TPTP Problem File: DAT266^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : DAT266^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : REPLICATE_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : REPLICATE_1.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 9 ( 1 unt; 7 typ; 0 def)
% Number of atoms : 3 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 0 ~; 0 |; 1 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 10 ( 0 ^; 7 !; 1 ?; 10 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_type_type/nums/num',type,
'type/nums/num': $tType ).
thf('thf_type_type/ind_types/list',type,
'type/ind_types/list': $tType > $tType ).
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/_0',type,
'const/nums/_0': 'type/nums/num' ).
thf('thf_const_const/lists/REPLICATE',type,
'const/lists/REPLICATE':
!>[A: $tType] : ( 'type/nums/num' > A > ( 'type/ind_types/list' @ A ) ) ).
thf('thf_const_const/ind_types/CONS',type,
'const/ind_types/CONS':
!>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
thf('thm/nums/num_RECURSION_',axiom,
! [A: $tType,A0: A,A1: A > 'type/nums/num' > A] :
? [A2: 'type/nums/num' > A] :
( ( ( A2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= A0 )
& ! [A3: 'type/nums/num'] :
( ( A2 @ ( 'const/nums/SUC' @ A3 ) )
= ( A1 @ ( A2 @ A3 ) @ A3 ) ) ) ).
thf('thm/lists/REPLICATE_1',conjecture,
! [A: $tType,A0: 'type/nums/num',A1: A] :
( ( 'const/lists/REPLICATE' @ A @ ( 'const/nums/SUC' @ A0 ) @ A1 )
= ( 'const/ind_types/CONS' @ A @ A1 @ ( 'const/lists/REPLICATE' @ A @ A0 @ A1 ) ) ) ).
%------------------------------------------------------------------------------