:: ALGSPEC1 semantic presentation
theorem Th1: :: ALGSPEC1:1
theorem Th2: :: ALGSPEC1:2
theorem Th3: :: ALGSPEC1:3
theorem Th4: :: ALGSPEC1:4
theorem Th5: :: ALGSPEC1:5
theorem Th6: :: ALGSPEC1:6
:: deftheorem Def1 defines -indexing ALGSPEC1:def 1 :
theorem Th7: :: ALGSPEC1:7
theorem Th8: :: ALGSPEC1:8
theorem Th9: :: ALGSPEC1:9
theorem Th10: :: ALGSPEC1:10
theorem Th11: :: ALGSPEC1:11
theorem Th12: :: ALGSPEC1:12
theorem Th13: :: ALGSPEC1:13
theorem Th14: :: ALGSPEC1:14
theorem Th15: :: ALGSPEC1:15
theorem Th16: :: ALGSPEC1:16
theorem Th17: :: ALGSPEC1:17
theorem Th18: :: ALGSPEC1:18
theorem Th19: :: ALGSPEC1:19
theorem Th20: :: ALGSPEC1:20
theorem Th21: :: ALGSPEC1:21
theorem Th22: :: ALGSPEC1:22
theorem Th23: :: ALGSPEC1:23
:: deftheorem Def2 defines rng-retract ALGSPEC1:def 2 :
theorem Th24: :: ALGSPEC1:24
theorem Th25: :: ALGSPEC1:25
theorem Th26: :: ALGSPEC1:26
theorem Th27: :: ALGSPEC1:27
theorem Th28: :: ALGSPEC1:28
theorem Th29: :: ALGSPEC1:29
:: deftheorem Def3 defines form_a_replacement_in ALGSPEC1:def 3 :
theorem Th30: :: ALGSPEC1:30
theorem Th31: :: ALGSPEC1:31
theorem Th32: :: ALGSPEC1:32
theorem Th33: :: ALGSPEC1:33
theorem Th34: :: ALGSPEC1:34
theorem Th35: :: ALGSPEC1:35
definition
let c
1 be non
empty non
void ManySortedSign ;
let c
2, c
3 be
Function;
assume E30:
c
2,c
3 form_a_replacement_in c
1
;
func c
1 with-replacement c
2,c
3 -> non
empty strict non
void ManySortedSign means :
Def4:
:: ALGSPEC1:def 4
( the
carrier of a
1 -indexing a
2,the
OperSymbols of a
1 -indexing a
3 form_morphism_between a
1,a
4 & the
carrier of a
4 = rng (the carrier of a1 -indexing a2) & the
OperSymbols of a
4 = rng (the OperSymbols of a1 -indexing a3) );
uniqueness
for b1, b2 being non empty strict non void ManySortedSign holds
( the carrier of c1 -indexing c2,the OperSymbols of c1 -indexing c3 form_morphism_between c1,b1 & the carrier of b1 = rng (the carrier of c1 -indexing c2) & the OperSymbols of b1 = rng (the OperSymbols of c1 -indexing c3) & the carrier of c1 -indexing c2,the OperSymbols of c1 -indexing c3 form_morphism_between c1,b2 & the carrier of b2 = rng (the carrier of c1 -indexing c2) & the OperSymbols of b2 = rng (the OperSymbols of c1 -indexing c3) implies b1 = b2 )
existence
ex b1 being non empty strict non void ManySortedSign st
( the carrier of c1 -indexing c2,the OperSymbols of c1 -indexing c3 form_morphism_between c1,b1 & the carrier of b1 = rng (the carrier of c1 -indexing c2) & the OperSymbols of b1 = rng (the OperSymbols of c1 -indexing c3) )
end;
:: deftheorem Def4 defines with-replacement ALGSPEC1:def 4 :
theorem Th36: :: ALGSPEC1:36
theorem Th37: :: ALGSPEC1:37
theorem Th38: :: ALGSPEC1:38
theorem Th39: :: ALGSPEC1:39
theorem Th40: :: ALGSPEC1:40
theorem Th41: :: ALGSPEC1:41
theorem Th42: :: ALGSPEC1:42
theorem Th43: :: ALGSPEC1:43
theorem Th44: :: ALGSPEC1:44
theorem Th45: :: ALGSPEC1:45
:: deftheorem Def5 defines Extension ALGSPEC1:def 5 :
theorem Th46: :: ALGSPEC1:46
canceled;
theorem Th47: :: ALGSPEC1:47
theorem Th48: :: ALGSPEC1:48
theorem Th49: :: ALGSPEC1:49
theorem Th50: :: ALGSPEC1:50
theorem Th51: :: ALGSPEC1:51
for b
1, b
2, b
3 being non
empty ManySortedSign for b
4, b
5, b
6, b
7 being
Function holds
( b
4 tolerates b
6 & b
4,b
5 form_morphism_between b
1,b
3 & b
6,b
7 form_morphism_between b
2,b
3 implies b
4 +* b
6,b
5 +* b
7 form_morphism_between b
1 +* b
2,b
3 )
theorem Th52: :: ALGSPEC1:52
theorem Th53: :: ALGSPEC1:53
theorem Th54: :: ALGSPEC1:54
theorem Th55: :: ALGSPEC1:55
theorem Th56: :: ALGSPEC1:56
:: deftheorem Def6 defines Algebra ALGSPEC1:def 6 :
:: deftheorem Def7 defines Algebra ALGSPEC1:def 7 :
theorem Th57: :: ALGSPEC1:57
theorem Th58: :: ALGSPEC1:58
theorem Th59: :: ALGSPEC1:59
theorem Th60: :: ALGSPEC1:60
theorem Th61: :: ALGSPEC1:61
theorem Th62: :: ALGSPEC1:62
theorem Th63: :: ALGSPEC1:63
theorem Th64: :: ALGSPEC1:64
theorem Th65: :: ALGSPEC1:65
theorem Th66: :: ALGSPEC1:66