ITP001 Axioms: ITP106^5.ax
%------------------------------------------------------------------------------
% File : ITP106^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : DeepSyntax^2.ax [Gau20]
% : HL4106^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 106 ( 15 unt; 39 typ; 0 def)
% Number of atoms : 3572 ( 164 equ; 0 cnn)
% Maximal formula atoms : 728 ( 33 avg)
% Number of connectives : 5480 ( 29 ~; 23 |; 214 &;4986 @)
% ( 56 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 12 avg;4986 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 87 usr; 70 con; 0-2 aty)
% Number of variables : 543 ( 33 ^ 432 !; 78 ?; 543 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2EDeepSyntax_2Edeep__form,type,
ty_2EDeepSyntax_2Edeep__form: del ).
thf(stp_ty_2EDeepSyntax_2Edeep__form,type,
tp__ty_2EDeepSyntax_2Edeep__form: $tType ).
thf(stp_inj_ty_2EDeepSyntax_2Edeep__form,type,
inj__ty_2EDeepSyntax_2Edeep__form: tp__ty_2EDeepSyntax_2Edeep__form > $i ).
thf(stp_surj_ty_2EDeepSyntax_2Edeep__form,type,
surj__ty_2EDeepSyntax_2Edeep__form: $i > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_inj_surj_ty_2EDeepSyntax_2Edeep__form,axiom,
! [X: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2EDeepSyntax_2Edeep__form,axiom,
! [X: tp__ty_2EDeepSyntax_2Edeep__form] : ( mem @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X ) @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_iso_mem_ty_2EDeepSyntax_2Edeep__form,axiom,
! [X: $i] :
( ( mem @ X @ ty_2EDeepSyntax_2Edeep__form )
=> ( X
= ( inj__ty_2EDeepSyntax_2Edeep__form @ ( surj__ty_2EDeepSyntax_2Edeep__form @ X ) ) ) ) ).
thf(tp_c_2EDeepSyntax_2EAset,type,
c_2EDeepSyntax_2EAset: $i ).
thf(mem_c_2EDeepSyntax_2EAset,axiom,
mem @ c_2EDeepSyntax_2EAset @ ( arr @ bool @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ) ).
thf(tp_c_2EDeepSyntax_2EBset,type,
c_2EDeepSyntax_2EBset: $i ).
thf(mem_c_2EDeepSyntax_2EBset,axiom,
mem @ c_2EDeepSyntax_2EBset @ ( arr @ bool @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ) ).
thf(tp_c_2EDeepSyntax_2EConjn,type,
c_2EDeepSyntax_2EConjn: $i ).
thf(mem_c_2EDeepSyntax_2EConjn,axiom,
mem @ c_2EDeepSyntax_2EConjn @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ) ).
thf(stp_fo_c_2EDeepSyntax_2EConjn,type,
fo__c_2EDeepSyntax_2EConjn: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2EConjn,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form,X1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2EConjn @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X1 ) ) ) ).
thf(tp_c_2EDeepSyntax_2EDisjn,type,
c_2EDeepSyntax_2EDisjn: $i ).
thf(mem_c_2EDeepSyntax_2EDisjn,axiom,
mem @ c_2EDeepSyntax_2EDisjn @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ) ).
thf(stp_fo_c_2EDeepSyntax_2EDisjn,type,
fo__c_2EDeepSyntax_2EDisjn: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2EDisjn,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form,X1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2EDisjn @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X1 ) ) ) ).
thf(tp_c_2EDeepSyntax_2ELTx,type,
c_2EDeepSyntax_2ELTx: $i ).
thf(mem_c_2EDeepSyntax_2ELTx,axiom,
mem @ c_2EDeepSyntax_2ELTx @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2ELTx,type,
fo__c_2EDeepSyntax_2ELTx: tp__ty_2Einteger_2Eint > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2ELTx,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2ELTx @ X0 ) )
= ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2ENegn,type,
c_2EDeepSyntax_2ENegn: $i ).
thf(mem_c_2EDeepSyntax_2ENegn,axiom,
mem @ c_2EDeepSyntax_2ENegn @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2ENegn,type,
fo__c_2EDeepSyntax_2ENegn: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2ENegn,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2ENegn @ X0 ) )
= ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2EUnrelatedBool,type,
c_2EDeepSyntax_2EUnrelatedBool: $i ).
thf(mem_c_2EDeepSyntax_2EUnrelatedBool,axiom,
mem @ c_2EDeepSyntax_2EUnrelatedBool @ ( arr @ bool @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(tp_c_2EDeepSyntax_2Ealldivide,type,
c_2EDeepSyntax_2Ealldivide: $i ).
thf(mem_c_2EDeepSyntax_2Ealldivide,axiom,
mem @ c_2EDeepSyntax_2Ealldivide @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).
thf(tp_c_2EDeepSyntax_2Edeep__form__CASE,type,
c_2EDeepSyntax_2Edeep__form__CASE: del > $i ).
thf(mem_c_2EDeepSyntax_2Edeep__form__CASE,axiom,
! [A_27a: del] : ( mem @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) @ ( arr @ ( arr @ bool @ A_27a ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ A_27a ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ A_27a ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ A_27a ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) @ A_27a ) ) ) ) ) ) ) ) ) ) ).
thf(tp_c_2EDeepSyntax_2Edeep__form__size,type,
c_2EDeepSyntax_2Edeep__form__size: $i ).
thf(mem_c_2EDeepSyntax_2Edeep__form__size,axiom,
mem @ c_2EDeepSyntax_2Edeep__form__size @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2EDeepSyntax_2Edeep__form__size,type,
fo__c_2EDeepSyntax_2Edeep__form__size: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2EDeepSyntax_2Edeep__form__size,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2EDeepSyntax_2Edeep__form__size @ X0 ) )
= ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2Eeval__form,type,
c_2EDeepSyntax_2Eeval__form: $i ).
thf(mem_c_2EDeepSyntax_2Eeval__form,axiom,
mem @ c_2EDeepSyntax_2Eeval__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).
thf(tp_c_2EDeepSyntax_2Eneginf,type,
c_2EDeepSyntax_2Eneginf: $i ).
thf(mem_c_2EDeepSyntax_2Eneginf,axiom,
mem @ c_2EDeepSyntax_2Eneginf @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2Eneginf,type,
fo__c_2EDeepSyntax_2Eneginf: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2Eneginf,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2Eneginf @ X0 ) )
= ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2Eposinf,type,
c_2EDeepSyntax_2Eposinf: $i ).
thf(mem_c_2EDeepSyntax_2Eposinf,axiom,
mem @ c_2EDeepSyntax_2Eposinf @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2Eposinf,type,
fo__c_2EDeepSyntax_2Eposinf: tp__ty_2EDeepSyntax_2Edeep__form > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2Eposinf,axiom,
! [X0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2Eposinf @ X0 ) )
= ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2ExDivided,type,
c_2EDeepSyntax_2ExDivided: $i ).
thf(mem_c_2EDeepSyntax_2ExDivided,axiom,
mem @ c_2EDeepSyntax_2ExDivided @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) ) ).
