TPTP Problem File: ANA126^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ANA126^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : POLYNOMIAL_FUNCTION_NEG
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : POLYNOMIAL_FUNCTION_NEG_.p [Kal16]
% Status : Theorem
% Rating : 0.60 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0
% Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 8 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 0 ~; 0 |; 0 &; 22 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% SPC : TH0_THM_EQU_NAR
% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
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_of_num',type,
'const/realax/real_of_num': 'type/nums/num' > '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_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/polynomial_function',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf('thm/realax/REAL_MUL_LID_',axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ A )
= A ) ).
thf('thm/calc_int/REAL_MUL_LNEG_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ A ) @ A0 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ A @ A0 ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ A0 @ ( A @ A1 ) ) ) ) ).
thf('thm/calc_int/REAL_NEG_NEG_',axiom,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_neg' @ A ) )
= A ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',conjecture,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [A0: 'type/realax/real'] : ( 'const/realax/real_neg' @ ( A @ A0 ) ) )
= ( 'const/iterate/polynomial_function' @ A ) ) ).
%------------------------------------------------------------------------------