:: BORSUK_4 semantic presentation
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 Th8: :: BORSUK_4:8
theorem Th9: :: BORSUK_4:9
theorem Th10: :: BORSUK_4:10
theorem Th11: :: BORSUK_4:11
theorem Th12: :: BORSUK_4:12
theorem Th13: :: BORSUK_4:13
theorem Th14: :: BORSUK_4:14
theorem Th15: :: BORSUK_4:15
theorem Th16: :: BORSUK_4:16
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 Th22: :: BORSUK_4:22
theorem Th23: :: BORSUK_4:23
theorem Th24: :: BORSUK_4:24
theorem Th25: :: BORSUK_4:25
theorem Th26: :: BORSUK_4:26
Lemma112:
for a, b being real number holds
( ].a,b.[ misses {b} & ].a,b.[ misses {a} )
theorem Th27: :: BORSUK_4:27
theorem Th28: :: BORSUK_4:28
theorem Th29: :: BORSUK_4:29
theorem Th30: :: BORSUK_4:30
theorem Th31: :: BORSUK_4:31
theorem Th32: :: BORSUK_4:32
theorem Th33: :: BORSUK_4:33
theorem Th34: :: BORSUK_4:34
theorem Th35: :: BORSUK_4:35
theorem Th36: :: BORSUK_4:36
theorem Th37: :: BORSUK_4:37
theorem Th38: :: BORSUK_4:38
theorem Th39: :: BORSUK_4:39
theorem Th40: :: BORSUK_4:40
theorem Th41: :: BORSUK_4:41
theorem Th42: :: BORSUK_4:42
theorem Th43: :: BORSUK_4:43
theorem Th44: :: BORSUK_4:44
theorem Th45: :: 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
Lemma141:
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 Th57: :: 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 Th63: :: BORSUK_4:63
theorem Th64: :: BORSUK_4:64
theorem Th65: :: BORSUK_4:65
theorem Th66: :: 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 Th78: :: BORSUK_4:78
theorem Th79: :: BORSUK_4:79
theorem Th80: :: BORSUK_4:80
theorem Th81: :: BORSUK_4:81
Lemma235:
for a, b, r, s being real number st ( a <= b or r <= s ) & [.a,b.] = [.r,s.] holds
( a = r & b = s )
theorem Th82: :: BORSUK_4:82
theorem Th83: :: BORSUK_4:83
theorem Th84: :: BORSUK_4:84