## TPTP Problem File: SEV465^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV465^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : FORALL_IN_IMAGE
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :    4 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   35 (   3 equality;  26 variable)
%            Maximal formula depth :   14 (  10 average)
%            Number of connectives :   27 (   0   ~;   0   |;   1   &;  24   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   16 (   0 sgn;  12   !;   1   ?;   0   ^)
%                                         (  16   :;   3  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
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/sets/IN_IMAGE_',axiom,(
! [B: \$tType,A: \$tType,A0: B,A1: A > \$o,A2: A > B] :
( ( 'const/sets/IN' @ B @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A1 ) )
= ( ? [A3: A] :
( ( A0
= ( A2 @ A3 ) )
& ( 'const/sets/IN' @ A @ A3 @ A1 ) ) ) ) )).

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

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