thf(stp_fo_c_2EDeepSyntax_2ExDivided,type,
fo__c_2EDeepSyntax_2ExDivided: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2ExDivided,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2ExDivided @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ( inj__ty_2Einteger_2Eint @ X1 ) ) ) ).
thf(tp_c_2EDeepSyntax_2ExEQ,type,
c_2EDeepSyntax_2ExEQ: $i ).
thf(mem_c_2EDeepSyntax_2ExEQ,axiom,
mem @ c_2EDeepSyntax_2ExEQ @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2ExEQ,type,
fo__c_2EDeepSyntax_2ExEQ: tp__ty_2Einteger_2Eint > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2ExEQ,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2ExEQ @ X0 ) )
= ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) ).
thf(tp_c_2EDeepSyntax_2ExLT,type,
c_2EDeepSyntax_2ExLT: $i ).
thf(mem_c_2EDeepSyntax_2ExLT,axiom,
mem @ c_2EDeepSyntax_2ExLT @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) ).
thf(stp_fo_c_2EDeepSyntax_2ExLT,type,
fo__c_2EDeepSyntax_2ExLT: tp__ty_2Einteger_2Eint > tp__ty_2EDeepSyntax_2Edeep__form ).
thf(stp_eq_fo_c_2EDeepSyntax_2ExLT,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2EDeepSyntax_2Edeep__form @ ( fo__c_2EDeepSyntax_2ExLT @ X0 ) )
= ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) ).
thf(stp_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $tType ).
thf(stp_inj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint > $i ).
thf(stp_surj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $i > tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint ).
thf(stp_inj_surj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] :
( ( surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] : ( mem @ ( inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
=> ( X
= ( inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] : ( mem @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
tp__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
inj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: tp__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,type,
surj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint: $i > tp__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( inj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ ( surj__c_ty_2Epair_2Eprod_ty_2Einteger_2Eint_ty_2Einteger_2Eint @ X ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Edeep__form__TY__DEF,axiom,
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ty_2EDeepSyntax_2Edeep__form )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V1a0_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ bool )
@ ^ [V2_27deep__form_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V3a0_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V4a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V5a1: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( ap
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V6a0: $i] :
( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V7a1: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V6a0 )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V7a1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) ) ) ) )
@ V4a0 )
@ V5a1 ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2_27deep__form_27 @ V4a0 ) ) @ ( ap @ V2_27deep__form_27 @ V5a1 ) ) ) ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V9a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V10a1: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( ap
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V11a0: $i] :
( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V12a1: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V11a0 )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V12a1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) ) ) ) )
@ V9a0 )
@ V10a1 ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2_27deep__form_27 @ V9a0 ) ) @ ( ap @ V2_27deep__form_27 @ V10a1 ) ) ) ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V14a: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) )
@ ^ [V15a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V15a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V16n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) ) )
@ V14a ) ) )
@ ( ap @ V2_27deep__form_27 @ V14a ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ bool )
@ ( lam @ bool
@ ^ [V17a: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( lam @ bool
@ ^ [V18a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ V18a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V19n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) )
@ V17a ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V20a: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V21a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ V21a ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V22n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) )
@ V20a ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V23a: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V24a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ V24a ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V25n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) )
@ V23a ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V26a: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V27a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ V27a ) @ ( c_2Ebool_2EARB @ ty_2Einteger_2Eint ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V28n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) )
@ V26a ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V29a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V30a1: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( ap
@ ( lam @ ty_2Einteger_2Eint
@ ^ [V31a0: $i] :
( lam @ ty_2Einteger_2Eint
@ ^ [V32a1: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) @ ( c_2Ebool_2EARB @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) @ V31a0 ) @ V32a1 ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V33n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ) ) ) ) )
@ V29a0 )
@ V30a1 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ V2_27deep__form_27 @ V3a0_27 ) ) ) ) )
@ ( ap @ V2_27deep__form_27 @ V1a0_27 ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Edeep__form__case__def,axiom,
! [A_27a: del] :
( ! [V0a0: tp__ty_2EDeepSyntax_2Edeep__form,V1a1: tp__ty_2EDeepSyntax_2Edeep__form,V2f: $i] :
( ( mem @ V2f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V3f1: $i] :
( ( mem @ V3f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V4f2: $i] :
( ( mem @ V4f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V5f3: $i] :
( ( mem @ V5f3 @ ( arr @ bool @ A_27a ) )
=> ! [V6f4: $i] :
( ( mem @ V6f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V7f5: $i] :
( ( mem @ V7f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V8f6: $i] :
( ( mem @ V8f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V9f7: $i] :
( ( mem @ V9f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) ) @ V2f ) @ V3f1 ) @ V4f2 ) @ V5f3 ) @ V6f4 ) @ V7f5 ) @ V8f6 ) @ V9f7 )
= ( ap @ ( ap @ V2f @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) ) ) ) ) ) ) ) ) )
& ! [V10a0: tp__ty_2EDeepSyntax_2Edeep__form,V11a1: tp__ty_2EDeepSyntax_2Edeep__form,V12f: $i] :
( ( mem @ V12f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V13f1: $i] :
( ( mem @ V13f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V14f2: $i] :
( ( mem @ V14f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V15f3: $i] :
( ( mem @ V15f3 @ ( arr @ bool @ A_27a ) )
=> ! [V16f4: $i] :
( ( mem @ V16f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V17f5: $i] :
( ( mem @ V17f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V18f6: $i] :
( ( mem @ V18f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V19f7: $i] :
