TPTP Problem File: ANA106^1.p
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% File : ANA106^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : SUM_SUB_NUMSEG
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : SUM_SUB_NUMSEG_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 9 ( 1 unt; 6 typ; 0 def)
% Number of atoms : 8 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 43 ( 0 ~; 0 |; 0 &; 42 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% Number of variables : 14 ( 2 ^; 10 !; 0 ?; 14 :)
% ( 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_type_type/nums/num',type,
'type/nums/num': $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/iterate/sum',type,
'const/iterate/sum':
!>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('thf_const_const/iterate/..',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf('thm/iterate/SUM_SUB_',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_sub' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ) ).
thf('thm/iterate/FINITE_NUMSEG_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
thf('thm/iterate/SUM_SUB_NUMSEG_',conjecture,
! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num' > 'type/realax/real',A1: 'type/nums/num',A2: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 )
@ ^ [A3: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ A3 ) @ ( A0 @ A3 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A1 @ A2 ) @ A0 ) ) ) ).
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