TPTP Problem File: SEV497^1.p
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% File : SEV497^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : ITERATE_CLAUSES
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : ITERATE_CLAUSES_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 12 ( 0 unt; 9 typ; 0 def)
% Number of atoms : 19 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 104 ( 0 ~; 0 |; 3 &; 96 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 14 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 0 con; 2-6 aty)
% Number of variables : 31 ( 0 ^; 20 !; 0 ?; 31 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_const_const/sets/INSERT',type,
'const/sets/INSERT':
!>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/FINITE',type,
'const/sets/FINITE':
!>[A: $tType] : ( ( A > $o ) > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/iterate/support',type,
'const/iterate/support':
!>[B: $tType,A: $tType] : ( ( B > B > B ) > ( A > B ) > ( A > $o ) > A > $o ) ).
thf('thf_const_const/iterate/neutral',type,
'const/iterate/neutral':
!>[A: $tType] : ( ( A > A > A ) > A ) ).
thf('thf_const_const/iterate/monoidal',type,
'const/iterate/monoidal':
!>[A: $tType] : ( ( A > A > A ) > $o ) ).
thf('thf_const_const/iterate/iterate',type,
'const/iterate/iterate':
!>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
thf('thf_const_const/class/COND',type,
'const/class/COND':
!>[A: $tType] : ( $o > A > A > A ) ).
thf('thm/iterate/ITERATE_CLAUSES_GEN_',axiom,
! [A: $tType,B: $tType,A0: B > B > B] :
( ( 'const/iterate/monoidal' @ B @ A0 )
=> ( ! [A1: A > B] :
( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/EMPTY' @ A ) @ A1 )
= ( 'const/iterate/neutral' @ B @ A0 ) )
& ! [A1: A > B,A2: A,A3: A > $o] :
( ( ( 'const/iterate/monoidal' @ B @ A0 )
& ( 'const/sets/FINITE' @ A @ ( 'const/iterate/support' @ B @ A @ A0 @ A1 @ A3 ) ) )
=> ( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/INSERT' @ A @ A2 @ A3 ) @ A1 )
= ( 'const/class/COND' @ B @ ( 'const/sets/IN' @ A @ A2 @ A3 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) @ ( A0 @ ( A1 @ A2 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) ) ) ) ) ) ) ).
thf('thm/iterate/FINITE_SUPPORT_',axiom,
! [A: $tType,A0: $tType,A1: A > A > A,A2: A0 > A,A3: A0 > $o] :
( ( 'const/sets/FINITE' @ A0 @ A3 )
=> ( 'const/sets/FINITE' @ A0 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) ) ) ).
thf('thm/iterate/ITERATE_CLAUSES_',conjecture,
! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
( ( 'const/iterate/monoidal' @ A1 @ A2 )
=> ( ! [A3: A > A1] :
( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
= ( 'const/iterate/neutral' @ A1 @ A2 ) )
& ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
( ( 'const/sets/FINITE' @ A0 @ A5 )
=> ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
= ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
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