( ( mem @ V19f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a1 ) ) ) @ V12f ) @ V13f1 ) @ V14f2 ) @ V15f3 ) @ V16f4 ) @ V17f5 ) @ V18f6 ) @ V19f7 )
= ( ap @ ( ap @ V13f1 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a1 ) ) ) ) ) ) ) ) ) ) )
& ! [V20a: tp__ty_2EDeepSyntax_2Edeep__form,V21f: $i] :
( ( mem @ V21f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V22f1: $i] :
( ( mem @ V22f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V23f2: $i] :
( ( mem @ V23f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V24f3: $i] :
( ( mem @ V24f3 @ ( arr @ bool @ A_27a ) )
=> ! [V25f4: $i] :
( ( mem @ V25f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V26f5: $i] :
( ( mem @ V26f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V27f6: $i] :
( ( mem @ V27f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V28f7: $i] :
( ( mem @ V28f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a ) ) ) @ V21f ) @ V22f1 ) @ V23f2 ) @ V24f3 ) @ V25f4 ) @ V26f5 ) @ V27f6 ) @ V28f7 )
= ( ap @ V23f2 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a ) ) ) ) ) ) ) ) ) ) )
& ! [V29a: $i] :
( ( mem @ V29a @ bool )
=> ! [V30f: $i] :
( ( mem @ V30f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V31f1: $i] :
( ( mem @ V31f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V32f2: $i] :
( ( mem @ V32f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V33f3: $i] :
( ( mem @ V33f3 @ ( arr @ bool @ A_27a ) )
=> ! [V34f4: $i] :
( ( mem @ V34f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V35f5: $i] :
( ( mem @ V35f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V36f6: $i] :
( ( mem @ V36f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V37f7: $i] :
( ( mem @ V37f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V29a ) ) @ V30f ) @ V31f1 ) @ V32f2 ) @ V33f3 ) @ V34f4 ) @ V35f5 ) @ V36f6 ) @ V37f7 )
= ( ap @ V33f3 @ V29a ) ) ) ) ) ) ) ) ) ) )
& ! [V38a: tp__ty_2Einteger_2Eint,V39f: $i] :
( ( mem @ V39f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V40f1: $i] :
( ( mem @ V40f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V41f2: $i] :
( ( mem @ V41f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V42f3: $i] :
( ( mem @ V42f3 @ ( arr @ bool @ A_27a ) )
=> ! [V43f4: $i] :
( ( mem @ V43f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V44f5: $i] :
( ( mem @ V44f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V45f6: $i] :
( ( mem @ V45f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V46f7: $i] :
( ( mem @ V46f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V38a ) ) ) @ V39f ) @ V40f1 ) @ V41f2 ) @ V42f3 ) @ V43f4 ) @ V44f5 ) @ V45f6 ) @ V46f7 )
= ( ap @ V43f4 @ ( inj__ty_2Einteger_2Eint @ V38a ) ) ) ) ) ) ) ) ) ) )
& ! [V47a: tp__ty_2Einteger_2Eint,V48f: $i] :
( ( mem @ V48f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V49f1: $i] :
( ( mem @ V49f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V50f2: $i] :
( ( mem @ V50f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V51f3: $i] :
( ( mem @ V51f3 @ ( arr @ bool @ A_27a ) )
=> ! [V52f4: $i] :
( ( mem @ V52f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V53f5: $i] :
( ( mem @ V53f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V54f6: $i] :
( ( mem @ V54f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V55f7: $i] :
( ( mem @ V55f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V47a ) ) ) @ V48f ) @ V49f1 ) @ V50f2 ) @ V51f3 ) @ V52f4 ) @ V53f5 ) @ V54f6 ) @ V55f7 )
= ( ap @ V53f5 @ ( inj__ty_2Einteger_2Eint @ V47a ) ) ) ) ) ) ) ) ) ) )
& ! [V56a: tp__ty_2Einteger_2Eint,V57f: $i] :
( ( mem @ V57f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V58f1: $i] :
( ( mem @ V58f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V59f2: $i] :
( ( mem @ V59f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V60f3: $i] :
( ( mem @ V60f3 @ ( arr @ bool @ A_27a ) )
=> ! [V61f4: $i] :
( ( mem @ V61f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V62f5: $i] :
( ( mem @ V62f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V63f6: $i] :
( ( mem @ V63f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V64f7: $i] :
( ( mem @ V64f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V56a ) ) ) @ V57f ) @ V58f1 ) @ V59f2 ) @ V60f3 ) @ V61f4 ) @ V62f5 ) @ V63f6 ) @ V64f7 )
= ( ap @ V63f6 @ ( inj__ty_2Einteger_2Eint @ V56a ) ) ) ) ) ) ) ) ) ) )
& ! [V65a0: tp__ty_2Einteger_2Eint,V66a1: tp__ty_2Einteger_2Eint,V67f: $i] :
( ( mem @ V67f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V68f1: $i] :
( ( mem @ V68f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V69f2: $i] :
( ( mem @ V69f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V70f3: $i] :
( ( mem @ V70f3 @ ( arr @ bool @ A_27a ) )
=> ! [V71f4: $i] :
( ( mem @ V71f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V72f5: $i] :
( ( mem @ V72f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V73f6: $i] :
( ( mem @ V73f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V74f7: $i] :
( ( mem @ V74f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V65a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V66a1 ) ) ) @ V67f ) @ V68f1 ) @ V69f2 ) @ V70f3 ) @ V71f4 ) @ V72f5 ) @ V73f6 ) @ V74f7 )
= ( ap @ ( ap @ V74f7 @ ( inj__ty_2Einteger_2Eint @ V65a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V66a1 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Edeep__form__size__def,axiom,
( ! [V0a0: tp__ty_2EDeepSyntax_2Edeep__form,V1a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a0 ) ) ) @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) ) ) ) )
& ! [V2a0: tp__ty_2EDeepSyntax_2Edeep__form,V3a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3a1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2a0 ) ) ) @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3a1 ) ) ) ) ) )
& ! [V4a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4a ) ) ) ) )
& ! [V5a: $i] :
( ( mem @ V5a @ bool )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2EbasicSize_2Ebool__size @ V5a ) ) ) ) )
& ! [V6a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V7a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V7a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V8a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V8a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
& ! [V9a0: tp__ty_2Einteger_2Eint,V10a1: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EDeepSyntax_2Edeep__form__size @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V9a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V10a1 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edatatype__deep__form,axiom,
! [V0deep__form: $i] :
( ( mem @ V0deep__form @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ) @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) ) @ ( arr @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ty_2EDeepSyntax_2Edeep__form ) @ ( arr @ ( arr @ bool @ ty_2EDeepSyntax_2Edeep__form ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) @ ( arr @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2EDeepSyntax_2Edeep__form ) ) @ bool ) ) ) ) ) ) ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ 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(conj_thm_2EDeepSyntax_2Edeep__form__11,axiom,
( ! [V0a0: tp__ty_2EDeepSyntax_2Edeep__form,V1a1: tp__ty_2EDeepSyntax_2Edeep__form,V2a0_27: tp__ty_2EDeepSyntax_2Edeep__form,V3a1_27: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2a0_27 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3a1_27 ) ) ) )
<=> ( ( V0a0 = V2a0_27 )
& ( V1a1 = V3a1_27 ) ) )
& ! [V4a0: tp__ty_2EDeepSyntax_2Edeep__form,V5a1: tp__ty_2EDeepSyntax_2Edeep__form,V6a0_27: tp__ty_2EDeepSyntax_2Edeep__form,V7a1_27: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5a1 ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6a0_27 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7a1_27 ) ) ) )
<=> ( ( V4a0 = V6a0_27 )
& ( V5a1 = V7a1_27 ) ) )
