f1 @ V32f2 @ V33f3 @ V34f4 @ V35f5 @ V36f6 @ V37f7 )
= ( V33f3 @ V29a ) )
& ! [V38a: tyop_2Einteger_2Eint,V39f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V40f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V41f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V42f3: $o > A_27a,V43f4: tyop_2Einteger_2Eint > A_27a,V44f5: tyop_2Einteger_2Eint > A_27a,V45f6: tyop_2Einteger_2Eint > A_27a,V46f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2ExLT @ V38a ) @ V39f @ V40f1 @ V41f2 @ V42f3 @ V43f4 @ V44f5 @ V45f6 @ V46f7 )
= ( V43f4 @ V38a ) )
& ! [V47a: tyop_2Einteger_2Eint,V48f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V49f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V50f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V51f3: $o > A_27a,V52f4: tyop_2Einteger_2Eint > A_27a,V53f5: tyop_2Einteger_2Eint > A_27a,V54f6: tyop_2Einteger_2Eint > A_27a,V55f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2ELTx @ V47a ) @ V48f @ V49f1 @ V50f2 @ V51f3 @ V52f4 @ V53f5 @ V54f6 @ V55f7 )
= ( V53f5 @ V47a ) )
& ! [V56a: tyop_2Einteger_2Eint,V57f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V58f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V59f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V60f3: $o > A_27a,V61f4: tyop_2Einteger_2Eint > A_27a,V62f5: tyop_2Einteger_2Eint > A_27a,V63f6: tyop_2Einteger_2Eint > A_27a,V64f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2ExEQ @ V56a ) @ V57f @ V58f1 @ V59f2 @ V60f3 @ V61f4 @ V62f5 @ V63f6 @ V64f7 )
= ( V63f6 @ V56a ) )
& ! [V65a0: tyop_2Einteger_2Eint,V66a1: tyop_2Einteger_2Eint,V67f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V68f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V69f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V70f3: $o > A_27a,V71f4: tyop_2Einteger_2Eint > A_27a,V72f5: tyop_2Einteger_2Eint > A_27a,V73f6: tyop_2Einteger_2Eint > A_27a,V74f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ ( c_2EDeepSyntax_2ExDivided @ V65a0 @ V66a1 ) @ V67f @ V68f1 @ V69f2 @ V70f3 @ V71f4 @ V72f5 @ V73f6 @ V74f7 )
= ( V74f7 @ V65a0 @ V66a1 ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__size__def,axiom,
( ! [V0a0: tyop_2EDeepSyntax_2Edeep__form,V1a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2EConjn @ V0a0 @ V1a1 ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2EDeepSyntax_2Edeep__form__size @ V0a0 ) @ ( c_2EDeepSyntax_2Edeep__form__size @ V1a1 ) ) ) )
& ! [V2a0: tyop_2EDeepSyntax_2Edeep__form,V3a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2EDisjn @ V2a0 @ V3a1 ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2E_2B @ ( c_2EDeepSyntax_2Edeep__form__size @ V2a0 ) @ ( c_2EDeepSyntax_2Edeep__form__size @ V3a1 ) ) ) )
& ! [V4a: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2ENegn @ V4a ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2EDeepSyntax_2Edeep__form__size @ V4a ) ) )
& ! [V5a: $o] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2EUnrelatedBool @ V5a ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2EbasicSize_2Ebool__size @ V5a ) ) )
& ! [V6a: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2ExLT @ V6a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
& ! [V7a: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2ELTx @ V7a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
& ! [V8a: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2ExEQ @ V8a ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
& ! [V9a0: tyop_2Einteger_2Eint,V10a1: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Edeep__form__size @ ( c_2EDeepSyntax_2ExDivided @ V9a0 @ V10a1 ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eeval__form__def,axiom,
( ! [V0f1: tyop_2EDeepSyntax_2Edeep__form,V1f2: tyop_2EDeepSyntax_2Edeep__form,V2x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2EConjn @ V0f1 @ V1f2 ) @ V2x )
<=> ( ( c_2EDeepSyntax_2Eeval__form @ V0f1 @ V2x )
& ( c_2EDeepSyntax_2Eeval__form @ V1f2 @ V2x ) ) )
& ! [V3f1: tyop_2EDeepSyntax_2Edeep__form,V4f2: tyop_2EDeepSyntax_2Edeep__form,V5x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2EDisjn @ V3f1 @ V4f2 ) @ V5x )
<=> ( ( c_2EDeepSyntax_2Eeval__form @ V3f1 @ V5x )
| ( c_2EDeepSyntax_2Eeval__form @ V4f2 @ V5x ) ) )
& ! [V6f: tyop_2EDeepSyntax_2Edeep__form,V7x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2ENegn @ V6f ) @ V7x )
<=> ( (~) @ ( c_2EDeepSyntax_2Eeval__form @ V6f @ V7x ) ) )
& ! [V8b: $o,V9x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2EUnrelatedBool @ V8b ) @ V9x )
= V8b )
& ! [V10i: tyop_2Einteger_2Eint,V11x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2ExLT @ V10i ) @ V11x )
= ( c_2Einteger_2Eint__lt @ V11x @ V10i ) )
& ! [V12i: tyop_2Einteger_2Eint,V13x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2ELTx @ V12i ) @ V13x )
= ( c_2Einteger_2Eint__lt @ V12i @ V13x ) )
& ! [V14i: tyop_2Einteger_2Eint,V15x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2ExEQ @ V14i ) @ V15x )
<=> ( V15x = V14i ) )
& ! [V16i1: tyop_2Einteger_2Eint,V17i2: tyop_2Einteger_2Eint,V18x: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2ExDivided @ V16i1 @ V17i2 ) @ V18x )
= ( c_2Einteger_2Eint__divides @ V16i1 @ ( c_2Einteger_2Eint__add @ V18x @ V17i2 ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eneginf__def,axiom,
( ! [V0f1: tyop_2EDeepSyntax_2Edeep__form,V1f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2EConjn @ V0f1 @ V1f2 ) )
= ( c_2EDeepSyntax_2EConjn @ ( c_2EDeepSyntax_2Eneginf @ V0f1 ) @ ( c_2EDeepSyntax_2Eneginf @ V1f2 ) ) )
& ! [V2f1: tyop_2EDeepSyntax_2Edeep__form,V3f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2EDisjn @ V2f1 @ V3f2 ) )
= ( c_2EDeepSyntax_2EDisjn @ ( c_2EDeepSyntax_2Eneginf @ V2f1 ) @ ( c_2EDeepSyntax_2Eneginf @ V3f2 ) ) )
& ! [V4f: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2ENegn @ V4f ) )
= ( c_2EDeepSyntax_2ENegn @ ( c_2EDeepSyntax_2Eneginf @ V4f ) ) )
& ! [V5b: $o] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2EUnrelatedBool @ V5b ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V5b ) )
& ! [V6i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2ExLT @ V6i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2ET ) )
& ! [V7i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2ELTx @ V7i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) )
& ! [V8i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2ExEQ @ V8i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) )
& ! [V9i1: tyop_2Einteger_2Eint,V10i2: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eneginf @ ( c_2EDeepSyntax_2ExDivided @ V9i1 @ V10i2 ) )
= ( c_2EDeepSyntax_2ExDivided @ V9i1 @ V10i2 ) ) ) ).
