:: YELLOW_2 semantic presentation
theorem Th1: :: YELLOW_2:1
theorem Th2: :: YELLOW_2:2
theorem Th3: :: YELLOW_2:3
theorem Th4: :: YELLOW_2:4
theorem Th5: :: YELLOW_2:5
theorem Th6: :: YELLOW_2:6
theorem Th7: :: YELLOW_2:7
theorem Th8: :: YELLOW_2:8
:: deftheorem Def1 defines <= YELLOW_2:def 1 :
for b
1 being
set for b
2 being
RelStr for b
3, b
4 being
Function of b
1,the
carrier of b
2 holds
( b
3 <= b
4 iff for b
5 being
set holds
not ( b
5 in b
1 & ( for b
6, b
7 being
Element of b
2 holds
not ( b
6 = b
3 . b
5 & b
7 = b
4 . b
5 & b
6 <= b
7 ) ) ) );
theorem Th9: :: YELLOW_2:9
canceled;
theorem Th10: :: YELLOW_2:10
:: deftheorem Def2 defines Image YELLOW_2:def 2 :
theorem Th11: :: YELLOW_2:11
theorem Th12: :: YELLOW_2:12
theorem Th13: :: YELLOW_2:13
theorem Th14: :: YELLOW_2:14
theorem Th15: :: YELLOW_2:15
theorem Th16: :: YELLOW_2:16
theorem Th17: :: YELLOW_2:17
theorem Th18: :: YELLOW_2:18
theorem Th19: :: YELLOW_2:19
theorem Th20: :: YELLOW_2:20
theorem Th21: :: YELLOW_2:21
theorem Th22: :: YELLOW_2:22
theorem Th23: :: YELLOW_2:23
theorem Th24: :: YELLOW_2:24
theorem Th25: :: YELLOW_2:25
theorem Th26: :: YELLOW_2:26
theorem Th27: :: YELLOW_2:27
theorem Th28: :: YELLOW_2:28
theorem Th29: :: YELLOW_2:29
theorem Th30: :: YELLOW_2:30
Lemma14:
for b1 being non empty Poset holds
( b1 is up-complete & b1 is /\-complete & b1 is upper-bounded implies b1 is non empty complete Poset )
theorem Th31: :: YELLOW_2:31
theorem Th32: :: YELLOW_2:32
theorem Th33: :: YELLOW_2:33
theorem Th34: :: YELLOW_2:34
theorem Th35: :: YELLOW_2:35
theorem Th36: :: YELLOW_2:36
theorem Th37: :: YELLOW_2:37
theorem Th38: :: YELLOW_2:38
theorem Th39: :: YELLOW_2:39
theorem Th40: :: YELLOW_2:40
theorem Th41: :: YELLOW_2:41
theorem Th42: :: YELLOW_2:42
theorem Th43: :: YELLOW_2:43
theorem Th44: :: YELLOW_2:44
theorem Th45: :: YELLOW_2:45
theorem Th46: :: YELLOW_2:46
theorem Th47: :: YELLOW_2:47
theorem Th48: :: YELLOW_2:48
theorem Th49: :: YELLOW_2:49
theorem Th50: :: YELLOW_2:50
:: deftheorem Def3 defines SupMap YELLOW_2:def 3 :
theorem Th51: :: YELLOW_2:51
theorem Th52: :: YELLOW_2:52
theorem Th53: :: YELLOW_2:53
:: deftheorem Def4 defines IdsMap YELLOW_2:def 4 :
theorem Th54: :: YELLOW_2:54
:: deftheorem Def5 defines \\/ YELLOW_2:def 5 :
:: deftheorem Def6 defines //\ YELLOW_2:def 6 :
theorem Th55: :: YELLOW_2:55
theorem Th56: :: YELLOW_2:56
theorem Th57: :: YELLOW_2:57