:: SYSREL semantic presentation
theorem Th1: :: SYSREL:1
canceled;
theorem Th2: :: SYSREL:2
canceled;
theorem Th3: :: SYSREL:3
canceled;
theorem Th4: :: SYSREL:4
canceled;
theorem Th5: :: SYSREL:5
canceled;
theorem Th6: :: SYSREL:6
canceled;
theorem Th7: :: SYSREL:7
canceled;
theorem Th8: :: SYSREL:8
canceled;
theorem Th9: :: SYSREL:9
canceled;
theorem Th10: :: SYSREL:10
canceled;
theorem Th11: :: SYSREL:11
canceled;
theorem Th12: :: SYSREL:12
theorem Th13: :: SYSREL:13
theorem Th14: :: SYSREL:14
theorem Th15: :: SYSREL:15
theorem Th16: :: SYSREL:16
theorem Th17: :: SYSREL:17
canceled;
theorem Th18: :: SYSREL:18
theorem Th19: :: SYSREL:19
canceled;
theorem Th20: :: SYSREL:20
theorem Th21: :: SYSREL:21
canceled;
theorem Th22: :: SYSREL:22
for
X,
Y,
x,
y being
set for
R being
Relation holds
( (
X misses Y &
R c= [:X,Y:] \/ [:Y,X:] &
[x,y] in R &
x in X implies ( not
x in Y & not
y in X &
y in Y ) ) & (
X misses Y &
R c= [:X,Y:] \/ [:Y,X:] &
[x,y] in R &
y in Y implies ( not
y in X & not
x in Y &
x in X ) ) & (
X misses Y &
R c= [:X,Y:] \/ [:Y,X:] &
[x,y] in R &
x in Y implies ( not
x in X & not
y in Y &
y in X ) ) & (
X misses Y &
R c= [:X,Y:] \/ [:Y,X:] &
[x,y] in R &
y in X implies ( not
x in X & not
y in Y &
x in Y ) ) )
theorem Th23: :: SYSREL:23
canceled;
theorem Th24: :: SYSREL:24
theorem Th25: :: SYSREL:25
theorem Th26: :: SYSREL:26
theorem Th27: :: SYSREL:27
Lemma37:
for X being set holds id X c= [:X,X:]
theorem Th28: :: SYSREL:28
canceled;
theorem Th29: :: SYSREL:29
theorem Th30: :: SYSREL:30
theorem Th31: :: SYSREL:31
theorem Th32: :: SYSREL:32
theorem Th33: :: SYSREL:33
theorem Th34: :: SYSREL:34
theorem Th35: :: SYSREL:35
theorem Th36: :: SYSREL:36
theorem Th37: :: SYSREL:37
theorem Th38: :: SYSREL:38
theorem Th39: :: SYSREL:39
theorem Th40: :: SYSREL:40
theorem Th41: :: SYSREL:41
theorem Th42: :: SYSREL:42
:: deftheorem Def1 defines CL SYSREL:def 1 :
theorem Th43: :: SYSREL:43
theorem Th44: :: SYSREL:44
theorem Th45: :: SYSREL:45
theorem Th46: :: SYSREL:46
theorem Th47: :: SYSREL:47
theorem Th48: :: SYSREL:48
theorem Th49: :: SYSREL:49
theorem Th50: :: SYSREL:50
theorem Th51: :: SYSREL:51
theorem Th52: :: SYSREL:52
theorem Th53: :: SYSREL:53
theorem Th54: :: SYSREL:54
theorem Th55: :: SYSREL:55
theorem Th56: :: SYSREL:56
theorem Th57: :: SYSREL:57
theorem Th58: :: SYSREL:58
theorem Th59: :: SYSREL:59