thf(thm_2EDeepSyntax_2Eposinf__def,axiom,
( ! [V0f1: tyop_2EDeepSyntax_2Edeep__form,V1f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2EConjn @ V0f1 @ V1f2 ) )
= ( c_2EDeepSyntax_2EConjn @ ( c_2EDeepSyntax_2Eposinf @ V0f1 ) @ ( c_2EDeepSyntax_2Eposinf @ V1f2 ) ) )
& ! [V2f1: tyop_2EDeepSyntax_2Edeep__form,V3f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2EDisjn @ V2f1 @ V3f2 ) )
= ( c_2EDeepSyntax_2EDisjn @ ( c_2EDeepSyntax_2Eposinf @ V2f1 ) @ ( c_2EDeepSyntax_2Eposinf @ V3f2 ) ) )
& ! [V4f: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2ENegn @ V4f ) )
= ( c_2EDeepSyntax_2ENegn @ ( c_2EDeepSyntax_2Eposinf @ V4f ) ) )
& ! [V5b: $o] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2EUnrelatedBool @ V5b ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V5b ) )
& ! [V6i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2ExLT @ V6i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) )
& ! [V7i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2ELTx @ V7i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2ET ) )
& ! [V8i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2ExEQ @ V8i ) )
= ( c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) )
& ! [V9i1: tyop_2Einteger_2Eint,V10i2: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Eposinf @ ( c_2EDeepSyntax_2ExDivided @ V9i1 @ V10i2 ) )
= ( c_2EDeepSyntax_2ExDivided @ V9i1 @ V10i2 ) ) ) ).
thf(thm_2EDeepSyntax_2Ealldivide__def,axiom,
( ! [V0f1: tyop_2EDeepSyntax_2Edeep__form,V1f2: tyop_2EDeepSyntax_2Edeep__form,V2d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2EConjn @ V0f1 @ V1f2 ) @ V2d )
<=> ( ( c_2EDeepSyntax_2Ealldivide @ V0f1 @ V2d )
& ( c_2EDeepSyntax_2Ealldivide @ V1f2 @ V2d ) ) )
& ! [V3f1: tyop_2EDeepSyntax_2Edeep__form,V4f2: tyop_2EDeepSyntax_2Edeep__form,V5d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2EDisjn @ V3f1 @ V4f2 ) @ V5d )
<=> ( ( c_2EDeepSyntax_2Ealldivide @ V3f1 @ V5d )
& ( c_2EDeepSyntax_2Ealldivide @ V4f2 @ V5d ) ) )
& ! [V6f: tyop_2EDeepSyntax_2Edeep__form,V7d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2ENegn @ V6f ) @ V7d )
= ( c_2EDeepSyntax_2Ealldivide @ V6f @ V7d ) )
& ! [V8b: $o,V9d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2EUnrelatedBool @ V8b ) @ V9d )
= c_2Ebool_2ET )
& ! [V10i: tyop_2Einteger_2Eint,V11d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2ExLT @ V10i ) @ V11d )
= c_2Ebool_2ET )
& ! [V12i: tyop_2Einteger_2Eint,V13d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2ELTx @ V12i ) @ V13d )
= c_2Ebool_2ET )
& ! [V14i: tyop_2Einteger_2Eint,V15d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2ExEQ @ V14i ) @ V15d )
= c_2Ebool_2ET )
& ! [V16i1: tyop_2Einteger_2Eint,V17i2: tyop_2Einteger_2Eint,V18d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ ( c_2EDeepSyntax_2ExDivided @ V16i1 @ V17i2 ) @ V18d )
= ( c_2Einteger_2Eint__divides @ V16i1 @ V18d ) ) ) ).
thf(thm_2EDeepSyntax_2EAset__def,axiom,
( ! [V0pos: $o,V1f1: tyop_2EDeepSyntax_2Edeep__form,V2f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EAset @ V0pos @ ( c_2EDeepSyntax_2EConjn @ V1f1 @ V2f2 ) )
= ( c_2Epred__set_2EUNION @ tyop_2Einteger_2Eint @ ( c_2EDeepSyntax_2EAset @ V0pos @ V1f1 ) @ ( c_2EDeepSyntax_2EAset @ V0pos @ V2f2 ) ) )
& ! [V3pos: $o,V4f1: tyop_2EDeepSyntax_2Edeep__form,V5f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EAset @ V3pos @ ( c_2EDeepSyntax_2EDisjn @ V4f1 @ V5f2 ) )
= ( c_2Epred__set_2EUNION @ tyop_2Einteger_2Eint @ ( c_2EDeepSyntax_2EAset @ V3pos @ V4f1 ) @ ( c_2EDeepSyntax_2EAset @ V3pos @ V5f2 ) ) )
& ! [V6pos: $o,V7f: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EAset @ V6pos @ ( c_2EDeepSyntax_2ENegn @ V7f ) )
= ( c_2EDeepSyntax_2EAset @ ( c_2Ebool_2E_7E @ V6pos ) @ V7f ) )
& ! [V8pos: $o,V9b: $o] :
( ( c_2EDeepSyntax_2EAset @ V8pos @ ( c_2EDeepSyntax_2EUnrelatedBool @ V9b ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) )
& ! [V10pos: $o,V11i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EAset @ V10pos @ ( c_2EDeepSyntax_2ExLT @ V11i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V10pos @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ V11i @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) )
& ! [V12pos: $o,V13i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EAset @ V12pos @ ( c_2EDeepSyntax_2ELTx @ V13i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V12pos @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__add @ V13i @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) )
& ! [V14pos: $o,V15i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EAset @ V14pos @ ( c_2EDeepSyntax_2ExEQ @ V15i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V14pos @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__add @ V15i @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ V15i @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) )
& ! [V16pos: $o,V17i1: tyop_2Einteger_2Eint,V18i2: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EAset @ V16pos @ ( c_2EDeepSyntax_2ExDivided @ V17i1 @ V18i2 ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) ).
