TPTP Problem File: ANA092^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ANA092^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : REAL_LE_INF_EQ
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : REAL_LE_INF_EQ_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 8 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 20 ( 3 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 55 ( 2 ~; 0 |; 4 &; 40 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% Number of variables : 18 ( 0 ^; 14 !; 2 ?; 18 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_type_type/realax/real',type,
'type/realax/real': $tType ).
thf('thf_const_const/sets/inf',type,
'const/sets/inf': ( '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_le',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('thm/realax/REAL_LE_TRANS_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ A0 )
& ( 'const/realax/real_le' @ A0 @ A1 ) )
=> ( 'const/realax/real_le' @ A @ A1 ) ) ).
thf('thm/sets/INF_',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' @ A0 @ A1 ) ) )
=> ( ! [A0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
& ! [A0: 'type/realax/real'] :
( ! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A0 @ A1 ) )
=> ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
thf('thm/sets/REAL_LE_INF_EQ_',conjecture,
! [A: $tType,A0: 'type/realax/real',A1: 'type/realax/real' > $o,A2: A] :
( ( ( A1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [A3: 'type/realax/real'] :
! [A4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A4 @ A1 )
=> ( 'const/realax/real_le' @ A3 @ A4 ) ) )
=> ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A1 ) )
= ( ! [A3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A3 @ A1 )
=> ( 'const/realax/real_le' @ A0 @ A3 ) ) ) ) ) ).
%------------------------------------------------------------------------------