:: FINSEQ_8 semantic presentation
theorem Th1: :: FINSEQ_8:1
theorem Th2: :: FINSEQ_8:2
theorem Th3: :: FINSEQ_8:3
:: deftheorem Def1 defines smid FINSEQ_8:def 1 :
theorem Th4: :: FINSEQ_8:4
theorem Th5: :: FINSEQ_8:5
theorem Th6: :: FINSEQ_8:6
theorem Th7: :: FINSEQ_8:7
theorem Th8: :: FINSEQ_8:8
theorem Th9: :: FINSEQ_8:9
definition
let c
1 be non
empty set ;
let c
2, c
3 be
FinSequence of c
1;
func ovlpart c
2,c
3 -> FinSequence of a
1 means :
Def2:
:: FINSEQ_8:def 2
(
len a
4 <= len a
3 & a
4 = smid a
3,1,
(len a4) & a
4 = smid a
2,
(((len a2) -' (len a4)) + 1),
(len a2) & ( for b
1 being
Nat holds
( b
1 <= len a
3 &
smid a
3,1,b
1 = smid a
2,
(((len a2) -' b1) + 1),
(len a2) implies b
1 <= len a
4 ) ) );
existence
ex b1 being FinSequence of c1 st
( len b1 <= len c3 & b1 = smid c3,1,(len b1) & b1 = smid c2,(((len c2) -' (len b1)) + 1),(len c2) & ( for b2 being Nat holds
( b2 <= len c3 & smid c3,1,b2 = smid c2,(((len c2) -' b2) + 1),(len c2) implies b2 <= len b1 ) ) )
uniqueness
for b1, b2 being FinSequence of c1 holds
( len b1 <= len c3 & b1 = smid c3,1,(len b1) & b1 = smid c2,(((len c2) -' (len b1)) + 1),(len c2) & ( for b3 being Nat holds
( b3 <= len c3 & smid c3,1,b3 = smid c2,(((len c2) -' b3) + 1),(len c2) implies b3 <= len b1 ) ) & len b2 <= len c3 & b2 = smid c3,1,(len b2) & b2 = smid c2,(((len c2) -' (len b2)) + 1),(len c2) & ( for b3 being Nat holds
( b3 <= len c3 & smid c3,1,b3 = smid c2,(((len c2) -' b3) + 1),(len c2) implies b3 <= len b2 ) ) implies b1 = b2 )
end;
:: deftheorem Def2 defines ovlpart FINSEQ_8:def 2 :
for b
1 being non
empty set for b
2, b
3, b
4 being
FinSequence of b
1 holds
( b
4 = ovlpart b
2,b
3 iff (
len b
4 <= len b
3 & b
4 = smid b
3,1,
(len b4) & b
4 = smid b
2,
(((len b2) -' (len b4)) + 1),
(len b2) & ( for b
5 being
Nat holds
( b
5 <= len b
3 &
smid b
3,1,b
5 = smid b
2,
(((len b2) -' b5) + 1),
(len b2) implies b
5 <= len b
4 ) ) ) );
theorem Th10: :: FINSEQ_8:10
:: deftheorem Def3 defines ovlcon FINSEQ_8:def 3 :
theorem Th11: :: FINSEQ_8:11
:: deftheorem Def4 defines ovlldiff FINSEQ_8:def 4 :
:: deftheorem Def5 defines ovlrdiff FINSEQ_8:def 5 :
theorem Th12: :: FINSEQ_8:12
theorem Th13: :: FINSEQ_8:13
theorem Th14: :: FINSEQ_8:14
theorem Th15: :: FINSEQ_8:15
theorem Th16: :: FINSEQ_8:16
:: deftheorem Def6 defines separates_uniquely FINSEQ_8:def 6 :
theorem Th17: :: FINSEQ_8:17
:: deftheorem Def7 defines is_substring_of FINSEQ_8:def 7 :
theorem Th18: :: FINSEQ_8:18
theorem Th19: :: FINSEQ_8:19
theorem Th20: :: FINSEQ_8:20
:: deftheorem Def8 defines c= FINSEQ_8:def 8 :
theorem Th21: :: FINSEQ_8:21
:: deftheorem Def9 defines is_postposition_of FINSEQ_8:def 9 :
theorem Th22: :: FINSEQ_8:22
theorem Th23: :: FINSEQ_8:23
theorem Th24: :: FINSEQ_8:24
theorem Th25: :: FINSEQ_8:25
theorem Th26: :: FINSEQ_8:26
theorem Th27: :: FINSEQ_8:27
:: deftheorem Def10 defines instr FINSEQ_8:def 10 :
:: deftheorem Def11 defines addcr FINSEQ_8:def 11 :
:: deftheorem Def12 defines is_terminated_by FINSEQ_8:def 12 :
theorem Th28: :: FINSEQ_8:28