thf(thm_2EDeepSyntax_2EBset__def,axiom,
( ! [V0pos: $o,V1f1: tyop_2EDeepSyntax_2Edeep__form,V2f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EBset @ V0pos @ ( c_2EDeepSyntax_2EConjn @ V1f1 @ V2f2 ) )
= ( c_2Epred__set_2EUNION @ tyop_2Einteger_2Eint @ ( c_2EDeepSyntax_2EBset @ V0pos @ V1f1 ) @ ( c_2EDeepSyntax_2EBset @ V0pos @ V2f2 ) ) )
& ! [V3pos: $o,V4f1: tyop_2EDeepSyntax_2Edeep__form,V5f2: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EBset @ V3pos @ ( c_2EDeepSyntax_2EDisjn @ V4f1 @ V5f2 ) )
= ( c_2Epred__set_2EUNION @ tyop_2Einteger_2Eint @ ( c_2EDeepSyntax_2EBset @ V3pos @ V4f1 ) @ ( c_2EDeepSyntax_2EBset @ V3pos @ V5f2 ) ) )
& ! [V6pos: $o,V7f: tyop_2EDeepSyntax_2Edeep__form] :
( ( c_2EDeepSyntax_2EBset @ V6pos @ ( c_2EDeepSyntax_2ENegn @ V7f ) )
= ( c_2EDeepSyntax_2EBset @ ( c_2Ebool_2E_7E @ V6pos ) @ V7f ) )
& ! [V8pos: $o,V9b: $o] :
( ( c_2EDeepSyntax_2EBset @ V8pos @ ( c_2EDeepSyntax_2EUnrelatedBool @ V9b ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) )
& ! [V10pos: $o,V11i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EBset @ V10pos @ ( c_2EDeepSyntax_2ExLT @ V11i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V10pos @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__add @ V11i @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) )
& ! [V12pos: $o,V13i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EBset @ V12pos @ ( c_2EDeepSyntax_2ELTx @ V13i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V12pos @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ V13i @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) )
& ! [V14pos: $o,V15i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EBset @ V14pos @ ( c_2EDeepSyntax_2ExEQ @ V15i ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Einteger_2Eint > $o ) @ V14pos @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__add @ V15i @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) @ ( c_2Epred__set_2EINSERT @ tyop_2Einteger_2Eint @ V15i @ ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) )
& ! [V16pos: $o,V17i1: tyop_2Einteger_2Eint,V18i2: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2EBset @ V16pos @ ( c_2EDeepSyntax_2ExDivided @ V17i1 @ V18i2 ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Einteger_2Eint ) ) ) ).
thf(thm_2EDeepSyntax_2Edatatype__deep__form,axiom,
! [V0deep__form: ( tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form ) > ( $o > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ) > ( tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2EDeepSyntax_2Edeep__form ) > $o] : ( c_2Ebool_2EDATATYPE @ $o @ ( V0deep__form @ c_2EDeepSyntax_2EConjn @ c_2EDeepSyntax_2EDisjn @ c_2EDeepSyntax_2ENegn @ c_2EDeepSyntax_2EUnrelatedBool @ c_2EDeepSyntax_2ExLT @ c_2EDeepSyntax_2ELTx @ c_2EDeepSyntax_2ExEQ @ c_2EDeepSyntax_2ExDivided ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__11,axiom,
( ! [V0a0: tyop_2EDeepSyntax_2Edeep__form,V1a1: tyop_2EDeepSyntax_2Edeep__form,V2a0_27: tyop_2EDeepSyntax_2Edeep__form,V3a1_27: tyop_2EDeepSyntax_2Edeep__form] :
( ( ( c_2EDeepSyntax_2EConjn @ V0a0 @ V1a1 )
= ( c_2EDeepSyntax_2EConjn @ V2a0_27 @ V3a1_27 ) )
<=> ( ( V0a0 = V2a0_27 )
& ( V1a1 = V3a1_27 ) ) )
& ! [V4a0: tyop_2EDeepSyntax_2Edeep__form,V5a1: tyop_2EDeepSyntax_2Edeep__form,V6a0_27: tyop_2EDeepSyntax_2Edeep__form,V7a1_27: tyop_2EDeepSyntax_2Edeep__form] :
( ( ( c_2EDeepSyntax_2EDisjn @ V4a0 @ V5a1 )
= ( c_2EDeepSyntax_2EDisjn @ V6a0_27 @ V7a1_27 ) )
<=> ( ( V4a0 = V6a0_27 )
& ( V5a1 = V7a1_27 ) ) )
& ! [V8a: tyop_2EDeepSyntax_2Edeep__form,V9a_27: tyop_2EDeepSyntax_2Edeep__form] :
( ( ( c_2EDeepSyntax_2ENegn @ V8a )
= ( c_2EDeepSyntax_2ENegn @ V9a_27 ) )
<=> ( V8a = V9a_27 ) )
& ! [V10a: $o,V11a_27: $o] :
( ( ( c_2EDeepSyntax_2EUnrelatedBool @ V10a )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V11a_27 ) )
<=> ( V10a = V11a_27 ) )
& ! [V12a: tyop_2Einteger_2Eint,V13a_27: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2ExLT @ V12a )
= ( c_2EDeepSyntax_2ExLT @ V13a_27 ) )
<=> ( V12a = V13a_27 ) )
& ! [V14a: tyop_2Einteger_2Eint,V15a_27: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2ELTx @ V14a )
= ( c_2EDeepSyntax_2ELTx @ V15a_27 ) )
<=> ( V14a = V15a_27 ) )
& ! [V16a: tyop_2Einteger_2Eint,V17a_27: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2ExEQ @ V16a )
= ( c_2EDeepSyntax_2ExEQ @ V17a_27 ) )
<=> ( V16a = V17a_27 ) )
& ! [V18a0: tyop_2Einteger_2Eint,V19a1: tyop_2Einteger_2Eint,V20a0_27: tyop_2Einteger_2Eint,V21a1_27: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2ExDivided @ V18a0 @ V19a1 )
