TPTP Problem File: ANA101^1.p
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% File : ANA101^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : SUM_SUB
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : SUM_SUB_.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 : 10 ( 2 unt; 6 typ; 0 def)
% Number of atoms : 6 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 0 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% Number of variables : 18 ( 3 ^; 13 !; 0 ?; 18 :)
% ( 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/FINITE',type,
'const/sets/FINITE':
!>[A: $tType] : ( ( A > $o ) > $o ) ).
thf('thf_const_const/realax/real_sub',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/realax/real_neg',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/realax/real_add',type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('thf_const_const/iterate/sum',type,
'const/iterate/sum':
!>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('thm/iterate/SUM_NEG_',axiom,
! [A: $tType,A0: A > 'type/realax/real',A1: A > $o] :
( ( 'const/iterate/sum' @ A @ A1
@ ^ [A2: A] : ( 'const/realax/real_neg' @ ( A0 @ A2 ) ) )
= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ A @ A1 @ A0 ) ) ) ).
thf('thm/iterate/SUM_ADD_',axiom,
! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
( ( 'const/sets/FINITE' @ A @ A2 )
=> ( ( 'const/iterate/sum' @ A @ A2
@ ^ [A3: A] : ( 'const/realax/real_add' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ) ).
thf('thm/realax/real_sub_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ A0 )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ A0 ) ) ) ).
thf('thm/iterate/SUM_SUB_',conjecture,
! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
( ( 'const/sets/FINITE' @ A @ A2 )
=> ( ( 'const/iterate/sum' @ A @ A2
@ ^ [A3: A] : ( 'const/realax/real_sub' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ) ).
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