TPTP Problem File: ANA129^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ANA129^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : POLYNOMIAL_FUNCTION_POW
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : POLYNOMIAL_FUNCTION_POW_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.4.0, 0.89 v7.3.0, 1.00 v7.0.0
% Syntax : Number of formulae : 16 ( 3 unt; 10 typ; 0 def)
% Number of atoms : 8 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 0 ~; 0 |; 2 &; 32 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 3 ^; 11 !; 0 ?; 14 :)
% 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_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/SUC',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
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/nums/num_INDUCTION_',axiom,
! [P: 'type/nums/num' > $o] :
( ( ( P @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
& ! [A: 'type/nums/num'] :
( ( P @ A )
=> ( P @ ( 'const/nums/SUC' @ A ) ) ) )
=> ! [A: 'type/nums/num'] : ( P @ A ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_MUL_',axiom,
! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ A )
& ( 'const/iterate/polynomial_function' @ A0 ) )
=> ( 'const/iterate/polynomial_function'
@ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
thf('thm/realax/real_pow_1',axiom,
! [A: 'type/realax/real',A0: 'type/nums/num'] :
( ( 'const/realax/real_pow' @ A @ ( 'const/nums/SUC' @ A0 ) )
= ( 'const/realax/real_mul' @ A @ ( 'const/realax/real_pow' @ A @ A0 ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_CONST_',axiom,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [A0: 'type/realax/real'] : 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/POLYNOMIAL_FUNCTION_POW_',conjecture,
! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/nums/num'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_pow' @ ( A @ A1 ) @ A0 ) ) ) ).
%------------------------------------------------------------------------------