= ( c_2EDeepSyntax_2ExDivided @ V20a0_27 @ V21a1_27 ) )
<=> ( ( V18a0 = V20a0_27 )
& ( V19a1 = V21a1_27 ) ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__distinct,axiom,
( ! [V0a1_27: tyop_2EDeepSyntax_2Edeep__form,V1a1: tyop_2EDeepSyntax_2Edeep__form,V2a0_27: tyop_2EDeepSyntax_2Edeep__form,V3a0: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V3a0 @ V1a1 )
= ( c_2EDeepSyntax_2EDisjn @ V2a0_27 @ V0a1_27 ) ) )
& ! [V4a1: tyop_2EDeepSyntax_2Edeep__form,V5a0: tyop_2EDeepSyntax_2Edeep__form,V6a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V5a0 @ V4a1 )
= ( c_2EDeepSyntax_2ENegn @ V6a ) ) )
& ! [V7a1: tyop_2EDeepSyntax_2Edeep__form,V8a0: tyop_2EDeepSyntax_2Edeep__form,V9a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V8a0 @ V7a1 )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V9a ) ) )
& ! [V10a1: tyop_2EDeepSyntax_2Edeep__form,V11a0: tyop_2EDeepSyntax_2Edeep__form,V12a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V11a0 @ V10a1 )
= ( c_2EDeepSyntax_2ExLT @ V12a ) ) )
& ! [V13a1: tyop_2EDeepSyntax_2Edeep__form,V14a0: tyop_2EDeepSyntax_2Edeep__form,V15a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V14a0 @ V13a1 )
= ( c_2EDeepSyntax_2ELTx @ V15a ) ) )
& ! [V16a1: tyop_2EDeepSyntax_2Edeep__form,V17a0: tyop_2EDeepSyntax_2Edeep__form,V18a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V17a0 @ V16a1 )
= ( c_2EDeepSyntax_2ExEQ @ V18a ) ) )
& ! [V19a1_27: tyop_2Einteger_2Eint,V20a1: tyop_2EDeepSyntax_2Edeep__form,V21a0_27: tyop_2Einteger_2Eint,V22a0: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2EConjn @ V22a0 @ V20a1 )
= ( c_2EDeepSyntax_2ExDivided @ V21a0_27 @ V19a1_27 ) ) )
& ! [V23a1: tyop_2EDeepSyntax_2Edeep__form,V24a0: tyop_2EDeepSyntax_2Edeep__form,V25a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V24a0 @ V23a1 )
= ( c_2EDeepSyntax_2ENegn @ V25a ) ) )
& ! [V26a1: tyop_2EDeepSyntax_2Edeep__form,V27a0: tyop_2EDeepSyntax_2Edeep__form,V28a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V27a0 @ V26a1 )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V28a ) ) )
& ! [V29a1: tyop_2EDeepSyntax_2Edeep__form,V30a0: tyop_2EDeepSyntax_2Edeep__form,V31a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V30a0 @ V29a1 )
= ( c_2EDeepSyntax_2ExLT @ V31a ) ) )
& ! [V32a1: tyop_2EDeepSyntax_2Edeep__form,V33a0: tyop_2EDeepSyntax_2Edeep__form,V34a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V33a0 @ V32a1 )
= ( c_2EDeepSyntax_2ELTx @ V34a ) ) )
& ! [V35a1: tyop_2EDeepSyntax_2Edeep__form,V36a0: tyop_2EDeepSyntax_2Edeep__form,V37a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V36a0 @ V35a1 )
= ( c_2EDeepSyntax_2ExEQ @ V37a ) ) )
& ! [V38a1_27: tyop_2Einteger_2Eint,V39a1: tyop_2EDeepSyntax_2Edeep__form,V40a0_27: tyop_2Einteger_2Eint,V41a0: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2EDisjn @ V41a0 @ V39a1 )
= ( c_2EDeepSyntax_2ExDivided @ V40a0_27 @ V38a1_27 ) ) )
& ! [V42a_27: $o,V43a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2ENegn @ V43a )
= ( c_2EDeepSyntax_2EUnrelatedBool @ V42a_27 ) ) )
& ! [V44a_27: tyop_2Einteger_2Eint,V45a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2ENegn @ V45a )
= ( c_2EDeepSyntax_2ExLT @ V44a_27 ) ) )
& ! [V46a_27: tyop_2Einteger_2Eint,V47a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2ENegn @ V47a )
= ( c_2EDeepSyntax_2ELTx @ V46a_27 ) ) )
& ! [V48a_27: tyop_2Einteger_2Eint,V49a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2ENegn @ V49a )
= ( c_2EDeepSyntax_2ExEQ @ V48a_27 ) ) )
& ! [V50a1: tyop_2Einteger_2Eint,V51a0: tyop_2Einteger_2Eint,V52a: tyop_2EDeepSyntax_2Edeep__form] :
( (~)
@ ( ( c_2EDeepSyntax_2ENegn @ V52a )
= ( c_2EDeepSyntax_2ExDivided @ V51a0 @ V50a1 ) ) )
& ! [V53a_27: tyop_2Einteger_2Eint,V54a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EUnrelatedBool @ V54a )
= ( c_2EDeepSyntax_2ExLT @ V53a_27 ) ) )
& ! [V55a_27: tyop_2Einteger_2Eint,V56a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EUnrelatedBool @ V56a )
= ( c_2EDeepSyntax_2ELTx @ V55a_27 ) ) )
& ! [V57a_27: tyop_2Einteger_2Eint,V58a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EUnrelatedBool @ V58a )
= ( c_2EDeepSyntax_2ExEQ @ V57a_27 ) ) )
& ! [V59a1: tyop_2Einteger_2Eint,V60a0: tyop_2Einteger_2Eint,V61a: $o] :
( (~)
@ ( ( c_2EDeepSyntax_2EUnrelatedBool @ V61a )
= ( c_2EDeepSyntax_2ExDivided @ V60a0 @ V59a1 ) ) )
& ! [V62a_27: tyop_2Einteger_2Eint,V63a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ExLT @ V63a )
