:: Some Properties of the Intervals
:: by J\'ozef Bia\las
::
:: Received February 5, 1994
:: Copyright (c) 1994 Association of Mizar Users
:: MEASURE6 semantic presentation
theorem :: MEASURE6:1
theorem :: MEASURE6:2
theorem :: MEASURE6:3
theorem :: MEASURE6:4
canceled;
theorem :: MEASURE6:5
canceled;
theorem :: MEASURE6:6
canceled;
theorem :: MEASURE6:7
canceled;
theorem Th8: :: MEASURE6:8
for
x,
y being
R_eal st
x is
Real holds
(
(y - x) + x = y &
(y + x) - x = y )
theorem :: MEASURE6:9
canceled;
theorem Th10: :: MEASURE6:10
theorem Th11: :: MEASURE6:11
theorem Th12: :: MEASURE6:12
:: deftheorem defines R_EAL MEASURE6:def 1 :
theorem :: MEASURE6:13
canceled;
theorem :: MEASURE6:14
canceled;
theorem :: MEASURE6:15
canceled;
theorem :: MEASURE6:16
canceled;
theorem :: MEASURE6:17
canceled;
theorem :: MEASURE6:18
canceled;
theorem Th19: :: MEASURE6:19
theorem :: MEASURE6:20
theorem Th21: :: MEASURE6:21
theorem Th22: :: MEASURE6:22
theorem Th23: :: MEASURE6:23
theorem Th24: :: MEASURE6:24
theorem :: MEASURE6:25
theorem Th26: :: MEASURE6:26
:: deftheorem Def2 defines Seg MEASURE6:def 2 :
:: deftheorem defines len MEASURE6:def 3 :
theorem Th27: :: MEASURE6:27
theorem Th28: :: MEASURE6:28
theorem Th29: :: MEASURE6:29
theorem Th30: :: MEASURE6:30
theorem :: MEASURE6:31
theorem :: MEASURE6:32
theorem :: MEASURE6:33
theorem :: MEASURE6:34
theorem Th35: :: MEASURE6:35
theorem Th36: :: MEASURE6:36
theorem Th37: :: MEASURE6:37
theorem Th38: :: MEASURE6:38
theorem Th39: :: MEASURE6:39
theorem Th40: :: MEASURE6:40
theorem Th41: :: MEASURE6:41
theorem Th42: :: MEASURE6:42
theorem Th43: :: MEASURE6:43
theorem Th44: :: MEASURE6:44
theorem Th45: :: MEASURE6:45
theorem Th46: :: MEASURE6:46
theorem :: MEASURE6:47
:: deftheorem Def4 defines inf MEASURE6:def 4 :
:: deftheorem Def5 defines sup MEASURE6:def 5 :
theorem Th48: :: MEASURE6:48
theorem Th49: :: MEASURE6:49
theorem Th50: :: MEASURE6:50
theorem Th51: :: MEASURE6:51
theorem Th52: :: MEASURE6:52
theorem :: MEASURE6:53
canceled;
theorem Th54: :: MEASURE6:54
theorem Th55: :: MEASURE6:55
theorem :: MEASURE6:56
theorem Th57: :: MEASURE6:57
theorem :: MEASURE6:58
:: deftheorem Def6 defines ++ MEASURE6:def 6 :
theorem Th59: :: MEASURE6:59
theorem :: MEASURE6:60
theorem :: MEASURE6:61
theorem Th62: :: MEASURE6:62
theorem Th63: :: MEASURE6:63
theorem Th64: :: MEASURE6:64
theorem Th65: :: MEASURE6:65
theorem Th66: :: MEASURE6:66
theorem Tx1: :: MEASURE6:67
theorem Tx2: :: MEASURE6:68
theorem :: MEASURE6:69