TPTP Problem File: ANA077^1.p
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% File : ANA077^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : REAL_ABS_SUP_LE
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : REAL_ABS_SUP_LE_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 10 ( 1 unt; 7 typ; 0 def)
% Number of atoms : 16 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 44 ( 2 ~; 0 |; 5 &; 33 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% Number of variables : 11 ( 0 ^; 9 !; 0 ?; 11 :)
% ( 2 !>; 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/sets/sup',type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
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_neg',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/realax/real_le',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('thf_const_const/realax/real_abs',type,
'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
thf('thm/sets/REAL_SUP_BOUNDS_',axiom,
! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [A2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
=> ( ( 'const/realax/real_le' @ A0 @ A2 )
& ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
=> ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A1 ) ) ) ).
thf('thm/real/REAL_ABS_BOUNDS_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A ) @ A0 )
= ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ A0 ) @ A )
& ( 'const/realax/real_le' @ A @ A0 ) ) ) ).
thf('thm/sets/REAL_ABS_SUP_LE_',conjecture,
! [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' @ ( 'const/realax/real_abs' @ A1 ) @ A0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ A ) ) @ A0 ) ) ).
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