TPTP Problem File: SEV477^1.p
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% File : SEV477^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : FINREC_UNIQUE_LEMMA
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : FINREC_UNIQUE_LEMMA_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 16 ( 3 unt; 9 typ; 0 def)
% Number of atoms : 27 ( 13 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 116 ( 3 ~; 0 |; 7 &; 97 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 1 con; 0-7 aty)
% Number of variables : 52 ( 0 ^; 43 !; 3 ?; 52 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/nums/num',type,
'type/nums/num': $tType ).
thf('thf_const_const/trivia/I',type,
'const/trivia/I':
!>[A: $tType] : ( A > A ) ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/FINREC',type,
'const/sets/FINREC':
!>[A: $tType,B: $tType] : ( ( A > B > B ) > B > ( A > $o ) > B > 'type/nums/num' > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/sets/DELETE',type,
'const/sets/DELETE':
!>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
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('thm/nums/num_INDUCTION_',axiom,
! [P: 'type/nums/num' > $o] :
( ( ( P @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
& ! [A: 'type/nums/num'] :
( ( P @ A )
=> ( P @ ( 'const/nums/SUC' @ A ) ) ) )
=> ! [A: 'type/nums/num'] : ( P @ A ) ) ).
thf('thm/trivia/I_THM_',axiom,
! [A: $tType,A0: A] :
( ( 'const/trivia/I' @ A @ A0 )
= A0 ) ).
thf('thm/sets/FINREC_SUC_LEMMA_',axiom,
! [A: $tType,B: $tType,A0: A > B > B,A1: B] :
( ! [A2: A,A3: A,A4: B] :
( ( A2 != A3 )
=> ( ( A0 @ A2 @ ( A0 @ A3 @ A4 ) )
= ( A0 @ A3 @ ( A0 @ A2 @ A4 ) ) ) )
=> ! [A2: 'type/nums/num',A3: A > $o,A4: B] :
( ( 'const/sets/FINREC' @ A @ B @ A0 @ A1 @ A3 @ A4 @ ( 'const/nums/SUC' @ A2 ) )
=> ! [A5: A] :
( ( 'const/sets/IN' @ A @ A5 @ A3 )
=> ? [A6: B] :
( ( 'const/sets/FINREC' @ A @ B @ A0 @ A1 @ ( 'const/sets/DELETE' @ A @ A3 @ A5 ) @ A6 @ A2 )
& ( A4
= ( A0 @ A5 @ A6 ) ) ) ) ) ) ).
thf('thm/sets/FINREC_1',axiom,
! [A: $tType,B: $tType,A0: B,A1: A > $o,A2: 'type/nums/num',A3: B,A4: A > B > B] :
( ( 'const/sets/FINREC' @ A @ B @ A4 @ A0 @ A1 @ A3 @ ( 'const/nums/SUC' @ A2 ) )
= ( ? [A5: A,A6: B] :
( ( 'const/sets/IN' @ A @ A5 @ A1 )
& ( 'const/sets/FINREC' @ A @ B @ A4 @ A0 @ ( 'const/sets/DELETE' @ A @ A1 @ A5 ) @ A6 @ A2 )
& ( A3
= ( A4 @ A5 @ A6 ) ) ) ) ) ).
thf('thm/sets/NOT_IN_EMPTY_',axiom,
! [A: $tType,A0: A] :
~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
thf('thm/sets/FINREC_0',axiom,
! [A: $tType,B: $tType,A0: A > B > B,A1: A > $o,A2: B,A3: B] :
( ( 'const/sets/FINREC' @ A @ B @ A0 @ A3 @ A1 @ A2 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( ( A1
= ( 'const/sets/EMPTY' @ A ) )
& ( A2 = A3 ) ) ) ).
thf('thm/sets/FINREC_UNIQUE_LEMMA_',conjecture,
! [A: $tType,B: $tType,A0: A > B > B,A1: B] :
( ! [A2: A,A3: A,A4: B] :
( ( A2 != A3 )
=> ( ( A0 @ A2 @ ( A0 @ A3 @ A4 ) )
= ( A0 @ A3 @ ( A0 @ A2 @ A4 ) ) ) )
=> ! [A2: 'type/nums/num',A3: 'type/nums/num',A4: A > $o,A5: B,A6: B] :
( ( ( 'const/sets/FINREC' @ A @ B @ A0 @ A1 @ A4 @ A5 @ A2 )
& ( 'const/sets/FINREC' @ A @ B @ A0 @ A1 @ A4 @ A6 @ A3 ) )
=> ( ( A5 = A6 )
& ( A2 = A3 ) ) ) ) ).
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