:: Graph Theoretical Properties of Arcs in the Plane and FashodaMeet Theorem
:: by Yatsuka Nakamura
::
:: Received August 21, 1998
:: Copyright (c) 1998 Association of Mizar Users
theorem :: JGRAPH_1:1
canceled;
theorem :: JGRAPH_1:2
canceled;
theorem :: JGRAPH_1:3
canceled;
theorem Th4: :: JGRAPH_1:4
definition
let X be
set ;
func PGraph X -> MultiGraphStruct equals :: JGRAPH_1:def 1
MultiGraphStruct(#
X,
[:X,X:],
(pr1 X,X),
(pr2 X,X) #);
coherence
MultiGraphStruct(# X,[:X,X:],(pr1 X,X),(pr2 X,X) #) is MultiGraphStruct
;
end;
:: deftheorem defines PGraph JGRAPH_1:def 1 :
theorem :: JGRAPH_1:5
canceled;
theorem :: JGRAPH_1:6
:: deftheorem Def2 defines PairF JGRAPH_1:def 2 :
theorem :: 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 :: 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 :: JGRAPH_1:23
theorem :: 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
a,
b,
r1,
r2 being
Real st
a <= r1 &
r1 <= b &
a <= r2 &
r2 <= b holds
abs (r1 - r2) <= b - a
theorem :: JGRAPH_1:32
canceled;
theorem :: JGRAPH_1:33
canceled;
theorem :: JGRAPH_1:34
canceled;
theorem :: JGRAPH_1:35
canceled;
theorem :: JGRAPH_1:36
canceled;
theorem :: JGRAPH_1:37
canceled;
theorem :: JGRAPH_1:38
canceled;
theorem :: JGRAPH_1:39
canceled;
theorem :: JGRAPH_1:40
canceled;
theorem :: JGRAPH_1:41
canceled;
theorem :: JGRAPH_1:42
canceled;
theorem :: JGRAPH_1:43
canceled;
theorem :: 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
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 :: 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 :: JGRAPH_1:65