& ! [V8a: tp__ty_2EDeepSyntax_2Edeep__form,V9a_27: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V8a ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V9a_27 ) ) ) )
<=> ( V8a = V9a_27 ) )
& ! [V10a: $i] :
( ( mem @ V10a @ bool )
=> ! [V11a_27: $i] :
( ( mem @ V11a_27 @ bool )
=> ( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V10a ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V11a_27 ) ) )
<=> ( ( p @ V10a )
<=> ( p @ V11a_27 ) ) ) ) )
& ! [V12a: tp__ty_2Einteger_2Eint,V13a_27: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V12a ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V13a_27 ) ) ) )
<=> ( V12a = V13a_27 ) )
& ! [V14a: tp__ty_2Einteger_2Eint,V15a_27: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V14a ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V15a_27 ) ) ) )
<=> ( V14a = V15a_27 ) )
& ! [V16a: tp__ty_2Einteger_2Eint,V17a_27: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V16a ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V17a_27 ) ) ) )
<=> ( V16a = V17a_27 ) )
& ! [V18a0: tp__ty_2Einteger_2Eint,V19a1: tp__ty_2Einteger_2Eint,V20a0_27: tp__ty_2Einteger_2Eint,V21a1_27: tp__ty_2Einteger_2Eint] :
( ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V18a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V19a1 ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V20a0_27 ) ) @ ( inj__ty_2Einteger_2Eint @ V21a1_27 ) ) ) )
<=> ( ( V18a0 = V20a0_27 )
& ( V19a1 = V21a1_27 ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__distinct,axiom,
( ! [V0a1_27: tp__ty_2EDeepSyntax_2Edeep__form,V1a1: tp__ty_2EDeepSyntax_2Edeep__form,V2a0_27: tp__ty_2EDeepSyntax_2Edeep__form,V3a0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2a0_27 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0a1_27 ) ) ) )
& ! [V4a1: tp__ty_2EDeepSyntax_2Edeep__form,V5a0: tp__ty_2EDeepSyntax_2Edeep__form,V6a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6a ) ) ) )
& ! [V7a1: tp__ty_2EDeepSyntax_2Edeep__form,V8a0: tp__ty_2EDeepSyntax_2Edeep__form,V9a: $i] :
( ( mem @ V9a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V8a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V9a ) ) ) )
& ! [V10a1: tp__ty_2EDeepSyntax_2Edeep__form,V11a0: tp__ty_2EDeepSyntax_2Edeep__form,V12a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V12a ) ) ) )
& ! [V13a1: tp__ty_2EDeepSyntax_2Edeep__form,V14a0: tp__ty_2EDeepSyntax_2Edeep__form,V15a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V14a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V15a ) ) ) )
& ! [V16a1: tp__ty_2EDeepSyntax_2Edeep__form,V17a0: tp__ty_2EDeepSyntax_2Edeep__form,V18a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V17a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V16a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V18a ) ) ) )
& ! [V19a1_27: tp__ty_2Einteger_2Eint,V20a1: tp__ty_2EDeepSyntax_2Edeep__form,V21a0_27: tp__ty_2Einteger_2Eint,V22a0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V22a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V21a0_27 ) ) @ ( inj__ty_2Einteger_2Eint @ V19a1_27 ) ) ) )
& ! [V23a1: tp__ty_2EDeepSyntax_2Edeep__form,V24a0: tp__ty_2EDeepSyntax_2Edeep__form,V25a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V24a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V23a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V25a ) ) ) )
& ! [V26a1: tp__ty_2EDeepSyntax_2Edeep__form,V27a0: tp__ty_2EDeepSyntax_2Edeep__form,V28a: $i] :
( ( mem @ V28a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V27a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V26a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V28a ) ) ) )
& ! [V29a1: tp__ty_2EDeepSyntax_2Edeep__form,V30a0: tp__ty_2EDeepSyntax_2Edeep__form,V31a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V30a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V29a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V31a ) ) ) )
& ! [V32a1: tp__ty_2EDeepSyntax_2Edeep__form,V33a0: tp__ty_2EDeepSyntax_2Edeep__form,V34a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V33a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V32a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V34a ) ) ) )
& ! [V35a1: tp__ty_2EDeepSyntax_2Edeep__form,V36a0: tp__ty_2EDeepSyntax_2Edeep__form,V37a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V36a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V35a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V37a ) ) ) )
& ! [V38a1_27: tp__ty_2Einteger_2Eint,V39a1: tp__ty_2EDeepSyntax_2Edeep__form,V40a0_27: tp__ty_2Einteger_2Eint,V41a0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V41a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V39a1 ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V40a0_27 ) ) @ ( inj__ty_2Einteger_2Eint @ V38a1_27 ) ) ) )
& ! [V42a_27: $i] :
( ( mem @ V42a_27 @ bool )
=> ! [V43a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V43a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V42a_27 ) ) ) )
& ! [V44a_27: tp__ty_2Einteger_2Eint,V45a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V45a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V44a_27 ) ) ) )
& ! [V46a_27: tp__ty_2Einteger_2Eint,V47a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V47a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V46a_27 ) ) ) )
& ! [V48a_27: tp__ty_2Einteger_2Eint,V49a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V49a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V48a_27 ) ) ) )
& ! [V50a1: tp__ty_2Einteger_2Eint,V51a0: tp__ty_2Einteger_2Eint,V52a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V52a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V51a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V50a1 ) ) ) )
& ! [V53a_27: tp__ty_2Einteger_2Eint,V54a: $i] :
( ( mem @ V54a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V54a ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V53a_27 ) ) ) ) )
& ! [V55a_27: tp__ty_2Einteger_2Eint,V56a: $i] :
( ( mem @ V56a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V56a ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V55a_27 ) ) ) ) )
& ! [V57a_27: tp__ty_2Einteger_2Eint,V58a: $i] :
( ( mem @ V58a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V58a ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V57a_27 ) ) ) ) )
& ! [V59a1: tp__ty_2Einteger_2Eint,V60a0: tp__ty_2Einteger_2Eint,V61a: $i] :
( ( mem @ V61a @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V61a ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V60a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V59a1 ) ) ) ) )
& ! [V62a_27: tp__ty_2Einteger_2Eint,V63a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V63a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V62a_27 ) ) ) )
& ! [V64a_27: tp__ty_2Einteger_2Eint,V65a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V65a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V64a_27 ) ) ) )
& ! [V66a1: tp__ty_2Einteger_2Eint,V67a0: tp__ty_2Einteger_2Eint,V68a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V68a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V67a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V66a1 ) ) ) )
& ! [V69a_27: tp__ty_2Einteger_2Eint,V70a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V70a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V69a_27 ) ) ) )
& ! [V71a1: tp__ty_2Einteger_2Eint,V72a0: tp__ty_2Einteger_2Eint,V73a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V73a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V72a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V71a1 ) ) ) )
& ! [V74a1: tp__ty_2Einteger_2Eint,V75a0: tp__ty_2Einteger_2Eint,V76a: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V76a ) ) )
!= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V75a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V74a1 ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__nchotomy,axiom,
