TPTP Problem File: ANA122^1.p
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% File : ANA122^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : POLYNOMIAL_FUNCTION_CONST
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : POLYNOMIAL_FUNCTION_CONST_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.2.0, 0.25 v7.1.0
% Syntax : Number of formulae : 16 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 9 ( 5 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 31 ( 0 ~; 0 |; 0 &; 31 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 12 ( 2 ^; 7 !; 2 ?; 12 :)
% ( 1 !>; 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/realax/real_pow',type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
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_mul',type,
'const/realax/real_mul': '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/BIT1',type,
'const/nums/BIT1': '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/polynomial_function',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf('thf_const_const/iterate/..',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf('thm/realarith/REAL_MUL_RID_',axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= A ) ).
thf('thm/realax/real_pow_0',axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ).
thf('thm/iterate/SUM_SING_NUMSEG_',axiom,
! [A: 'type/nums/num' > 'type/realax/real',A0: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A0 ) @ A )
= ( A @ A0 ) ) ).
thf('thm/iterate/polynomial_function_',axiom,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
= ( ? [A0: 'type/nums/num',A1: 'type/nums/num' > 'type/realax/real'] :
! [A2: 'type/realax/real'] :
( ( A @ A2 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ A0 )
@ ^ [A3: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( A1 @ A3 ) @ ( 'const/realax/real_pow' @ A2 @ A3 ) ) ) ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_CONST_',conjecture,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [A0: 'type/realax/real'] : A ) ).
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