TPTP Problem File: ANA127^1.p
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% File : ANA127^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : POLYNOMIAL_FUNCTION_SUB
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : POLYNOMIAL_FUNCTION_SUB_.p [Kal16]
% Status : Theorem
% Rating : 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0
% Syntax : Number of formulae : 9 ( 2 unt; 5 typ; 0 def)
% Number of atoms : 10 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 27 ( 0 ~; 0 |; 2 &; 23 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 10 ( 3 ^; 7 !; 0 ?; 10 :)
% SPC : TH0_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_const_const/realax/real_sub',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > '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_add',type,
'const/realax/real_add': 'type/realax/real' > '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('thm/iterate/POLYNOMIAL_FUNCTION_ADD_',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_add' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_NEG_',axiom,
! [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 ) ) ).
thf('thm/realax/real_sub_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ A0 )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ A0 ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_SUB_',conjecture,
! [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_sub' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) ).
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