TPTP Problem File: ANA075^1.p
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% File : ANA075^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : REAL_SUP_LE_SUBSET
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : REAL_SUP_LE_SUBSET_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.2.0, 0.25 v7.1.0
% Syntax : Number of formulae : 15 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 34 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 86 ( 4 ~; 0 |; 5 &; 67 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% Number of variables : 32 ( 0 ^; 26 !; 2 ?; 32 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/realax/real',type,
'type/realax/real': $tType ).
thf('thf_const_const/trivia/I',type,
'const/trivia/I':
!>[A: $tType] : ( A > A ) ).
thf('thf_const_const/sets/sup',type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
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/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/realax/real_le',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('thm/sets/REAL_SUP_LE_',axiom,
! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A1 @ A0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ).
thf('thm/trivia/I_THM_',axiom,
! [A: $tType,A0: A] :
( ( 'const/trivia/I' @ A @ A0 )
= A0 ) ).
thf('thm/sets/IN_',axiom,
! [A: $tType,P: A > $o,A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ P )
= ( P @ A0 ) ) ).
thf('thm/sets/NOT_IN_EMPTY_',axiom,
! [A: $tType,A0: A] :
~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
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/SUP_',axiom,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [A0: 'type/realax/real'] :
! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A1 @ A0 ) ) )
=> ( ! [A0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
=> ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
& ! [A0: 'type/realax/real'] :
( ! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A1 @ A0 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
thf('thm/sets/REAL_SUP_LE_SUBSET_',conjecture,
! [A: 'type/realax/real' > $o,A0: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( 'const/sets/SUBSET' @ 'type/realax/real' @ A @ A0 )
& ? [A1: 'type/realax/real'] :
! [A2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A0 )
=> ( 'const/realax/real_le' @ A2 @ A1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ ( 'const/sets/sup' @ A0 ) ) ) ).
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