TPTP Problem File: ITP002^5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP002^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Eoption_2EOPTION__MAP2__THM.p, 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 : thm_2Eoption_2EOPTION__MAP2__THM.p [Gau20]
% : HL400501^5.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 996 ( 56 unt; 178 typ; 0 def)
% Number of atoms : 9653 ( 376 equ; 0 cnn)
% Maximal formula atoms : 61 ( 11 avg)
% Number of connectives : 19420 ( 141 ~; 151 |; 479 &;16179 @)
% ( 356 <=>;2114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Number of types : 7 ( 5 usr)
% Number of type conns : 221 ( 221 >; 0 *; 0 +; 0 <<)
% Number of symbols : 192 ( 189 usr; 47 con; 0-4 aty)
% Number of variables : 2779 ( 145 ^;2540 !; 94 ?;2779 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
include('Axioms/ITP001/ITP002^5.ax').
include('Axioms/ITP001/ITP003^5.ax').
include('Axioms/ITP001/ITP004^5.ax').
include('Axioms/ITP001/ITP007^5.ax').
include('Axioms/ITP001/ITP006^5.ax').
include('Axioms/ITP001/ITP005^5.ax').
include('Axioms/ITP001/ITP008^5.ax').
include('Axioms/ITP001/ITP009^5.ax').
include('Axioms/ITP001/ITP010^5.ax').
include('Axioms/ITP001/ITP012^5.ax').
include('Axioms/ITP001/ITP011^5.ax').
%------------------------------------------------------------------------------
thf(tp_ty_2Eoption_2Eoption,type,
ty_2Eoption_2Eoption: del > del ).
thf(tp_c_2Eoption_2EIS__NONE,type,
c_2Eoption_2EIS__NONE: del > $i ).
thf(mem_c_2Eoption_2EIS__NONE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
thf(tp_c_2Eoption_2EIS__SOME,type,
c_2Eoption_2EIS__SOME: del > $i ).
thf(mem_c_2Eoption_2EIS__SOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
thf(tp_c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE: del > $i ).
thf(mem_c_2Eoption_2ENONE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ).
thf(tp_c_2Eoption_2EOPTION__ALL,type,
c_2Eoption_2EOPTION__ALL: del > $i ).
thf(mem_c_2Eoption_2EOPTION__ALL,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__APPLY,type,
c_2Eoption_2EOPTION__APPLY: del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__APPLY,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__APPLY @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( arr @ A_27b @ A_27a ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__BIND,type,
c_2Eoption_2EOPTION__BIND: del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__BIND,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__CHOICE,type,
c_2Eoption_2EOPTION__CHOICE: del > $i ).
thf(mem_c_2Eoption_2EOPTION__CHOICE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(stp_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: $i > tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone] :
( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) ) ).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) )
=> ( X
= ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__GUARD,type,
c_2Eoption_2EOPTION__GUARD: $i ).
thf(mem_c_2Eoption_2EOPTION__GUARD,axiom,
mem @ c_2Eoption_2EOPTION__GUARD @ ( arr @ bool @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) ) ).
thf(tp_c_2Eoption_2EOPTION__IGNORE__BIND,type,
c_2Eoption_2EOPTION__IGNORE__BIND: del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__IGNORE__BIND,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__JOIN,type,
c_2Eoption_2EOPTION__JOIN: del > $i ).
thf(mem_c_2Eoption_2EOPTION__JOIN,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__MAP,type,
c_2Eoption_2EOPTION__MAP: del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__MAP,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__MAP2,type,
c_2Eoption_2EOPTION__MAP2: del > del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__MAP2,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27c ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__MCOMP,type,
c_2Eoption_2EOPTION__MCOMP: del > del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__MCOMP,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eoption_2EOPTION__MCOMP @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTREL,type,
c_2Eoption_2EOPTREL: del > del > $i ).
thf(mem_c_2Eoption_2EOPTREL,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ bool ) ) ) ) ).
thf(tp_c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME: del > $i ).
thf(mem_c_2Eoption_2ESOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ESOME @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Eoption_2ETHE,type,
c_2Eoption_2ETHE: del > $i ).
thf(mem_c_2Eoption_2ETHE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ETHE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ) ).
thf(tp_c_2Eoption_2Eoption__ABS,type,
c_2Eoption_2Eoption__ABS: del > $i ).
