TPTP Problem File: SEV490^1.p
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% File : SEV490^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : INJECTIVE_ON_PREIMAGE
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : INJECTIVE_ON_PREIMAGE_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.2.0, 0.75 v7.1.0
% Syntax : Number of formulae : 15 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 42 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 102 ( 1 ~; 1 |; 5 &; 93 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 0 con; 2-5 aty)
% Number of variables : 47 ( 3 ^; 32 !; 4 ?; 47 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_const_const/sets/SUBSET',type,
'const/sets/SUBSET':
!>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/SETSPEC',type,
'const/sets/SETSPEC':
!>[A: $tType] : ( A > $o > A > $o ) ).
thf('thf_const_const/sets/INSERT',type,
'const/sets/INSERT':
!>[A: $tType] : ( A > ( A > $o ) > A > $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('thf_const_const/sets/GSPEC',type,
'const/sets/GSPEC':
!>[A: $tType] : ( ( A > $o ) > A > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thm/sets/IN_',axiom,
! [A: $tType,P: A > $o,A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ P )
= ( P @ A0 ) ) ).
thf('thm/sets/IN_ELIM_THM_1',axiom,
! [A: $tType,A0: A > $o,A1: A] :
( ( 'const/sets/IN' @ A @ A1
@ ( 'const/sets/GSPEC' @ A
@ ^ [A2: A] :
? [A3: A] : ( 'const/sets/SETSPEC' @ A @ A2 @ ( A0 @ A3 ) @ A3 ) ) )
= ( A0 @ A1 ) ) ).
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/EXTENSION_',axiom,
! [A: $tType,A0: A > $o,A1: A > $o] :
( ( A0 = A1 )
= ( ! [A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ A0 )
= ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
thf('thm/sets/SUBSET_',axiom,
! [A: $tType,A0: A > $o,A1: A > $o] :
( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
= ( ! [A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ A0 )
=> ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
thf('thm/sets/NOT_IN_EMPTY_',axiom,
! [A: $tType,A0: A] :
~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
thf('thm/sets/IN_INSERT_',axiom,
! [A: $tType,A0: A,A1: A,A2: A > $o] :
( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
= ( ( A0 = A1 )
| ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) ).
thf('thm/sets/INJECTIVE_ON_PREIMAGE_',conjecture,
! [B: $tType,A: $tType,A0: A > B,A1: A > $o,A2: B > $o] :
( ( ! [A3: B > $o,A4: B > $o] :
( ( ( 'const/sets/SUBSET' @ B @ A3 @ A2 )
& ( 'const/sets/SUBSET' @ B @ A4 @ A2 )
& ( ( 'const/sets/GSPEC' @ A
@ ^ [A5: A] :
? [A6: A] :
( 'const/sets/SETSPEC' @ A @ A5
@ ( ( 'const/sets/IN' @ A @ A6 @ A1 )
& ( 'const/sets/IN' @ B @ ( A0 @ A6 ) @ A3 ) )
@ A6 ) )
= ( 'const/sets/GSPEC' @ A
@ ^ [A5: A] :
? [A6: A] :
( 'const/sets/SETSPEC' @ A @ A5
@ ( ( 'const/sets/IN' @ A @ A6 @ A1 )
& ( 'const/sets/IN' @ B @ ( A0 @ A6 ) @ A4 ) )
@ A6 ) ) ) )
=> ( A3 = A4 ) ) )
= ( 'const/sets/SUBSET' @ B @ A2 @ ( 'const/sets/IMAGE' @ A @ B @ A0 @ A1 ) ) ) ).
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