! [V0dd: tp__ty_2EDeepSyntax_2Edeep__form] :
( ? [V1d: tp__ty_2EDeepSyntax_2Edeep__form,V2d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2d0 ) ) ) )
| ? [V3d: tp__ty_2EDeepSyntax_2Edeep__form,V4d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4d0 ) ) ) )
| ? [V5d: tp__ty_2EDeepSyntax_2Edeep__form] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5d ) ) ) )
| ? [V6b: $i] :
( ( mem @ V6b @ bool )
& ( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V6b ) ) ) )
| ? [V7i: tp__ty_2Einteger_2Eint] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V7i ) ) ) )
| ? [V8i: tp__ty_2Einteger_2Eint] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V8i ) ) ) )
| ? [V9i: tp__ty_2Einteger_2Eint] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V9i ) ) ) )
| ? [V10i: tp__ty_2Einteger_2Eint,V11i0: tp__ty_2Einteger_2Eint] :
( V0dd
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V10i ) ) @ ( inj__ty_2Einteger_2Eint @ V11i0 ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__Axiom,axiom,
! [A_27a: del,V0f0: $i] :
( ( mem @ V0f0 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) )
=> ! [V1f1: $i] :
( ( mem @ V1f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) )
=> ! [V2f2: $i] :
( ( mem @ V2f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V3f3: $i] :
( ( mem @ V3f3 @ ( arr @ bool @ A_27a ) )
=> ! [V4f4: $i] :
( ( mem @ V4f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V5f5: $i] :
( ( mem @ V5f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V6f6: $i] :
( ( mem @ V6f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V7f7: $i] :
( ( mem @ V7f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ? [V8fn: $i] :
( ( mem @ V8fn @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
& ! [V9a0: tp__ty_2EDeepSyntax_2Edeep__form,V10a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ V8fn @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V9a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a1 ) ) )
= ( ap @ ( ap @ ( ap @ ( ap @ V0f0 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V9a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a1 ) ) @ ( ap @ V8fn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V9a0 ) ) ) @ ( ap @ V8fn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10a1 ) ) ) )
& ! [V11a0: tp__ty_2EDeepSyntax_2Edeep__form,V12a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ V8fn @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12a1 ) ) )
= ( ap @ ( ap @ ( ap @ ( ap @ V1f1 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12a1 ) ) @ ( ap @ V8fn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11a0 ) ) ) @ ( ap @ V8fn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12a1 ) ) ) )
& ! [V13a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ V8fn @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13a ) ) )
= ( ap @ ( ap @ V2f2 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13a ) ) @ ( ap @ V8fn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13a ) ) ) )
& ! [V14a: $i] :
( ( mem @ V14a @ bool )
=> ( ( ap @ V8fn @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V14a ) )
= ( ap @ V3f3 @ V14a ) ) )
& ! [V15a: tp__ty_2Einteger_2Eint] :
( ( ap @ V8fn @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V15a ) ) )
= ( ap @ V4f4 @ ( inj__ty_2Einteger_2Eint @ V15a ) ) )
& ! [V16a: tp__ty_2Einteger_2Eint] :
( ( ap @ V8fn @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V16a ) ) )
= ( ap @ V5f5 @ ( inj__ty_2Einteger_2Eint @ V16a ) ) )
& ! [V17a: tp__ty_2Einteger_2Eint] :
( ( ap @ V8fn @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V17a ) ) )
= ( ap @ V6f6 @ ( inj__ty_2Einteger_2Eint @ V17a ) ) )
& ! [V18a0: tp__ty_2Einteger_2Eint,V19a1: tp__ty_2Einteger_2Eint] :
( ( ap @ V8fn @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V18a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V19a1 ) ) )
= ( ap @ ( ap @ V7f7 @ ( inj__ty_2Einteger_2Eint @ V18a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V19a1 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__induction,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ bool ) )
=> ( ( ! [V1d: tp__ty_2EDeepSyntax_2Edeep__form,V2d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1d ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2d0 ) ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2d0 ) ) ) ) )
& ! [V3d: tp__ty_2EDeepSyntax_2Edeep__form,V4d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3d ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4d0 ) ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4d0 ) ) ) ) )
& ! [V5d: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5d ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5d ) ) ) ) )
& ! [V6b: $i] :
( ( mem @ V6b @ bool )
=> ( p @ ( ap @ V0P @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V6b ) ) ) )
& ! [V7i: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ V0P @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V7i ) ) ) )
& ! [V8i: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ V0P @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V8i ) ) ) )
& ! [V9i: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ V0P @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V9i ) ) ) )
& ! [V10i: tp__ty_2Einteger_2Eint,V11i0: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V10i ) ) @ ( inj__ty_2Einteger_2Eint @ V11i0 ) ) ) ) )
=> ! [V12d: tp__ty_2EDeepSyntax_2Edeep__form] : ( p @ ( ap @ V0P @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12d ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__case__cong,axiom,
! [A_27a: del,V0f_27: $i] :
( ( mem @ V0f_27 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V1f1_27: $i] :
( ( mem @ V1f1_27 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V2f2_27: $i] :
( ( mem @ V2f2_27 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V3f3_27: $i] :
( ( mem @ V3f3_27 @ ( arr @ bool @ A_27a ) )
=> ! [V4f4_27: $i] :
( ( mem @ V4f4_27 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V5f5_27: $i] :
( ( mem @ V5f5_27 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V6f6_27: $i] :
( ( mem @ V6f6_27 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V7f7_27: $i] :
( ( mem @ V7f7_27 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ! [V8M: tp__ty_2EDeepSyntax_2Edeep__form,V9M_27: tp__ty_2EDeepSyntax_2Edeep__form,V10f: $i] :
( ( mem @ V10f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V11f1: $i] :
( ( mem @ V11f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V12f2: $i] :
( ( mem @ V12f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V13f3: $i] :
( ( mem @ V13f3 @ ( arr @ bool @ A_27a ) )
=> ! [V14f4: $i] :
( ( mem @ V14f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V15f5: $i] :
( ( mem @ V15f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V16f6: $i] :
( ( mem @ V16f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V17f7: $i] :
( ( mem @ V17f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ( ( ( V8M = V9M_27 )
& ! [V18a0: tp__ty_2EDeepSyntax_2Edeep__form,V19a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V18a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V19a1 ) ) ) )
=> ( ( ap @ ( ap @ V10f @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V18a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V19a1 ) )
= ( ap @ ( ap @ V0f_27 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V18a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V19a1 ) ) ) )
& ! [V20a0: tp__ty_2EDeepSyntax_2Edeep__form,V21a1: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V21a1 ) ) ) )
=> ( ( ap @ ( ap @ V11f1 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V21a1 ) )
= ( ap @ ( ap @ V1f1_27 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V20a0 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V21a1 ) ) ) )
