## TPTP Problem File: SEV475^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV475^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : EXISTS_SUBSET_IMAGE_INJ
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : EXISTS_SUBSET_IMAGE_INJ_.p [Kal16]

% Status   : Theorem
% Rating   : 0.75 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% Syntax   : Number of formulae    :    7 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   80 (  10 equality;  57 variable)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :   57 (   0   ~;   0   |;   7   &;  48   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   24 (   0 sgn;  16   !;   3   ?;   0   ^)
%                                         (  24   :;   5  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_const_const/trivia/I',type,(
'const/trivia/I':
!>[A: \$tType] :
( A > A ) )).

thf('thf_const_const/sets/SUBSET',type,(
'const/sets/SUBSET':
!>[A: \$tType] :
( ( A > \$o ) > ( A > \$o ) > \$o ) )).

thf('thf_const_const/sets/IN',type,(
'const/sets/IN':
!>[A: \$tType] :
( A > ( A > \$o ) > \$o ) )).

thf('thf_const_const/sets/IMAGE',type,(
'const/sets/IMAGE':
!>[A: \$tType,B: \$tType] :
( ( A > B ) > ( A > \$o ) > B > \$o ) )).

thf('thm/trivia/I_THM_',axiom,(
! [A: \$tType,A0: A] :
( ( 'const/trivia/I' @ A @ A0 )
= A0 ) )).

thf('thm/sets/SUBSET_IMAGE_INJ_',axiom,(
! [B: \$tType,A: \$tType,A0: A > B,A1: B > \$o,A2: A > \$o] :
( ( 'const/sets/SUBSET' @ B @ A1 @ ( 'const/sets/IMAGE' @ A @ B @ A0 @ A2 ) )
= ( ? [A3: A > \$o] :
( ( 'const/sets/SUBSET' @ A @ A3 @ A2 )
& ! [A4: A,A5: A] :
( ( ( 'const/sets/IN' @ A @ A4 @ A3 )
& ( 'const/sets/IN' @ A @ A5 @ A3 ) )
=> ( ( ( A0 @ A4 )
= ( A0 @ A5 ) )
= ( A4 = A5 ) ) )
& ( A1
= ( 'const/sets/IMAGE' @ A @ B @ A0 @ A3 ) ) ) ) ) )).

thf('thm/sets/EXISTS_SUBSET_IMAGE_INJ_',conjecture,(
! [A: \$tType,A0: \$tType,P: ( A > \$o ) > \$o,A1: A0 > A,A2: A0 > \$o] :
( ( ? [A3: A > \$o] :
( ( 'const/sets/SUBSET' @ A @ A3 @ ( 'const/sets/IMAGE' @ A0 @ A @ A1 @ A2 ) )
& ( P @ A3 ) ) )
= ( ? [A3: A0 > \$o] :
( ( 'const/sets/SUBSET' @ A0 @ A3 @ A2 )
& ! [A4: A0,A5: A0] :
( ( ( 'const/sets/IN' @ A0 @ A4 @ A3 )
& ( 'const/sets/IN' @ A0 @ A5 @ A3 ) )
=> ( ( ( A1 @ A4 )
= ( A1 @ A5 ) )
= ( A4 = A5 ) ) )
& ( P @ ( 'const/sets/IMAGE' @ A0 @ A @ A1 @ A3 ) ) ) ) ) )).

%------------------------------------------------------------------------------
```