:: Basic properties of even and odd functions
:: by Bo Li and Yanhong Men
::
:: Received May 25, 2009
:: Copyright (c) 2009 Association of Mizar Users
:: deftheorem Def1 defines symmetrical FUNCT_8:def 1 :
:: deftheorem Def2 defines with_symmetrical_domain FUNCT_8:def 2 :
:: deftheorem Def3 defines quasi_even FUNCT_8:def 3 :
:: deftheorem Def4 defines even FUNCT_8:def 4 :
:: deftheorem Def5 defines is_even_on FUNCT_8:def 5 :
:: deftheorem Def6 defines quasi_odd FUNCT_8:def 6 :
:: deftheorem Def7 defines odd FUNCT_8:def 7 :
:: deftheorem Def8 defines is_odd_on FUNCT_8:def 8 :
theorem :: FUNCT_8:1
theorem :: FUNCT_8:2
theorem :: FUNCT_8:3
theorem :: FUNCT_8:4
theorem :: FUNCT_8:5
theorem :: FUNCT_8:6
theorem :: FUNCT_8:7
theorem :: FUNCT_8:8
theorem :: FUNCT_8:9
theorem :: FUNCT_8:10
theorem :: FUNCT_8:11
theorem :: FUNCT_8:12
theorem :: FUNCT_8:13
theorem :: FUNCT_8:14
theorem :: FUNCT_8:15
theorem Th16: :: FUNCT_8:16
theorem Th17: :: FUNCT_8:17
theorem Th18: :: FUNCT_8:18
theorem Th19: :: FUNCT_8:19
theorem Th20: :: FUNCT_8:20
theorem Th21: :: FUNCT_8:21
theorem Th22: :: FUNCT_8:22
theorem Th23: :: FUNCT_8:23
theorem :: FUNCT_8:24
theorem :: FUNCT_8:25
theorem :: FUNCT_8:26
theorem :: FUNCT_8:27
theorem :: FUNCT_8:28
theorem :: FUNCT_8:29
theorem :: FUNCT_8:30
theorem :: FUNCT_8:31
theorem :: FUNCT_8:32
theorem :: FUNCT_8:33
theorem :: FUNCT_8:34
theorem :: FUNCT_8:35
theorem :: FUNCT_8:36
theorem :: FUNCT_8:37
theorem :: FUNCT_8:38
theorem :: FUNCT_8:39
theorem :: FUNCT_8:40
theorem :: FUNCT_8:41
theorem :: FUNCT_8:42
theorem :: FUNCT_8:43
theorem :: FUNCT_8:44
theorem :: FUNCT_8:45
theorem :: FUNCT_8:46
theorem :: FUNCT_8:47
theorem :: FUNCT_8:48
theorem :: FUNCT_8:49
theorem :: FUNCT_8:50
theorem :: FUNCT_8:51
theorem :: FUNCT_8:52
theorem :: FUNCT_8:53
theorem :: FUNCT_8:54
theorem :: FUNCT_8:55
:: deftheorem Def9 defines signum FUNCT_8:def 9 :
theorem Th56: :: FUNCT_8:56
theorem Th57: :: FUNCT_8:57
theorem Th58: :: FUNCT_8:58
theorem Th59: :: FUNCT_8:59
theorem :: FUNCT_8:60
theorem Th61: :: FUNCT_8:61
theorem Th62: :: FUNCT_8:62
theorem Th63: :: FUNCT_8:63
theorem :: FUNCT_8:64
theorem Th65: :: FUNCT_8:65
theorem Th66: :: FUNCT_8:66
theorem :: FUNCT_8:67
theorem :: FUNCT_8:68
theorem :: FUNCT_8:69
theorem :: FUNCT_8:70
theorem :: FUNCT_8:71
theorem :: FUNCT_8:72
theorem :: FUNCT_8:73
theorem :: FUNCT_8:74
theorem :: FUNCT_8:75
theorem :: FUNCT_8:76
theorem :: FUNCT_8:77
theorem :: FUNCT_8:78
theorem :: FUNCT_8:79
theorem :: FUNCT_8:80
theorem Th81: :: FUNCT_8:81
theorem :: FUNCT_8:82
theorem Th83: :: FUNCT_8:83
theorem :: FUNCT_8:84