& ! [V22a: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V22a ) ) ) )
=> ( ( ap @ V12f2 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V22a ) )
= ( ap @ V2f2_27 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V22a ) ) ) )
& ! [V23a: $i] :
( ( mem @ V23a @ bool )
=> ( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V23a ) ) )
=> ( ( ap @ V13f3 @ V23a )
= ( ap @ V3f3_27 @ V23a ) ) ) )
& ! [V24a: tp__ty_2Einteger_2Eint] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V24a ) ) ) )
=> ( ( ap @ V14f4 @ ( inj__ty_2Einteger_2Eint @ V24a ) )
= ( ap @ V4f4_27 @ ( inj__ty_2Einteger_2Eint @ V24a ) ) ) )
& ! [V25a: tp__ty_2Einteger_2Eint] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V25a ) ) ) )
=> ( ( ap @ V15f5 @ ( inj__ty_2Einteger_2Eint @ V25a ) )
= ( ap @ V5f5_27 @ ( inj__ty_2Einteger_2Eint @ V25a ) ) ) )
& ! [V26a: tp__ty_2Einteger_2Eint] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V26a ) ) ) )
=> ( ( ap @ V16f6 @ ( inj__ty_2Einteger_2Eint @ V26a ) )
= ( ap @ V6f6_27 @ ( inj__ty_2Einteger_2Eint @ V26a ) ) ) )
& ! [V27a0: tp__ty_2Einteger_2Eint,V28a1: tp__ty_2Einteger_2Eint] :
( ( V9M_27
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V27a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V28a1 ) ) ) )
=> ( ( ap @ ( ap @ V17f7 @ ( inj__ty_2Einteger_2Eint @ V27a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V28a1 ) )
= ( ap @ ( ap @ V7f7_27 @ ( inj__ty_2Einteger_2Eint @ V27a0 ) ) @ ( inj__ty_2Einteger_2Eint @ V28a1 ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V8M ) ) @ V10f ) @ V11f1 ) @ V12f2 ) @ V13f3 ) @ V14f4 ) @ V15f5 ) @ V16f6 ) @ V17f7 )
= ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V9M_27 ) ) @ V0f_27 ) @ V1f1_27 ) @ V2f2_27 ) @ V3f3_27 ) @ V4f4_27 ) @ V5f5_27 ) @ V6f6_27 ) @ V7f7_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Edeep__form__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2EDeepSyntax_2Edeep__form,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V2f1: $i] :
( ( mem @ V2f1 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) ) )
=> ! [V3f2: $i] :
( ( mem @ V3f2 @ ( arr @ ty_2EDeepSyntax_2Edeep__form @ A_27a ) )
=> ! [V4f3: $i] :
( ( mem @ V4f3 @ ( arr @ bool @ A_27a ) )
=> ! [V5f4: $i] :
( ( mem @ V5f4 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V6f5: $i] :
( ( mem @ V6f5 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V7f6: $i] :
( ( mem @ V7f6 @ ( arr @ ty_2Einteger_2Eint @ A_27a ) )
=> ! [V8f7: $i] :
( ( mem @ V8f7 @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ A_27a ) ) )
=> ! [V9v: $i] :
( ( mem @ V9v @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDeepSyntax_2Edeep__form__CASE @ A_27a ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0x ) ) @ V1f ) @ V2f1 ) @ V3f2 ) @ V4f3 ) @ V5f4 ) @ V6f5 ) @ V7f6 ) @ V8f7 )
= V9v )
<=> ( ? [V10d: tp__ty_2EDeepSyntax_2Edeep__form,V11d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11d0 ) ) ) )
& ( ( ap @ ( ap @ V1f @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V10d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V11d0 ) )
= V9v ) )
| ? [V12d: tp__ty_2EDeepSyntax_2Edeep__form,V13d0: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13d0 ) ) ) )
& ( ( ap @ ( ap @ V2f1 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V12d ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V13d0 ) )
= V9v ) )
| ? [V14d: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V14d ) ) ) )
& ( ( ap @ V3f2 @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V14d ) )
= V9v ) )
| ? [V15b: $i] :
( ( mem @ V15b @ bool )
& ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V15b ) ) )
& ( ( ap @ V4f3 @ V15b )
= V9v ) )
| ? [V16i: tp__ty_2Einteger_2Eint] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V16i ) ) ) )
& ( ( ap @ V5f4 @ ( inj__ty_2Einteger_2Eint @ V16i ) )
= V9v ) )
| ? [V17i: tp__ty_2Einteger_2Eint] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V17i ) ) ) )
& ( ( ap @ V6f5 @ ( inj__ty_2Einteger_2Eint @ V17i ) )
= V9v ) )
| ? [V18i: tp__ty_2Einteger_2Eint] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V18i ) ) ) )
& ( ( ap @ V7f6 @ ( inj__ty_2Einteger_2Eint @ V18i ) )
= V9v ) )
| ? [V19i: tp__ty_2Einteger_2Eint,V20i0: tp__ty_2Einteger_2Eint] :
( ( V0x
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V19i ) ) @ ( inj__ty_2Einteger_2Eint @ V20i0 ) ) ) )
& ( ( ap @ ( ap @ V8f7 @ ( inj__ty_2Einteger_2Eint @ V19i ) ) @ ( inj__ty_2Einteger_2Eint @ V20i0 ) )
= V9v ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Eeval__form__def,axiom,
( ! [V0f1: tp__ty_2EDeepSyntax_2Edeep__form,V1f2: tp__ty_2EDeepSyntax_2Edeep__form,V2x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) ) ) )
& ! [V3f1: tp__ty_2EDeepSyntax_2Edeep__form,V4f2: tp__ty_2EDeepSyntax_2Edeep__form,V5x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5x ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f1 ) ) @ ( inj__ty_2Einteger_2Eint @ V5x ) ) )
| ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f2 ) ) @ ( inj__ty_2Einteger_2Eint @ V5x ) ) ) ) )
& ! [V6f: tp__ty_2EDeepSyntax_2Edeep__form,V7x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V7x ) ) )
<=> ~ ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6f ) ) @ ( inj__ty_2Einteger_2Eint @ V7x ) ) ) )
& ! [V8b: $i] :
( ( mem @ V8b @ bool )
=> ! [V9x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V8b ) ) @ ( inj__ty_2Einteger_2Eint @ V9x ) ) )
<=> ( p @ V8b ) ) )
& ! [V10i: tp__ty_2Einteger_2Eint,V11x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V10i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V11x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V11x ) ) @ ( inj__ty_2Einteger_2Eint @ V10i ) ) ) )
& ! [V12i: tp__ty_2Einteger_2Eint,V13x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V12i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V13x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V12i ) ) @ ( inj__ty_2Einteger_2Eint @ V13x ) ) ) )
& ! [V14i: tp__ty_2Einteger_2Eint,V15x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V14i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V15x ) ) )
<=> ( V15x = V14i ) )
& ! [V16i1: tp__ty_2Einteger_2Eint,V17i2: tp__ty_2Einteger_2Eint,V18x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V16i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V17i2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V18x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V16i1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V18x ) ) @ ( inj__ty_2Einteger_2Eint @ V17i2 ) ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Eneginf__def,axiom,
( ! [V0f1: tp__ty_2EDeepSyntax_2Edeep__form,V1f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) ) @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) ) )
& ! [V2f1: tp__ty_2EDeepSyntax_2Edeep__form,V3f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f1 ) ) ) @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f2 ) ) ) ) )
& ! [V4f: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ! [V5b: $i] :
( ( mem @ V5b @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5b ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5b ) ) ) )
& ! [V6i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2ET ) ) )
& ! [V7i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V7i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) ) )
& ! [V8i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V8i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) ) )
& ! [V9i1: tp__ty_2Einteger_2Eint,V10i2: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V9i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V10i2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V9i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V10i2 ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Eposinf__def,axiom,