= ( c_2EDeepSyntax_2ELTx @ V62a_27 ) ) )
& ! [V64a_27: tyop_2Einteger_2Eint,V65a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ExLT @ V65a )
= ( c_2EDeepSyntax_2ExEQ @ V64a_27 ) ) )
& ! [V66a1: tyop_2Einteger_2Eint,V67a0: tyop_2Einteger_2Eint,V68a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ExLT @ V68a )
= ( c_2EDeepSyntax_2ExDivided @ V67a0 @ V66a1 ) ) )
& ! [V69a_27: tyop_2Einteger_2Eint,V70a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ELTx @ V70a )
= ( c_2EDeepSyntax_2ExEQ @ V69a_27 ) ) )
& ! [V71a1: tyop_2Einteger_2Eint,V72a0: tyop_2Einteger_2Eint,V73a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ELTx @ V73a )
= ( c_2EDeepSyntax_2ExDivided @ V72a0 @ V71a1 ) ) )
& ! [V74a1: tyop_2Einteger_2Eint,V75a0: tyop_2Einteger_2Eint,V76a: tyop_2Einteger_2Eint] :
( (~)
@ ( ( c_2EDeepSyntax_2ExEQ @ V76a )
= ( c_2EDeepSyntax_2ExDivided @ V75a0 @ V74a1 ) ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__nchotomy,axiom,
! [V0dd: tyop_2EDeepSyntax_2Edeep__form] :
( ? [V1d: tyop_2EDeepSyntax_2Edeep__form,V2d0: tyop_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( c_2EDeepSyntax_2EConjn @ V1d @ V2d0 ) )
| ? [V3d: tyop_2EDeepSyntax_2Edeep__form,V4d0: tyop_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( c_2EDeepSyntax_2EDisjn @ V3d @ V4d0 ) )
| ? [V5d: tyop_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( c_2EDeepSyntax_2ENegn @ V5d ) )
| ? [V6b: $o] :
( V0dd
= ( c_2EDeepSyntax_2EUnrelatedBool @ V6b ) )
| ? [V7i: tyop_2Einteger_2Eint] :
( V0dd
= ( c_2EDeepSyntax_2ExLT @ V7i ) )
| ? [V8i: tyop_2Einteger_2Eint] :
( V0dd
= ( c_2EDeepSyntax_2ELTx @ V8i ) )
| ? [V9i: tyop_2Einteger_2Eint] :
( V0dd
= ( c_2EDeepSyntax_2ExEQ @ V9i ) )
| ? [V10i: tyop_2Einteger_2Eint,V11i0: tyop_2Einteger_2Eint] :
( V0dd
= ( c_2EDeepSyntax_2ExDivided @ V10i @ V11i0 ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__Axiom,axiom,
! [A_27a: $tType,V0f0: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a > A_27a > A_27a,V1f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a > A_27a > A_27a,V2f2: tyop_2EDeepSyntax_2Edeep__form > A_27a > A_27a,V3f3: $o > A_27a,V4f4: tyop_2Einteger_2Eint > A_27a,V5f5: tyop_2Einteger_2Eint > A_27a,V6f6: tyop_2Einteger_2Eint > A_27a,V7f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
? [V8fn: tyop_2EDeepSyntax_2Edeep__form > A_27a] :
( ! [V9a0: tyop_2EDeepSyntax_2Edeep__form,V10a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( V8fn @ ( c_2EDeepSyntax_2EConjn @ V9a0 @ V10a1 ) )
= ( V0f0 @ V9a0 @ V10a1 @ ( V8fn @ V9a0 ) @ ( V8fn @ V10a1 ) ) )
& ! [V11a0: tyop_2EDeepSyntax_2Edeep__form,V12a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( V8fn @ ( c_2EDeepSyntax_2EDisjn @ V11a0 @ V12a1 ) )
= ( V1f1 @ V11a0 @ V12a1 @ ( V8fn @ V11a0 ) @ ( V8fn @ V12a1 ) ) )
& ! [V13a: tyop_2EDeepSyntax_2Edeep__form] :
( ( V8fn @ ( c_2EDeepSyntax_2ENegn @ V13a ) )
= ( V2f2 @ V13a @ ( V8fn @ V13a ) ) )
& ! [V14a: $o] :
( ( V8fn @ ( c_2EDeepSyntax_2EUnrelatedBool @ V14a ) )
= ( V3f3 @ V14a ) )
& ! [V15a: tyop_2Einteger_2Eint] :
( ( V8fn @ ( c_2EDeepSyntax_2ExLT @ V15a ) )
= ( V4f4 @ V15a ) )
& ! [V16a: tyop_2Einteger_2Eint] :
( ( V8fn @ ( c_2EDeepSyntax_2ELTx @ V16a ) )
= ( V5f5 @ V16a ) )
& ! [V17a: tyop_2Einteger_2Eint] :
( ( V8fn @ ( c_2EDeepSyntax_2ExEQ @ V17a ) )
= ( V6f6 @ V17a ) )
& ! [V18a0: tyop_2Einteger_2Eint,V19a1: tyop_2Einteger_2Eint] :
( ( V8fn @ ( c_2EDeepSyntax_2ExDivided @ V18a0 @ V19a1 ) )
= ( V7f7 @ V18a0 @ V19a1 ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__induction,axiom,
! [V0P: tyop_2EDeepSyntax_2Edeep__form > $o] :
( ( ! [V1d: tyop_2EDeepSyntax_2Edeep__form,V2d0: tyop_2EDeepSyntax_2Edeep__form] :
( ( ( V0P @ V1d )
& ( V0P @ V2d0 ) )
=> ( V0P @ ( c_2EDeepSyntax_2EConjn @ V1d @ V2d0 ) ) )
& ! [V3d: tyop_2EDeepSyntax_2Edeep__form,V4d0: tyop_2EDeepSyntax_2Edeep__form] :
( ( ( V0P @ V3d )
& ( V0P @ V4d0 ) )
=> ( V0P @ ( c_2EDeepSyntax_2EDisjn @ V3d @ V4d0 ) ) )
& ! [V5d: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0P @ V5d )
=> ( V0P @ ( c_2EDeepSyntax_2ENegn @ V5d ) ) )
& ! [V6b: $o] : ( V0P @ ( c_2EDeepSyntax_2EUnrelatedBool @ V6b ) )
& ! [V7i: tyop_2Einteger_2Eint] : ( V0P @ ( c_2EDeepSyntax_2ExLT @ V7i ) )
& ! [V8i: tyop_2Einteger_2Eint] : ( V0P @ ( c_2EDeepSyntax_2ELTx @ V8i ) )
& ! [V9i: tyop_2Einteger_2Eint] : ( V0P @ ( c_2EDeepSyntax_2ExEQ @ V9i ) )
& ! [V10i: tyop_2Einteger_2Eint,V11i0: tyop_2Einteger_2Eint] : ( V0P @ ( c_2EDeepSyntax_2ExDivided @ V10i @ V11i0 ) ) )
=> ! [V12d: tyop_2EDeepSyntax_2Edeep__form] : ( V0P @ V12d ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__case__cong,axiom,