thf(mem_c_2Eoption_2Eoption__ABS,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE: del > del > $i ).
thf(mem_c_2Eoption_2Eoption__CASE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) ) ) ) ).
thf(tp_c_2Eoption_2Eoption__REP,type,
c_2Eoption_2Eoption__REP: del > $i ).
thf(mem_c_2Eoption_2Eoption__REP,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Eoption_2Esome,type,
c_2Eoption_2Esome: del > $i ).
thf(mem_c_2Eoption_2Esome,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2Esome @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(ax_thm_2Eoption_2Eoption__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ( lam @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone )
@ ^ [V1x: $i] : c_2Ebool_2ET ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Eoption_2Eoption__REP__ABS__DEF,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( ( mem @ V0a @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ V0a ) )
= V0a ) )
& ! [V1r: $i] :
( ( mem @ V1r @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) )
=> ( ( p
@ ( ap
@ ( lam @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone )
@ ^ [V2x: $i] : c_2Ebool_2ET )
@ V1r ) )
<=> ( ( ap @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ V1r ) )
= V1r ) ) ) ) ).
thf(ax_thm_2Eoption_2ESOME__DEF,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
= ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ ty_2Eone_2Eone ) @ V0x ) ) ) ) ).
thf(ax_thm_2Eoption_2ENONE__DEF,axiom,
! [A_27a: del] :
( ( c_2Eoption_2ENONE @ A_27a )
= ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ ty_2Eone_2Eone ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) ) ).
thf(conj_thm_2Eoption_2Eoption__Axiom,axiom,
! [A_27a: del,A_27b: del,V0e: $i] :
( ( mem @ V0e @ A_27b )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ? [V2fn: $i] :
( ( mem @ V2fn @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b ) )
& ( ( ap @ V2fn @ ( c_2Eoption_2ENONE @ A_27a ) )
= V0e )
& ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( ap @ V2fn @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
= ( ap @ V1f @ V3x ) ) ) ) ) ) ).
thf(conj_thm_2Eoption_2Eoption__induction,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
& ! [V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1a ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
thf(conj_thm_2Eoption_2Eoption__nchotomy,axiom,
! [A_27a: del,V0opt: $i] :
( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( V0opt
= ( c_2Eoption_2ENONE @ A_27a ) )
| ? [V1x: $i] :
( ( mem @ V1x @ A_27a )
& ( V0opt
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) ) ) ) ).
thf(ax_thm_2Eoption_2Eoption__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ A_27b )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V0v ) @ V1f )
= V0v ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27b )
=> ! [V4f: $i] :
( ( mem @ V4f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) @ V3v ) @ V4f )
= ( ap @ V4f @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Eoption_2EFORALL__OPTION,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
=> ( ! [V1opt: $i] :
( ( mem @ V1opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( p @ ( ap @ V0P @ V1opt ) ) )
<=> ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ) ) ).
thf(conj_thm_2Eoption_2EEXISTS__OPTION,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
=> ( ? [V1opt: $i] :
( ( mem @ V1opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
& ( p @ ( ap @ V0P @ V1opt ) ) )
<=> ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
| ? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ) ) ).
thf(conj_thm_2Eoption_2ESOME__11,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1y ) )
<=> ( V0x = V1y ) ) ) ) ).
thf(conj_thm_2Eoption_2ENOT__NONE__SOME,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( c_2Eoption_2ENONE @ A_27a )
!= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) ) ).
thf(conj_thm_2Eoption_2ENOT__SOME__NONE,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
!= ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
thf(ax_thm_2Eoption_2EOPTION__MAP__DEF,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ ( ap @ V0f @ V1x ) ) ) ) )
& ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V2f ) @ ( c_2Eoption_2ENONE @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ).
thf(ax_thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
<=> $true ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $false ) ) ).
thf(ax_thm_2Eoption_2EIS__NONE__DEF,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
<=> $false ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $true ) ) ).
thf(ax_thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) )
= V0x ) ) ).
thf(ax_thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27b ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27c ) @ V2y ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Eoption_2ETHE @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27c ) @ V2y ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
thf(ax_thm_2Eoption_2EOPTION__JOIN__DEF,axiom,
! [A_27a: del] :
( ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ! [V0x: $i] :
( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0x ) )
= V0x ) ) ) ).
thf(conj_thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
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