( ! [V0f1: tp__ty_2EDeepSyntax_2Edeep__form,V1f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) ) @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) ) )
& ! [V2f1: tp__ty_2EDeepSyntax_2Edeep__form,V3f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f1 ) ) ) @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f2 ) ) ) ) )
& ! [V4f: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2ENegn @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ! [V5b: $i] :
( ( mem @ V5b @ bool )
=> ( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5b ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5b ) ) ) )
& ! [V6i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) ) )
& ! [V7i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V7i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2ET ) ) )
& ! [V8i: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V8i ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ c_2Ebool_2EF ) ) )
& ! [V9i1: tp__ty_2Einteger_2Eint,V10i2: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V9i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V10i2 ) ) ) )
= ( surj__ty_2EDeepSyntax_2Edeep__form @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V9i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V10i2 ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eneginf__ok,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form] :
? [V1y: tp__ty_2Einteger_2Eint] :
! [V2x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V2x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eposinf__ok,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form] :
? [V1y: tp__ty_2Einteger_2Eint] :
! [V2x: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V1y ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2Ealldivide__def,axiom,
( ! [V0f1: tp__ty_2EDeepSyntax_2Edeep__form,V1f2: tp__ty_2EDeepSyntax_2Edeep__form,V2d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2d ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f1 ) ) @ ( inj__ty_2Einteger_2Eint @ V2d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f2 ) ) @ ( inj__ty_2Einteger_2Eint @ V2d ) ) ) ) )
& ! [V3f1: tp__ty_2EDeepSyntax_2Edeep__form,V4f2: tp__ty_2EDeepSyntax_2Edeep__form,V5d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5d ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V3f1 ) ) @ ( inj__ty_2Einteger_2Eint @ V5d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f2 ) ) @ ( inj__ty_2Einteger_2Eint @ V5d ) ) ) ) )
& ! [V6f: tp__ty_2EDeepSyntax_2Edeep__form,V7d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V7d ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V6f ) ) @ ( inj__ty_2Einteger_2Eint @ V7d ) ) ) )
& ! [V8b: $i] :
( ( mem @ V8b @ bool )
=> ! [V9d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V8b ) ) @ ( inj__ty_2Einteger_2Eint @ V9d ) ) )
<=> $true ) )
& ! [V10i: tp__ty_2Einteger_2Eint,V11d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V10i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V11d ) ) )
<=> $true )
& ! [V12i: tp__ty_2Einteger_2Eint,V13d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V12i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V13d ) ) )
<=> $true )
& ! [V14i: tp__ty_2Einteger_2Eint,V15d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V14i ) ) ) @ ( inj__ty_2Einteger_2Eint @ V15d ) ) )
<=> $true )
& ! [V16i1: tp__ty_2Einteger_2Eint,V17i2: tp__ty_2Einteger_2Eint,V18d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V16i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V17i2 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V18d ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V16i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V18d ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eadd__d__neginf,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1x: tp__ty_2Einteger_2Eint,V2y: tp__ty_2Einteger_2Eint,V3d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V3d ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( inj__ty_2Einteger_2Eint @ V2y ) ) @ ( inj__ty_2Einteger_2Eint @ V3d ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eadd__d__posinf,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1x: tp__ty_2Einteger_2Eint,V2y: tp__ty_2Einteger_2Eint,V3d: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V3d ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1x ) ) )
<=> ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V1x ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( inj__ty_2Einteger_2Eint @ V2y ) ) @ ( inj__ty_2Einteger_2Eint @ V3d ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eneginf__disj1__implies__exoriginal,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint,V2i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V2i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2i ) ) ) )
=> ? [V3x: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V3x ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eposinf__disj1__implies__exoriginal,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint,V2i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V2i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V2i ) ) ) )
=> ? [V3x: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V3x ) ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2EAset__def,axiom,
( ! [V0pos: $i] :
( ( mem @ V0pos @ bool )
=> ! [V1f1: tp__ty_2EDeepSyntax_2Edeep__form,V2f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ! [V3pos: $i] :
( ( mem @ V3pos @ bool )
=> ! [V4f1: tp__ty_2EDeepSyntax_2Edeep__form,V5f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V3pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5f2 ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V3pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f1 ) ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V3pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5f2 ) ) ) ) )
& ! [V6pos: $i] :
( ( mem @ V6pos @ bool )
=> ! [V7f: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V6pos ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7f ) ) )
= ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ ( ap @ c_2Ebool_2E_7E @ V6pos ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7f ) ) ) )
& ! [V8pos: $i] :
( ( mem @ V8pos @ bool )
=> ! [V9b: $i] :
( ( mem @ V9b @ bool )
=> ( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V8pos ) @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V9b ) )
= ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) )
& ! [V10pos: $i] :
( ( mem @ V10pos @ bool )
=> ! [V11i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V10pos ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V11i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V10pos ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V11i ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) )
& ! [V12pos: $i] :
( ( mem @ V12pos @ bool )
=> ! [V13i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V12pos ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V13i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V12pos ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V13i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) )
& ! [V14pos: $i] :
( ( mem @ V14pos @ bool )
=> ! [V15i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V14pos ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V15i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V14pos ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V15i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V15i ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) )
& ! [V16pos: $i] :
( ( mem @ V16pos @ bool )
=> ! [V17i1: tp__ty_2Einteger_2Eint,V18i2: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V16pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V17i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V18i2 ) ) )
= ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) ).
