:: On the Decompositions of Intervals and Simple Closed Curves
:: by Adam Grabowski
::
:: Received August 7, 2002
:: Copyright (c) 2002 Association of Mizar Users
theorem Th1: :: BORSUK_4:1
theorem Th2: :: BORSUK_4:2
theorem Th3: :: BORSUK_4:3
theorem Th4: :: BORSUK_4:4
theorem Th5: :: BORSUK_4:5
theorem Th6: :: BORSUK_4:6
theorem Th7: :: BORSUK_4:7
theorem :: BORSUK_4:8
theorem :: BORSUK_4:9
theorem :: BORSUK_4:10
canceled;
theorem :: BORSUK_4:11
canceled;
theorem :: BORSUK_4:12
canceled;
theorem :: BORSUK_4:13
canceled;
theorem :: BORSUK_4:14
canceled;
theorem :: BORSUK_4:15
canceled;
theorem :: BORSUK_4:16
canceled;
theorem Th17: :: BORSUK_4:17
theorem Th18: :: BORSUK_4:18
theorem Th19: :: BORSUK_4:19
theorem Th20: :: BORSUK_4:20
theorem Th21: :: BORSUK_4:21
theorem :: BORSUK_4:22
theorem Th23: :: BORSUK_4:23
theorem Th24: :: BORSUK_4:24
theorem :: BORSUK_4:25
canceled;
theorem :: BORSUK_4:26
canceled;
theorem :: BORSUK_4:27
canceled;
theorem :: BORSUK_4:28
canceled;
theorem :: BORSUK_4:29
canceled;
theorem :: BORSUK_4:30
canceled;
theorem :: BORSUK_4:31
canceled;
theorem Th32: :: BORSUK_4:32
theorem Th33: :: BORSUK_4:33
theorem :: BORSUK_4:34
canceled;
theorem :: BORSUK_4:35
canceled;
theorem :: BORSUK_4:36
canceled;
theorem :: BORSUK_4:37
canceled;
theorem :: BORSUK_4:38
canceled;
theorem :: BORSUK_4:39
canceled;
theorem :: BORSUK_4:40
canceled;
theorem :: BORSUK_4:41
canceled;
theorem :: BORSUK_4:42
canceled;
theorem :: BORSUK_4:43
theorem Th44: :: BORSUK_4:44
theorem :: BORSUK_4:45
theorem Th46: :: BORSUK_4:46
theorem Th47: :: BORSUK_4:47
theorem Th48: :: BORSUK_4:48
theorem Th49: :: BORSUK_4:49
theorem Th50: :: BORSUK_4:50
theorem Th51: :: BORSUK_4:51
Lm1:
I[01] is closed SubSpace of R^1
by TOPMETR:27, TREAL_1:5;
theorem Th52: :: BORSUK_4:52
theorem Th53: :: BORSUK_4:53
theorem Th54: :: BORSUK_4:54
theorem Th55: :: BORSUK_4:55
theorem Th56: :: BORSUK_4:56
:: deftheorem Def1 defines I(01) BORSUK_4:def 1 :
theorem :: BORSUK_4:57
theorem Th58: :: BORSUK_4:58
theorem Th59: :: BORSUK_4:59
theorem Th60: :: BORSUK_4:60
theorem Th61: :: BORSUK_4:61
theorem Th62: :: BORSUK_4:62
theorem :: BORSUK_4:63
theorem :: BORSUK_4:64
theorem Th65: :: BORSUK_4:65
theorem :: BORSUK_4:66
theorem Th67: :: BORSUK_4:67
theorem Th68: :: BORSUK_4:68
theorem Th69: :: BORSUK_4:69
theorem Th70: :: BORSUK_4:70
theorem Th71: :: BORSUK_4:71
theorem Th72: :: BORSUK_4:72
theorem Th73: :: BORSUK_4:73
theorem Th74: :: BORSUK_4:74
theorem Th75: :: BORSUK_4:75
theorem Th76: :: BORSUK_4:76
theorem Th77: :: BORSUK_4:77
theorem :: BORSUK_4:78
theorem Th79: :: BORSUK_4:79
theorem Th80: :: BORSUK_4:80
theorem :: BORSUK_4:81
:: deftheorem Def2 defines real-membered BORSUK_4:def 2 :
theorem Th82: :: BORSUK_4:82
theorem Th83: :: BORSUK_4:83
theorem :: BORSUK_4:84