TPTP Problem File: SEV451^1.p
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% File : SEV451^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : UNION_UNIV_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : UNION_UNIV_1.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 8 ( 4 unt; 3 typ; 0 def)
% Number of atoms : 18 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 32 ( 0 ~; 1 |; 0 &; 31 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% Number of variables : 18 ( 0 ^; 15 !; 0 ?; 18 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_const_const/sets/UNIV',type,
'const/sets/UNIV':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/sets/UNION',type,
'const/sets/UNION':
!>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thm/sets/IN_UNIV_',axiom,
! [A: $tType,A0: A] : ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
thf('thm/sets/IN_',axiom,
! [A: $tType,P: A > $o,A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ P )
= ( P @ A0 ) ) ).
thf('thm/sets/IN_UNION_',axiom,
! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) )
= ( ( 'const/sets/IN' @ A @ A2 @ A0 )
| ( 'const/sets/IN' @ A @ A2 @ 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/UNION_UNIV_1',conjecture,
! [A: $tType,A0: A > $o] :
( ( 'const/sets/UNION' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) )
= ( 'const/sets/UNIV' @ A ) ) ).
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