TPTP Problem File: ANA131^1.p
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% File : ANA131^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : POLYNOMIAL_FUNCTION_o
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : POLYNOMIAL_FUNCTION_o_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 11 ( 3 unt; 5 typ; 0 def)
% Number of atoms : 12 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 63 ( 0 ~; 0 |; 8 &; 48 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 1-6 aty)
% Number of variables : 30 ( 8 ^; 19 !; 0 ?; 30 :)
% ( 3 !>; 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_const_const/trivia/o',type,
'const/trivia/o':
!>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
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/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_INDUCT_',axiom,
! [P: ( 'type/realax/real' > 'type/realax/real' ) > $o] :
( ( ( P
@ ^ [A: 'type/realax/real'] : A )
& ! [A: 'type/realax/real'] :
( P
@ ^ [A0: 'type/realax/real'] : A )
& ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
( ( ( P @ A )
& ( P @ A0 ) )
=> ( P
@ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_add' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) )
& ! [A: 'type/realax/real' > 'type/realax/real',A0: 'type/realax/real' > 'type/realax/real'] :
( ( ( P @ A )
& ( P @ A0 ) )
=> ( P
@ ^ [A1: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ A1 ) @ ( A0 @ A1 ) ) ) ) )
=> ! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( P @ A ) ) ) ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_CONST_',axiom,
! [A: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [A0: 'type/realax/real'] : A ) ).
thf('thm/trivia/o_DEF_',axiom,
! [C: $tType,B: $tType,A: $tType,A0: B > C,A1: A > B] :
( ( 'const/trivia/o' @ B @ A @ C @ A0 @ A1 )
= ( ^ [A2: A] : ( A0 @ ( A1 @ A2 ) ) ) ) ).
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/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_o_',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' @ ( 'const/trivia/o' @ 'type/realax/real' @ 'type/realax/real' @ 'type/realax/real' @ A @ A0 ) ) ) ).
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