:: FLANG_2 semantic presentation
theorem LmNum19: :: FLANG_2:1
for
m,
k,
i,
n being
Nat st
m + k <= i &
i <= n + k holds
ex
mn being
Nat st
(
mn + k = i &
m <= mn &
mn <= n )
theorem LmNum20: :: FLANG_2:2
for
m,
n,
k,
l,
i being
Nat st
m <= n &
k <= l &
m + k <= i &
i <= n + l holds
ex
mn,
kl being
Nat st
(
mn + kl = i &
m <= mn &
mn <= n &
k <= kl &
kl <= l )
theorem LmNum30: :: FLANG_2:3
for
m,
n being
Nat st
m < n holds
ex
k being
Nat st
(
m + k = n &
k > 0 )
theorem LmSeq20: :: FLANG_2:4
theorem :: FLANG_2:5
theorem :: FLANG_2:6
theorem LmLang20: :: FLANG_2:7
theorem :: FLANG_2:8
theorem LmLang31: :: FLANG_2:9
theorem LmLang32: :: FLANG_2:10
theorem :: FLANG_2:11
theorem LmLang50: :: FLANG_2:12
theorem :: FLANG_2:13
theorem :: FLANG_2:14
theorem :: FLANG_2:15
theorem LmLang70: :: FLANG_2:16
theorem LmLang80: :: FLANG_2:17
theorem :: FLANG_2:18
:: deftheorem defines |^ FLANG_2:def 1 :
theorem ThRange10: :: FLANG_2:19
theorem ThRange20: :: FLANG_2:20
theorem ThRange30: :: FLANG_2:21
theorem ThRange40: :: FLANG_2:22
theorem ThRange50: :: FLANG_2:23
theorem :: FLANG_2:24
theorem ThRange70: :: FLANG_2:25
theorem ThRange80: :: FLANG_2:26
theorem :: FLANG_2:27
theorem ThRange100: :: FLANG_2:28
theorem ThRange110: :: FLANG_2:29
theorem ThRange120: :: FLANG_2:30
theorem ThRange130: :: FLANG_2:31
theorem ThRange140: :: FLANG_2:32
theorem ThRange150: :: FLANG_2:33
theorem ThRange160: :: FLANG_2:34
theorem ThRange240: :: FLANG_2:35
theorem ThRange170: :: FLANG_2:36
theorem ThRange190: :: FLANG_2:37
theorem ThRange180: :: FLANG_2:38
theorem ThRange200: :: FLANG_2:39
theorem ThRange210: :: FLANG_2:40
theorem ThRange211: :: FLANG_2:41
theorem ThRange220: :: FLANG_2:42
theorem :: FLANG_2:43
theorem :: FLANG_2:44
theorem ThRange250: :: FLANG_2:45
theorem ThRange260: :: FLANG_2:46
theorem :: FLANG_2:47
theorem :: FLANG_2:48
theorem :: FLANG_2:49
theorem :: FLANG_2:50
theorem ThRange302: :: FLANG_2:51
theorem ThRange310: :: FLANG_2:52
theorem ThRange320: :: FLANG_2:53
theorem :: FLANG_2:54
theorem :: FLANG_2:55
theorem :: FLANG_2:56
theorem :: FLANG_2:57
theorem :: FLANG_2:58
theorem :: FLANG_2:59
theorem :: FLANG_2:60
theorem :: FLANG_2:61
theorem :: FLANG_2:62
theorem :: FLANG_2:63
theorem ThRange440: :: FLANG_2:64
theorem :: FLANG_2:65
theorem ThRange450: :: FLANG_2:66
theorem :: FLANG_2:67
theorem ThRange470: :: FLANG_2:68
theorem ThRange480: :: FLANG_2:69
theorem :: FLANG_2:70
theorem ThRange500: :: FLANG_2:71
theorem ThRange520: :: FLANG_2:72
:: deftheorem defines ? FLANG_2:def 2 :
theorem ThOpt10: :: FLANG_2:73
theorem :: FLANG_2:74
theorem ThOpt40: :: FLANG_2:75
theorem ThOpt50: :: FLANG_2:76
theorem :: FLANG_2:77
theorem ThOpt60: :: FLANG_2:78
theorem ThOpt70: :: FLANG_2:79
theorem ThOpt80: :: FLANG_2:80
theorem :: FLANG_2:81
theorem :: FLANG_2:82
theorem :: FLANG_2:83
theorem :: FLANG_2:84
theorem :: FLANG_2:85
theorem :: FLANG_2:86
theorem :: FLANG_2:87
theorem :: FLANG_2:88
theorem :: FLANG_2:89
theorem :: FLANG_2:90
theorem :: FLANG_2:91
theorem :: FLANG_2:92
theorem ThOpt210: :: FLANG_2:93
theorem ThOpt220: :: FLANG_2:94
theorem ThOpt230: :: FLANG_2:95
theorem ThOpt340: :: FLANG_2:96
theorem ThOpt350: :: FLANG_2:97
theorem ThOpt360: :: FLANG_2:98
theorem :: FLANG_2:99
theorem :: FLANG_2:100
theorem :: FLANG_2:101
theorem :: FLANG_2:102
theorem :: FLANG_2:103
theorem :: FLANG_2:104
theorem ThOpt280: :: FLANG_2:105
theorem :: FLANG_2:106
theorem :: FLANG_2:107
theorem :: FLANG_2:108
theorem :: FLANG_2:109
theorem :: FLANG_2:110
theorem :: FLANG_2:111
theorem :: FLANG_2:112
theorem :: FLANG_2:113
theorem :: FLANG_2:114
theorem :: FLANG_2:115
theorem :: FLANG_2:116
theorem :: FLANG_2:117