TPTP Problem File: SEV482^1.p
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% File : SEV482^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : FORALL_IN_CROSS
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : FORALL_IN_CROSS_.p [Kal16]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% Syntax : Number of formulae : 7 ( 3 unt; 4 typ; 0 def)
% Number of atoms : 11 ( 3 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 62 ( 0 ~; 0 |; 2 &; 58 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 2-5 aty)
% Number of variables : 25 ( 0 ^; 20 !; 0 ?; 25 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/pair/prod',type,
'type/pair/prod': $tType > $tType > $tType ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/CROSS',type,
'const/sets/CROSS':
!>[A: $tType,A0: $tType] : ( ( A > $o ) > ( A0 > $o ) > ( 'type/pair/prod' @ A @ A0 ) > $o ) ).
thf('thf_const_const/pair/,',type,
'const/pair/,':
!>[A: $tType,B: $tType] : ( A > B > ( 'type/pair/prod' @ A @ B ) ) ).
thf('thm/sets/IN_CROSS_',axiom,
! [A: $tType,A0: $tType,A1: A,A2: A0,A3: A > $o,A4: A0 > $o] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) @ ( 'const/sets/CROSS' @ A @ A0 @ A3 @ A4 ) )
= ( ( 'const/sets/IN' @ A @ A1 @ A3 )
& ( 'const/sets/IN' @ A0 @ A2 @ A4 ) ) ) ).
thf('thm/pair/FORALL_PAIR_THM_',axiom,
! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o] :
( ( ! [A1: 'type/pair/prod' @ A @ A0] : ( P @ A1 ) )
= ( ! [A1: A,A2: A0] : ( P @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) ) ) ) ).
thf('thm/sets/FORALL_IN_CROSS_',conjecture,
! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o,A1: A > $o,A2: A0 > $o] :
( ( ! [A3: 'type/pair/prod' @ A @ A0] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ A3 @ ( 'const/sets/CROSS' @ A @ A0 @ A1 @ A2 ) )
=> ( P @ A3 ) ) )
= ( ! [A3: A,A4: A0] :
( ( ( 'const/sets/IN' @ A @ A3 @ A1 )
& ( 'const/sets/IN' @ A0 @ A4 @ A2 ) )
=> ( P @ ( 'const/pair/,' @ A @ A0 @ A3 @ A4 ) ) ) ) ) ).
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