:: Properties of Real Functions
:: by Jaros{\l}aw Kotowicz
::
:: Received June 18, 1990
:: Copyright (c) 1990 Association of Mizar Users
:: RFUNCT_2 semantic presentation
theorem :: RFUNCT_2:1
canceled;
theorem :: RFUNCT_2:2
theorem :: RFUNCT_2:3
theorem Th4: :: RFUNCT_2:4
theorem :: RFUNCT_2:5
theorem Th6: :: RFUNCT_2:6
theorem Th7: :: RFUNCT_2:7
theorem Th8: :: RFUNCT_2:8
theorem Th9: :: RFUNCT_2:9
theorem :: RFUNCT_2:10
theorem Th11: :: RFUNCT_2:11
theorem :: RFUNCT_2:12
theorem Th13: :: RFUNCT_2:13
theorem Th14: :: RFUNCT_2:14
theorem :: RFUNCT_2:15
theorem Th16: :: RFUNCT_2:16
theorem :: RFUNCT_2:17
theorem :: RFUNCT_2:18
theorem :: RFUNCT_2:19
:: deftheorem Def1 defines * RFUNCT_2:def 1 :
theorem :: RFUNCT_2:20
canceled;
theorem Th21: :: RFUNCT_2:21
theorem Th22: :: RFUNCT_2:22
theorem Th23: :: RFUNCT_2:23
theorem Th24: :: RFUNCT_2:24
theorem :: RFUNCT_2:25
theorem :: RFUNCT_2:26
theorem :: RFUNCT_2:27
theorem Th28: :: RFUNCT_2:28
theorem :: RFUNCT_2:29
theorem :: RFUNCT_2:30
theorem :: RFUNCT_2:31
theorem :: RFUNCT_2:32
theorem :: RFUNCT_2:33
theorem :: RFUNCT_2:34
theorem :: RFUNCT_2:35
theorem :: RFUNCT_2:36
theorem :: RFUNCT_2:37
theorem Th38: :: RFUNCT_2:38
theorem :: RFUNCT_2:39
theorem :: RFUNCT_2:40
theorem Th41: :: RFUNCT_2:41
theorem :: RFUNCT_2:42
:: deftheorem Def2 defines is_increasing_on RFUNCT_2:def 2 :
:: deftheorem Def3 defines is_decreasing_on RFUNCT_2:def 3 :
:: deftheorem Def4 defines is_non_decreasing_on RFUNCT_2:def 4 :
:: deftheorem Def5 defines is_non_increasing_on RFUNCT_2:def 5 :
:: deftheorem Def6 defines is_monotone_on RFUNCT_2:def 6 :
theorem :: RFUNCT_2:43
canceled;
theorem :: RFUNCT_2:44
canceled;
theorem :: RFUNCT_2:45
canceled;
theorem :: RFUNCT_2:46
canceled;
theorem :: RFUNCT_2:47
canceled;
theorem Th48: :: RFUNCT_2:48
theorem Th49: :: RFUNCT_2:49
theorem Th50: :: RFUNCT_2:50
theorem Th51: :: RFUNCT_2:51
theorem :: RFUNCT_2:52
theorem :: RFUNCT_2:53
theorem :: RFUNCT_2:54
theorem :: RFUNCT_2:55
theorem :: RFUNCT_2:56
theorem :: RFUNCT_2:57
theorem :: RFUNCT_2:58
theorem :: RFUNCT_2:59
theorem :: RFUNCT_2:60
theorem :: RFUNCT_2:61
theorem :: RFUNCT_2:62
theorem :: RFUNCT_2:63
theorem Th64: :: RFUNCT_2:64
theorem :: RFUNCT_2:65
theorem Th66: :: RFUNCT_2:66
theorem :: RFUNCT_2:67
theorem Th68: :: RFUNCT_2:68
theorem :: RFUNCT_2:69
theorem :: RFUNCT_2:70
theorem :: RFUNCT_2:71
theorem :: RFUNCT_2:72
theorem :: RFUNCT_2:73
theorem :: RFUNCT_2:74
theorem :: RFUNCT_2:75
theorem :: RFUNCT_2:76
theorem :: RFUNCT_2:77
theorem :: RFUNCT_2:78
theorem :: RFUNCT_2:79
theorem :: RFUNCT_2:80
theorem :: RFUNCT_2:81
theorem :: RFUNCT_2:82
theorem :: RFUNCT_2:83
theorem :: RFUNCT_2:84