:: JGRAPH_1 semantic presentation
theorem Th1: :: JGRAPH_1:1
canceled;
theorem Th2: :: JGRAPH_1:2
theorem Th3: :: JGRAPH_1:3
theorem Th4: :: JGRAPH_1:4
definition
let c
1 be
set ;
func PGraph c
1 -> MultiGraphStruct equals :: JGRAPH_1:def 1
MultiGraphStruct(# a
1,
[:a1,a1:],
(pr1 a1,a1),
(pr2 a1,a1) #);
coherence
MultiGraphStruct(# c1,[:c1,c1:],(pr1 c1,c1),(pr2 c1,c1) #) is MultiGraphStruct
;
end;
:: deftheorem Def1 defines PGraph JGRAPH_1:def 1 :
theorem Th5: :: JGRAPH_1:5
theorem Th6: :: JGRAPH_1:6
:: deftheorem Def2 defines PairF JGRAPH_1:def 2 :
theorem Th7: :: JGRAPH_1:7
theorem Th8: :: JGRAPH_1:8
theorem Th9: :: JGRAPH_1:9
theorem Th10: :: JGRAPH_1:10
theorem Th11: :: JGRAPH_1:11
:: deftheorem Def3 defines is_Shortcut_of JGRAPH_1:def 3 :
theorem Th12: :: JGRAPH_1:12
theorem Th13: :: JGRAPH_1:13
theorem Th14: :: JGRAPH_1:14
theorem Th15: :: JGRAPH_1:15
:: deftheorem Def4 defines nodic JGRAPH_1:def 4 :
theorem Th16: :: JGRAPH_1:16
theorem Th17: :: JGRAPH_1:17
theorem Th18: :: JGRAPH_1:18
theorem Th19: :: JGRAPH_1:19
theorem Th20: :: JGRAPH_1:20
theorem Th21: :: JGRAPH_1:21
theorem Th22: :: JGRAPH_1:22
theorem Th23: :: JGRAPH_1:23
theorem Th24: :: JGRAPH_1:24
theorem Th25: :: JGRAPH_1:25
theorem Th26: :: JGRAPH_1:26
theorem Th27: :: JGRAPH_1:27
theorem Th28: :: JGRAPH_1:28
theorem Th29: :: JGRAPH_1:29
theorem Th30: :: JGRAPH_1:30
theorem Th31: :: JGRAPH_1:31
for b
1, b
2, b
3, b
4 being
Real holds
( b
1 <= b
3 & b
3 <= b
2 & b
1 <= b
4 & b
4 <= b
2 implies
abs (b3 - b4) <= b
2 - b
1 )
:: deftheorem Def5 defines |. JGRAPH_1:def 5 :
theorem Th32: :: JGRAPH_1:32
canceled;
theorem Th33: :: JGRAPH_1:33
canceled;
theorem Th34: :: JGRAPH_1:34
canceled;
theorem Th35: :: JGRAPH_1:35
canceled;
theorem Th36: :: JGRAPH_1:36
canceled;
theorem Th37: :: JGRAPH_1:37
canceled;
theorem Th38: :: JGRAPH_1:38
canceled;
theorem Th39: :: JGRAPH_1:39
canceled;
theorem Th40: :: JGRAPH_1:40
canceled;
theorem Th41: :: JGRAPH_1:41
canceled;
theorem Th42: :: JGRAPH_1:42
canceled;
theorem Th43: :: JGRAPH_1:43
canceled;
theorem Th44: :: JGRAPH_1:44
canceled;
theorem Th45: :: JGRAPH_1:45
theorem Th46: :: JGRAPH_1:46
theorem Th47: :: JGRAPH_1:47
theorem Th48: :: JGRAPH_1:48
theorem Th49: :: JGRAPH_1:49
theorem Th50: :: JGRAPH_1:50
theorem Th51: :: JGRAPH_1:51
theorem Th52: :: JGRAPH_1:52
for b
1 being
Natfor b
2, b
3, b
4 being
Point of
(TOP-REAL b1) holds
not ( b
2 in LSeg b
3,b
4 & ( for b
5 being
Real holds
not ( 0
<= b
5 & b
5 <= 1 & b
2 = ((1 - b5) * b3) + (b5 * b4) ) ) )
theorem Th53: :: JGRAPH_1:53
theorem Th54: :: JGRAPH_1:54
theorem Th55: :: JGRAPH_1:55
theorem Th56: :: JGRAPH_1:56
theorem Th57: :: JGRAPH_1:57
theorem Th58: :: JGRAPH_1:58
canceled;
theorem Th59: :: JGRAPH_1:59
theorem Th60: :: JGRAPH_1:60
theorem Th61: :: JGRAPH_1:61
theorem Th62: :: JGRAPH_1:62
theorem Th63: :: JGRAPH_1:63
theorem Th64: :: JGRAPH_1:64
theorem Th65: :: JGRAPH_1:65