thf(ax_thm_2EDeepSyntax_2EBset__def,axiom,
( ! [V0pos: $i] :
( ( mem @ V0pos @ bool )
=> ! [V1f1: tp__ty_2EDeepSyntax_2Edeep__form,V2f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ! [V3pos: $i] :
( ( mem @ V3pos @ bool )
=> ! [V4f1: tp__ty_2EDeepSyntax_2Edeep__form,V5f2: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V3pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5f2 ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V3pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f1 ) ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V3pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V5f2 ) ) ) ) )
& ! [V6pos: $i] :
( ( mem @ V6pos @ bool )
=> ! [V7f: tp__ty_2EDeepSyntax_2Edeep__form] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V6pos ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7f ) ) )
= ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ ( ap @ c_2Ebool_2E_7E @ V6pos ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V7f ) ) ) )
& ! [V8pos: $i] :
( ( mem @ V8pos @ bool )
=> ! [V9b: $i] :
( ( mem @ V9b @ bool )
=> ( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V8pos ) @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V9b ) )
= ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) )
& ! [V10pos: $i] :
( ( mem @ V10pos @ bool )
=> ! [V11i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V10pos ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V11i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V10pos ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V11i ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) )
& ! [V12pos: $i] :
( ( mem @ V12pos @ bool )
=> ! [V13i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V12pos ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V13i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V12pos ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V13i ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) )
& ! [V14pos: $i] :
( ( mem @ V14pos @ bool )
=> ! [V15i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V14pos ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V15i ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Einteger_2Eint @ bool ) ) @ V14pos ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V15i ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V15i ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) )
& ! [V16pos: $i] :
( ( mem @ V16pos @ bool )
=> ! [V17i1: tp__ty_2Einteger_2Eint,V18i2: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V16pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V17i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V18i2 ) ) )
= ( c_2Epred__set_2EEMPTY @ ty_2Einteger_2Eint ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eneginf__exoriginal__implies__rhs,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint,V2x: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
=> ( ? [V3i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V3i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) )
| ? [V4j: tp__ty_2Einteger_2Eint,V5b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V4j ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V4j ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V5b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V5b ) ) @ ( inj__ty_2Einteger_2Eint @ V4j ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eposinf__exoriginal__implies__rhs,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint,V2x: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
=> ( ? [V3i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V3i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) )
| ? [V4j: tp__ty_2Einteger_2Eint,V5b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V4j ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V4j ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V5b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V5b ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V4j ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eneginf__exoriginal__eq__rhs,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) )
=> ( ? [V2x: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
<=> ( ? [V3i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V3i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eneginf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) )
| ? [V4b: tp__ty_2Einteger_2Eint,V5j: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V4b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V5j ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V4b ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Eposinf__exoriginal__eq__rhs,axiom,
! [V0f: tp__ty_2EDeepSyntax_2Edeep__form,V1d: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Ealldivide @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) )
=> ( ? [V2x: tp__ty_2Einteger_2Eint] : ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( inj__ty_2Einteger_2Eint @ V2x ) ) )
<=> ( ? [V3i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V3i ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( ap @ c_2EDeepSyntax_2Eposinf @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) @ ( inj__ty_2Einteger_2Eint @ V3i ) ) ) )
| ? [V4b: tp__ty_2Einteger_2Eint,V5j: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V4b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V5j ) ) @ ( inj__ty_2Einteger_2Eint @ V1d ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) )
& ( p @ ( ap @ ( ap @ c_2EDeepSyntax_2Eeval__form @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V0f ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V4b ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Einteger_2Eint @ V5j ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Ein__bset,axiom,
! [V0pos: $i] :
( ( mem @ V0pos @ bool )
=> ! [V1f1: tp__ty_2EDeepSyntax_2Edeep__form,V2f2: tp__ty_2EDeepSyntax_2Edeep__form,V3P: $i] :
( ( mem @ V3P @ ( arr @ ty_2Einteger_2Eint @ bool ) )
=> ! [V4f: tp__ty_2EDeepSyntax_2Edeep__form,V5b0: $i] :
( ( mem @ V5b0 @ bool )
=> ! [V6i: tp__ty_2Einteger_2Eint,V7i1: tp__ty_2Einteger_2Eint,V8i2: tp__ty_2Einteger_2Eint] :
( ( ? [V9b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V9b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V9b ) ) ) )
<=> ( ? [V10b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V10b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V10b ) ) ) )
| ? [V11b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V11b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V11b ) ) ) ) ) )
& ( ? [V12b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V12b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V12b ) ) ) )
<=> ( ? [V13b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V13b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V13b ) ) ) )
| ? [V14b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V14b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V14b ) ) ) ) ) )
& ( ? [V15b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V15b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V15b ) ) ) )
<=> ? [V16b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V16b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2EF ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V16b ) ) ) ) )
& ( ? [V17b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V17b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V17b ) ) ) )
<=> ? [V18b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V18b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V18b ) ) ) ) )
& ( ? [V19b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V19b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5b0 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V19b ) ) ) )
<=> $false )
& ( ? [V20b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V20b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V20b ) ) ) )
<=> $false )
& ( ? [V21b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V21b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V21b ) ) ) )
<=> ( p @ ( ap @ V3P @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V6i ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ? [V22b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V22b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V22b ) ) ) )
<=> ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
& ( ? [V23b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V23b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V23b ) ) ) )
<=> $false )
& ( ? [V24b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V24b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V24b ) ) ) )
<=> ( p @ ( ap @ V3P @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V6i ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
& ( ? [V25b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V25b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V25b ) ) ) )
<=> ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
& ( ? [V26b: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V26b ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EBset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V7i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V8i2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V26b ) ) ) )
<=> $false ) ) ) ) ) ).
thf(conj_thm_2EDeepSyntax_2Ein__aset,axiom,
! [V0pos: $i] :
( ( mem @ V0pos @ bool )
=> ! [V1f1: tp__ty_2EDeepSyntax_2Edeep__form,V2f2: tp__ty_2EDeepSyntax_2Edeep__form,V3P: $i] :
( ( mem @ V3P @ ( arr @ ty_2Einteger_2Eint @ bool ) )
=> ! [V4f: tp__ty_2EDeepSyntax_2Edeep__form,V5a0: $i] :
( ( mem @ V5a0 @ bool )
=> ! [V6i: tp__ty_2Einteger_2Eint,V7i1: tp__ty_2Einteger_2Eint,V8i2: tp__ty_2Einteger_2Eint] :
( ( ? [V9a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V9a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EConjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V9a ) ) ) )
<=> ( ? [V10a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V10a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V10a ) ) ) )
| ? [V11a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V11a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V11a ) ) ) ) ) )
& ( ? [V12a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V12a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EDisjn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V12a ) ) ) )
<=> ( ? [V13a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V13a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V1f1 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V13a ) ) ) )
| ? [V14a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V14a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V2f2 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V14a ) ) ) ) ) )
& ( ? [V15a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V15a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V15a ) ) ) )
<=> ? [V16a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V16a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2EF ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V16a ) ) ) ) )
& ( ? [V17a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V17a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ENegn @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V17a ) ) ) )
<=> ? [V18a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V18a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( inj__ty_2EDeepSyntax_2Edeep__form @ V4f ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V18a ) ) ) ) )
& ( ? [V19a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V19a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( ap @ c_2EDeepSyntax_2EUnrelatedBool @ V5a0 ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V19a ) ) ) )
<=> $false )
& ( ? [V20a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V20a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V20a ) ) ) )
<=> ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
& ( ? [V21a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V21a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ExLT @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V21a ) ) ) )
<=> $false )
& ( ? [V22a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V22a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V22a ) ) ) )
<=> $false )
& ( ? [V23a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V23a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ELTx @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V23a ) ) ) )
<=> ( p @ ( ap @ V3P @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V6i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ? [V24a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V24a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2ET ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V24a ) ) ) )
<=> ( p @ ( ap @ V3P @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V6i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( ? [V25a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V25a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ c_2Ebool_2EF ) @ ( ap @ c_2EDeepSyntax_2ExEQ @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V25a ) ) ) )
<=> ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V6i ) ) ) )
& ( ? [V26a: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Einteger_2Eint ) @ ( inj__ty_2Einteger_2Eint @ V26a ) ) @ ( ap @ ( ap @ c_2EDeepSyntax_2EAset @ V0pos ) @ ( ap @ ( ap @ c_2EDeepSyntax_2ExDivided @ ( inj__ty_2Einteger_2Eint @ V7i1 ) ) @ ( inj__ty_2Einteger_2Eint @ V8i2 ) ) ) ) )
& ( p @ ( ap @ V3P @ ( inj__ty_2Einteger_2Eint @ V26a ) ) ) )
<=> $false ) ) ) ) ) ).
%------------------------------------------------------------------------------