TPTP Problem File: DAT276^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : DAT276^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : MAP2_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : MAP2_1.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 9 ( 4 unt; 5 typ; 0 def)
% Number of atoms : 4 ( 4 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 71 ( 0 ~; 0 |; 0 &; 71 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 0 con; 1-6 aty)
% Number of variables : 27 ( 0 ^; 21 !; 0 ?; 27 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_type_type/ind_types/list',type,
'type/ind_types/list': $tType > $tType ).
thf('thf_const_const/lists/TL',type,
'const/lists/TL':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
thf('thf_const_const/lists/MAP2',type,
'const/lists/MAP2':
!>[A: $tType,A0: $tType,A1: $tType] : ( ( A > A0 > A1 ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > ( 'type/ind_types/list' @ A1 ) ) ).
thf('thf_const_const/lists/HD',type,
'const/lists/HD':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 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/lists/TL_',axiom,
! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
= A1 ) ).
thf('thm/lists/HD_',axiom,
! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
= A1 ) ).
thf('thm/lists/MAP2_DEF_1',axiom,
! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A0 > A1 > A,A4: 'type/ind_types/list' @ A0,A5: 'type/ind_types/list' @ A1] :
( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A4 ) @ A5 )
= ( 'const/ind_types/CONS' @ A @ ( A3 @ A2 @ ( 'const/lists/HD' @ A1 @ A5 ) ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ A4 @ ( 'const/lists/TL' @ A1 @ A5 ) ) ) ) ).
thf('thm/lists/MAP2_1',conjecture,
! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A1,A4: A0 > A1 > A,A5: 'type/ind_types/list' @ A0,A6: 'type/ind_types/list' @ A1] :
( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A5 ) @ ( 'const/ind_types/CONS' @ A1 @ A3 @ A6 ) )
= ( 'const/ind_types/CONS' @ A @ ( A4 @ A2 @ A3 ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ A5 @ A6 ) ) ) ).
%------------------------------------------------------------------------------