! [A_27a: $tType,V0f7_27: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a,V1f6_27: tyop_2Einteger_2Eint > A_27a,V2f5_27: tyop_2Einteger_2Eint > A_27a,V3f4_27: tyop_2Einteger_2Eint > A_27a,V4f3_27: $o > A_27a,V5f2_27: tyop_2EDeepSyntax_2Edeep__form > A_27a,V6f1_27: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V7f_27: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V8M: tyop_2EDeepSyntax_2Edeep__form,V9M_27: tyop_2EDeepSyntax_2Edeep__form,V10f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V11f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V12f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V13f3: $o > A_27a,V14f4: tyop_2Einteger_2Eint > A_27a,V15f5: tyop_2Einteger_2Eint > A_27a,V16f6: tyop_2Einteger_2Eint > A_27a,V17f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a] :
( ( ( V8M = V9M_27 )
& ! [V18a0: tyop_2EDeepSyntax_2Edeep__form,V19a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( c_2EDeepSyntax_2EConjn @ V18a0 @ V19a1 ) )
=> ( ( V10f @ V18a0 @ V19a1 )
= ( V7f_27 @ V18a0 @ V19a1 ) ) )
& ! [V20a0: tyop_2EDeepSyntax_2Edeep__form,V21a1: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( c_2EDeepSyntax_2EDisjn @ V20a0 @ V21a1 ) )
=> ( ( V11f1 @ V20a0 @ V21a1 )
= ( V6f1_27 @ V20a0 @ V21a1 ) ) )
& ! [V22a: tyop_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( c_2EDeepSyntax_2ENegn @ V22a ) )
=> ( ( V12f2 @ V22a )
= ( V5f2_27 @ V22a ) ) )
& ! [V23a: $o] :
( ( V9M_27
= ( c_2EDeepSyntax_2EUnrelatedBool @ V23a ) )
=> ( ( V13f3 @ V23a )
= ( V4f3_27 @ V23a ) ) )
& ! [V24a: tyop_2Einteger_2Eint] :
( ( V9M_27
= ( c_2EDeepSyntax_2ExLT @ V24a ) )
=> ( ( V14f4 @ V24a )
= ( V3f4_27 @ V24a ) ) )
& ! [V25a: tyop_2Einteger_2Eint] :
( ( V9M_27
= ( c_2EDeepSyntax_2ELTx @ V25a ) )
=> ( ( V15f5 @ V25a )
= ( V2f5_27 @ V25a ) ) )
& ! [V26a: tyop_2Einteger_2Eint] :
( ( V9M_27
= ( c_2EDeepSyntax_2ExEQ @ V26a ) )
=> ( ( V16f6 @ V26a )
= ( V1f6_27 @ V26a ) ) )
& ! [V27a0: tyop_2Einteger_2Eint,V28a1: tyop_2Einteger_2Eint] :
( ( V9M_27
= ( c_2EDeepSyntax_2ExDivided @ V27a0 @ V28a1 ) )
=> ( ( V17f7 @ V27a0 @ V28a1 )
= ( V0f7_27 @ V27a0 @ V28a1 ) ) ) )
=> ( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ V8M @ V10f @ V11f1 @ V12f2 @ V13f3 @ V14f4 @ V15f5 @ V16f6 @ V17f7 )
= ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ V9M_27 @ V7f_27 @ V6f1_27 @ V5f2_27 @ V4f3_27 @ V3f4_27 @ V2f5_27 @ V1f6_27 @ V0f7_27 ) ) ) ).
thf(thm_2EDeepSyntax_2Edeep__form__case__eq,axiom,
! [A_27a: $tType,V0x: tyop_2EDeepSyntax_2Edeep__form,V1v: A_27a,V2f7: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > A_27a,V3f6: tyop_2Einteger_2Eint > A_27a,V4f5: tyop_2Einteger_2Eint > A_27a,V5f4: tyop_2Einteger_2Eint > A_27a,V6f3: $o > A_27a,V7f2: tyop_2EDeepSyntax_2Edeep__form > A_27a,V8f1: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a,V9f: tyop_2EDeepSyntax_2Edeep__form > tyop_2EDeepSyntax_2Edeep__form > A_27a] :
( ( ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a @ V0x @ V9f @ V8f1 @ V7f2 @ V6f3 @ V5f4 @ V4f5 @ V3f6 @ V2f7 )
= V1v )
<=> ( ? [V10d: tyop_2EDeepSyntax_2Edeep__form,V11d0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( c_2EDeepSyntax_2EConjn @ V10d @ V11d0 ) )
& ( ( V9f @ V10d @ V11d0 )
= V1v ) )
| ? [V12d: tyop_2EDeepSyntax_2Edeep__form,V13d0: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( c_2EDeepSyntax_2EDisjn @ V12d @ V13d0 ) )
& ( ( V8f1 @ V12d @ V13d0 )
= V1v ) )
| ? [V14d: tyop_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( c_2EDeepSyntax_2ENegn @ V14d ) )
& ( ( V7f2 @ V14d )
= V1v ) )
| ? [V15b: $o] :
( ( V0x
= ( c_2EDeepSyntax_2EUnrelatedBool @ V15b ) )
& ( ( V6f3 @ V15b )
= V1v ) )
| ? [V16i: tyop_2Einteger_2Eint] :
( ( V0x
= ( c_2EDeepSyntax_2ExLT @ V16i ) )
& ( ( V5f4 @ V16i )
= V1v ) )
| ? [V17i: tyop_2Einteger_2Eint] :
( ( V0x
= ( c_2EDeepSyntax_2ELTx @ V17i ) )
& ( ( V4f5 @ V17i )
= V1v ) )
| ? [V18i: tyop_2Einteger_2Eint] :
( ( V0x
= ( c_2EDeepSyntax_2ExEQ @ V18i ) )
& ( ( V3f6 @ V18i )
= V1v ) )
| ? [V19i: tyop_2Einteger_2Eint,V20i0: tyop_2Einteger_2Eint] :
( ( V0x
= ( c_2EDeepSyntax_2ExDivided @ V19i @ V20i0 ) )
& ( ( V2f7 @ V19i @ V20i0 )
= V1v ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eneginf__ok,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form] :
? [V1y: tyop_2Einteger_2Eint] :
! [V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ V1y )
=> ( ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
= ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ V2x ) ) ) ).
