TPTP Problem File: SEV507^1.p
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% File : SEV507^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : SUM_CLAUSES_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : SUM_CLAUSES_0.p [Kal16]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% Syntax : Number of formulae : 20 ( 4 unt; 15 typ; 1 def)
% Number of atoms : 12 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 0 ~; 0 |; 1 &; 56 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 1 con; 0-5 aty)
% Number of variables : 21 ( 0 ^; 11 !; 0 ?; 21 :)
% ( 10 !>; 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/INSERT',type,
'const/sets/INSERT':
!>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/FINITE',type,
'const/sets/FINITE':
!>[A: $tType] : ( ( A > $o ) > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/realax/real_of_num',type,
'const/realax/real_of_num': 'type/nums/num' > '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/nums/NUMERAL',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('thf_const_const/nums/_0',type,
'const/nums/_0': 'type/nums/num' ).
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/neutral',type,
'const/iterate/neutral':
!>[A: $tType] : ( ( A > A > A ) > A ) ).
thf('thf_const_const/iterate/monoidal',type,
'const/iterate/monoidal':
!>[A: $tType] : ( ( A > A > A ) > $o ) ).
thf('thf_const_const/iterate/iterate',type,
'const/iterate/iterate':
!>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
thf('thf_const_const/class/COND',type,
'const/class/COND':
!>[A: $tType] : ( $o > A > A > A ) ).
thf('thm/iterate/ITERATE_CLAUSES_',axiom,
! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
( ( 'const/iterate/monoidal' @ A1 @ A2 )
=> ( ! [A3: A > A1] :
( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
= ( 'const/iterate/neutral' @ A1 @ A2 ) )
& ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
( ( 'const/sets/FINITE' @ A0 @ A5 )
=> ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
= ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
thf('thm/iterate/sum_',definition,
! [A: $tType] :
( ( 'const/iterate/sum' @ A )
= ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
thf('thm/iterate/NEUTRAL_REAL_ADD_',axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
thf('thm/iterate/SUM_CLAUSES_0',conjecture,
! [A: $tType,A0: A > 'type/realax/real'] :
( ( 'const/iterate/sum' @ A @ ( 'const/sets/EMPTY' @ A ) @ A0 )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
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