:: Basic Properties of Real Numbers
:: by Krzysztof Hryniewiecki
::
:: Received January 8, 1989
:: Copyright (c) 1990 Association of Mizar Users
:: REAL_1 semantic presentation
theorem :: REAL_1:1
canceled;
theorem :: REAL_1:2
canceled;
theorem :: REAL_1:3
canceled;
theorem :: REAL_1:4
canceled;
theorem :: REAL_1:5
canceled;
theorem :: REAL_1:6
canceled;
theorem :: REAL_1:7
canceled;
theorem :: REAL_1:8
canceled;
theorem :: REAL_1:9
canceled;
theorem :: REAL_1:10
canceled;
theorem :: REAL_1:11
canceled;
theorem :: REAL_1:12
canceled;
theorem :: REAL_1:13
canceled;
theorem :: REAL_1:14
canceled;
theorem :: REAL_1:15
canceled;
theorem :: REAL_1:16
canceled;
theorem :: REAL_1:17
canceled;
theorem :: REAL_1:18
canceled;
theorem :: REAL_1:19
canceled;
theorem :: REAL_1:20
canceled;
theorem :: REAL_1:21
canceled;
theorem :: REAL_1:22
canceled;
theorem :: REAL_1:23
canceled;
theorem :: REAL_1:24
canceled;
theorem :: REAL_1:25
theorem :: REAL_1:26
:: deftheorem REAL_1:def 1 :
canceled;
:: deftheorem REAL_1:def 2 :
canceled;
:: deftheorem REAL_1:def 3 :
canceled;
:: deftheorem REAL_1:def 4 :
canceled;
:: deftheorem defines < REAL_1:def 5 :
for
y,
x being
real number holds
( not
x < y iff ( not
x <= y or not
x <> y ) );
theorem :: REAL_1:27
canceled;
theorem :: REAL_1:28
canceled;
theorem :: REAL_1:29
canceled;
theorem :: REAL_1:30
canceled;
theorem :: REAL_1:31
canceled;
theorem :: REAL_1:32
canceled;
theorem :: REAL_1:33
canceled;
theorem :: REAL_1:34
canceled;
theorem :: REAL_1:35
canceled;
theorem :: REAL_1:36
canceled;
theorem :: REAL_1:37
canceled;
theorem :: REAL_1:38
canceled;
theorem :: REAL_1:39
canceled;
theorem :: REAL_1:40
canceled;
theorem :: REAL_1:41
canceled;
theorem :: REAL_1:42
canceled;
theorem :: REAL_1:43
canceled;
theorem :: REAL_1:44
canceled;
theorem :: REAL_1:45
canceled;
theorem :: REAL_1:46
canceled;
theorem :: REAL_1:47
canceled;
theorem :: REAL_1:48
canceled;
theorem :: REAL_1:49
canceled;
theorem :: REAL_1:50
canceled;
theorem :: REAL_1:51
canceled;
theorem :: REAL_1:52
canceled;
theorem :: REAL_1:53
canceled;
theorem :: REAL_1:54
canceled;
theorem :: REAL_1:55
canceled;
theorem :: REAL_1:56
canceled;
theorem :: REAL_1:57
canceled;
theorem :: REAL_1:58
canceled;
theorem :: REAL_1:59
canceled;
theorem :: REAL_1:60
canceled;
theorem :: REAL_1:61
canceled;
theorem :: REAL_1:62
canceled;
theorem :: REAL_1:63
canceled;
theorem :: REAL_1:64
canceled;
theorem :: REAL_1:65
canceled;
theorem :: REAL_1:66
canceled;
theorem :: REAL_1:67
canceled;
theorem :: REAL_1:68
canceled;
theorem :: REAL_1:69
canceled;
theorem :: REAL_1:70
canceled;
theorem :: REAL_1:71
canceled;
theorem :: REAL_1:72
canceled;
theorem :: REAL_1:73
theorem :: REAL_1:74
theorem :: REAL_1:75
canceled;
theorem :: REAL_1:76
canceled;
theorem :: REAL_1:77
canceled;
theorem :: REAL_1:78
canceled;
theorem :: REAL_1:79
canceled;
theorem :: REAL_1:80
canceled;
theorem :: REAL_1:81
canceled;
theorem :: REAL_1:82
canceled;
theorem :: REAL_1:83
canceled;
theorem :: REAL_1:84
canceled;
theorem :: REAL_1:85
canceled;
theorem :: REAL_1:86
canceled;
theorem :: REAL_1:87
canceled;
theorem :: REAL_1:88
canceled;
theorem :: REAL_1:89
canceled;
theorem :: REAL_1:90
canceled;
theorem :: REAL_1:91
canceled;
theorem :: REAL_1:92