thf(thm_2EDeepSyntax_2Eposinf__ok,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form] :
? [V1y: tyop_2Einteger_2Eint] :
! [V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V1y @ V2x )
=> ( ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
= ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ V2x ) ) ) ).
thf(thm_2EDeepSyntax_2Eadd__d__neginf,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1x: tyop_2Einteger_2Eint,V2y: tyop_2Einteger_2Eint,V3d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V3d )
=> ( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ V1x )
= ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ V2y @ V3d ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eadd__d__posinf,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1x: tyop_2Einteger_2Eint,V2y: tyop_2Einteger_2Eint,V3d: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V3d )
=> ( ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ V1x )
= ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ V2y @ V3d ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eneginf__disj1__implies__exoriginal,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint,V2i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
=> ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V2i )
& ( c_2Einteger_2Eint__le @ V2i @ V1d )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ V2i ) )
=> ? [V3x: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form @ V0f @ V3x ) ) ) ).
thf(thm_2EDeepSyntax_2Eposinf__disj1__implies__exoriginal,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint,V2i: tyop_2Einteger_2Eint] :
( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
=> ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V2i )
& ( c_2Einteger_2Eint__le @ V2i @ V1d )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ V2i ) )
=> ? [V3x: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form @ V0f @ V3x ) ) ) ).
thf(thm_2EDeepSyntax_2Eneginf__exoriginal__implies__rhs,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V1d ) )
=> ( ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
=> ( ? [V3i: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V3i )
& ( c_2Einteger_2Eint__le @ V3i @ V1d )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ V3i ) )
| ? [V4j: tyop_2Einteger_2Eint,V5b: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V4j )
& ( c_2Einteger_2Eint__le @ V4j @ V1d )
& ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V5b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ V0f ) )
& ( c_2EDeepSyntax_2Eeval__form @ V0f @ ( c_2Einteger_2Eint__add @ V5b @ V4j ) ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eposinf__exoriginal__implies__rhs,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V1d ) )
=> ( ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
=> ( ? [V3i: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V3i )
& ( c_2Einteger_2Eint__le @ V3i @ V1d )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ V3i ) )
| ? [V4j: tyop_2Einteger_2Eint,V5b: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V4j )
& ( c_2Einteger_2Eint__le @ V4j @ V1d )
& ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V5b @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ V0f ) )
& ( c_2EDeepSyntax_2Eeval__form @ V0f @ ( c_2Einteger_2Eint__add @ V5b @ ( c_2Einteger_2Eint__neg @ V4j ) ) ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eneginf__exoriginal__eq__rhs,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V1d ) )
=> ( ? [V2x: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
<=> ( ? [V3i: tyop_2Einteger_2Eint] :
( ( c_2Ecombin_2EK @ $o @ tyop_2Einteger_2Eint @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V3i ) @ ( c_2Einteger_2Eint__le @ V3i @ V1d ) ) @ V3i )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eneginf @ V0f ) @ V3i ) )
| ? [V4b: tyop_2Einteger_2Eint,V5j: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V4b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ V0f ) )
& ( c_2Ecombin_2EK @ $o @ tyop_2Einteger_2Eint @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V5j ) @ ( c_2Einteger_2Eint__le @ V5j @ V1d ) ) @ V5j )
& ( c_2EDeepSyntax_2Eeval__form @ V0f @ ( c_2Einteger_2Eint__add @ V4b @ V5j ) ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Eposinf__exoriginal__eq__rhs,axiom,
! [V0f: tyop_2EDeepSyntax_2Edeep__form,V1d: tyop_2Einteger_2Eint] :
( ( ( c_2EDeepSyntax_2Ealldivide @ V0f @ V1d )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V1d ) )
=> ( ? [V2x: tyop_2Einteger_2Eint] : ( c_2EDeepSyntax_2Eeval__form @ V0f @ V2x )
<=> ( ? [V3i: tyop_2Einteger_2Eint] :
( ( c_2Ecombin_2EK @ $o @ tyop_2Einteger_2Eint @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V3i ) @ ( c_2Einteger_2Eint__le @ V3i @ V1d ) ) @ V3i )
& ( c_2EDeepSyntax_2Eeval__form @ ( c_2EDeepSyntax_2Eposinf @ V0f ) @ V3i ) )
| ? [V4b: tyop_2Einteger_2Eint,V5j: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V4b @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ V0f ) )
& ( c_2Ecombin_2EK @ $o @ tyop_2Einteger_2Eint @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V5j ) @ ( c_2Einteger_2Eint__le @ V5j @ V1d ) ) @ V5j )
& ( c_2EDeepSyntax_2Eeval__form @ V0f @ ( c_2Einteger_2Eint__add @ V4b @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V5j ) ) ) ) ) ) ) ).
thf(thm_2EDeepSyntax_2Ein__bset,axiom,
! [V0pos: $o,V1i2: tyop_2Einteger_2Eint,V2i1: tyop_2Einteger_2Eint,V3i: tyop_2Einteger_2Eint,V4f2: tyop_2EDeepSyntax_2Edeep__form,V5f1: tyop_2EDeepSyntax_2Edeep__form,V6f: tyop_2EDeepSyntax_2Edeep__form,V7b0: $o,V8P: tyop_2Einteger_2Eint > $o] :
( ( ? [V9b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V9b @ ( c_2EDeepSyntax_2EBset @ V0pos @ ( c_2EDeepSyntax_2EConjn @ V5f1 @ V4f2 ) ) )
& ( V8P @ V9b ) )
<=> ( ? [V10b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V10b @ ( c_2EDeepSyntax_2EBset @ V0pos @ V5f1 ) )
& ( V8P @ V10b ) )
| ? [V11b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V11b @ ( c_2EDeepSyntax_2EBset @ V0pos @ V4f2 ) )
& ( V8P @ V11b ) ) ) )
& ( ? [V12b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V12b @ ( c_2EDeepSyntax_2EBset @ V0pos @ ( c_2EDeepSyntax_2EDisjn @ V5f1 @ V4f2 ) ) )
& ( V8P @ V12b ) )
<=> ( ? [V13b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V13b @ ( c_2EDeepSyntax_2EBset @ V0pos @ V5f1 ) )
& ( V8P @ V13b ) )
| ? [V14b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V14b @ ( c_2EDeepSyntax_2EBset @ V0pos @ V4f2 ) )
& ( V8P @ V14b ) ) ) )
& ( ? [V15b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V15b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ENegn @ V6f ) ) )
& ( V8P @ V15b ) )
<=> ? [V16b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V16b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2EF @ V6f ) )
& ( V8P @ V16b ) ) )
& ( ? [V17b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V17b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ENegn @ V6f ) ) )
& ( V8P @ V17b ) )
<=> ? [V18b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V18b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ V6f ) )
& ( V8P @ V18b ) ) )
& ( ? [V19b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V19b @ ( c_2EDeepSyntax_2EBset @ V0pos @ ( c_2EDeepSyntax_2EUnrelatedBool @ V7b0 ) ) )
& ( V8P @ V19b ) )
<=> c_2Ebool_2EF )
& ( ? [V20b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V20b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ExLT @ V3i ) ) )
& ( V8P @ V20b ) )
<=> c_2Ebool_2EF )
& ( ? [V21b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V21b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ExLT @ V3i ) ) )
& ( V8P @ V21b ) )
<=> ( V8P @ ( c_2Einteger_2Eint__add @ V3i @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ? [V22b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V22b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ELTx @ V3i ) ) )
& ( V8P @ V22b ) )
<=> ( V8P @ V3i ) )
& ( ? [V23b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V23b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ELTx @ V3i ) ) )
& ( V8P @ V23b ) )
<=> c_2Ebool_2EF )
& ( ? [V24b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V24b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ExEQ @ V3i ) ) )
& ( V8P @ V24b ) )
<=> ( V8P @ ( c_2Einteger_2Eint__add @ V3i @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ? [V25b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V25b @ ( c_2EDeepSyntax_2EBset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ExEQ @ V3i ) ) )
& ( V8P @ V25b ) )
<=> ( V8P @ V3i ) )
& ( ? [V26b: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V26b @ ( c_2EDeepSyntax_2EBset @ V0pos @ ( c_2EDeepSyntax_2ExDivided @ V2i1 @ V1i2 ) ) )
& ( V8P @ V26b ) )
<=> c_2Ebool_2EF ) ) ).
thf(thm_2EDeepSyntax_2Ein__aset,axiom,
! [V0pos: $o,V1i2: tyop_2Einteger_2Eint,V2i1: tyop_2Einteger_2Eint,V3i: tyop_2Einteger_2Eint,V4f2: tyop_2EDeepSyntax_2Edeep__form,V5f1: tyop_2EDeepSyntax_2Edeep__form,V6f: tyop_2EDeepSyntax_2Edeep__form,V7a0: $o,V8P: tyop_2Einteger_2Eint > $o] :
( ( ? [V9a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V9a @ ( c_2EDeepSyntax_2EAset @ V0pos @ ( c_2EDeepSyntax_2EConjn @ V5f1 @ V4f2 ) ) )
& ( V8P @ V9a ) )
<=> ( ? [V10a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V10a @ ( c_2EDeepSyntax_2EAset @ V0pos @ V5f1 ) )
& ( V8P @ V10a ) )
| ? [V11a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V11a @ ( c_2EDeepSyntax_2EAset @ V0pos @ V4f2 ) )
& ( V8P @ V11a ) ) ) )
& ( ? [V12a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V12a @ ( c_2EDeepSyntax_2EAset @ V0pos @ ( c_2EDeepSyntax_2EDisjn @ V5f1 @ V4f2 ) ) )
& ( V8P @ V12a ) )
<=> ( ? [V13a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V13a @ ( c_2EDeepSyntax_2EAset @ V0pos @ V5f1 ) )
& ( V8P @ V13a ) )
| ? [V14a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V14a @ ( c_2EDeepSyntax_2EAset @ V0pos @ V4f2 ) )
& ( V8P @ V14a ) ) ) )
& ( ? [V15a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V15a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ENegn @ V6f ) ) )
& ( V8P @ V15a ) )
<=> ? [V16a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V16a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2EF @ V6f ) )
& ( V8P @ V16a ) ) )
& ( ? [V17a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V17a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ENegn @ V6f ) ) )
& ( V8P @ V17a ) )
<=> ? [V18a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V18a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ V6f ) )
& ( V8P @ V18a ) ) )
& ( ? [V19a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V19a @ ( c_2EDeepSyntax_2EAset @ V0pos @ ( c_2EDeepSyntax_2EUnrelatedBool @ V7a0 ) ) )
& ( V8P @ V19a ) )
<=> c_2Ebool_2EF )
& ( ? [V20a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V20a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ExLT @ V3i ) ) )
& ( V8P @ V20a ) )
<=> ( V8P @ V3i ) )
& ( ? [V21a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V21a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ExLT @ V3i ) ) )
& ( V8P @ V21a ) )
<=> c_2Ebool_2EF )
& ( ? [V22a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V22a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ELTx @ V3i ) ) )
& ( V8P @ V22a ) )
<=> c_2Ebool_2EF )
& ( ? [V23a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V23a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ELTx @ V3i ) ) )
& ( V8P @ V23a ) )
<=> ( V8P @ ( c_2Einteger_2Eint__add @ V3i @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ? [V24a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V24a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2ET @ ( c_2EDeepSyntax_2ExEQ @ V3i ) ) )
& ( V8P @ V24a ) )
<=> ( V8P @ ( c_2Einteger_2Eint__add @ V3i @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ? [V25a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V25a @ ( c_2EDeepSyntax_2EAset @ c_2Ebool_2EF @ ( c_2EDeepSyntax_2ExEQ @ V3i ) ) )
& ( V8P @ V25a ) )
<=> ( V8P @ V3i ) )
& ( ? [V26a: tyop_2Einteger_2Eint] :
( ( c_2Ebool_2EIN @ tyop_2Einteger_2Eint @ V26a @ ( c_2EDeepSyntax_2EAset @ V0pos @ ( c_2EDeepSyntax_2ExDivided @ V2i1 @ V1i2 ) ) )
& ( V8P @ V26a ) )
<=> c_2Ebool_2EF ) ) ).
%------------------------------------------------------------------------------