:: CFCONT_1 semantic presentation
:: deftheorem Def1 defines * CFCONT_1:def 1 :
:: deftheorem Def2 defines is_continuous_in CFCONT_1:def 2 :
theorem :: CFCONT_1:1
canceled;
theorem Th2: :: CFCONT_1:2
theorem Th3: :: CFCONT_1:3
theorem Th4: :: CFCONT_1:4
theorem Th5: :: CFCONT_1:5
theorem :: CFCONT_1:6
theorem Th7: :: CFCONT_1:7
theorem :: CFCONT_1:8
theorem Th9: :: CFCONT_1:9
theorem Th10: :: CFCONT_1:10
theorem :: CFCONT_1:11
theorem Th12: :: CFCONT_1:12
theorem :: CFCONT_1:13
theorem :: CFCONT_1:14
theorem :: CFCONT_1:15
canceled;
theorem Th16: :: CFCONT_1:16
theorem Th17: :: CFCONT_1:17
theorem Th18: :: CFCONT_1:18
theorem Th19: :: CFCONT_1:19
theorem :: CFCONT_1:20
theorem Th21: :: CFCONT_1:21
theorem Th22: :: CFCONT_1:22
theorem Th23: :: CFCONT_1:23
theorem Th24: :: CFCONT_1:24
theorem Th25: :: CFCONT_1:25
theorem Th26: :: CFCONT_1:26
theorem :: CFCONT_1:27
theorem :: CFCONT_1:28
theorem :: CFCONT_1:29
theorem :: CFCONT_1:30
theorem :: CFCONT_1:31
theorem :: CFCONT_1:32
theorem :: CFCONT_1:33
:: deftheorem CFCONT_1:def 3 :
canceled;
:: deftheorem Def4 defines constant CFCONT_1:def 4 :
Lm1:
for seq being Complex_Sequence holds
( ( ex g being Element of COMPLEX st
for n being Element of NAT holds seq . n = g implies ex g being Element of COMPLEX st rng seq = {g} ) & ( ex g being Element of COMPLEX st rng seq = {g} implies for n being Element of NAT holds seq . n = seq . (n + 1) ) & ( ( for n being Element of NAT holds seq . n = seq . (n + 1) ) implies for n, k being Element of NAT holds seq . n = seq . (n + k) ) & ( ( for n, k being Element of NAT holds seq . n = seq . (n + k) ) implies for n, m being Element of NAT holds seq . n = seq . m ) & ( ( for n, m being Element of NAT holds seq . n = seq . m ) implies ex g being Element of COMPLEX st
for n being Element of NAT holds seq . n = g ) )
theorem Th34: :: CFCONT_1:34
theorem Th35: :: CFCONT_1:35
theorem Th36: :: CFCONT_1:36
theorem :: CFCONT_1:37
theorem Th38: :: CFCONT_1:38
theorem Th39: :: CFCONT_1:39
theorem Th40: :: CFCONT_1:40
theorem Th41: :: CFCONT_1:41
theorem :: CFCONT_1:42
theorem Th43: :: CFCONT_1:43
theorem Th44: :: CFCONT_1:44
theorem :: CFCONT_1:45
theorem Th46: :: CFCONT_1:46
theorem :: CFCONT_1:47
theorem Th48: :: CFCONT_1:48
theorem Th49: :: CFCONT_1:49
theorem :: CFCONT_1:50
theorem :: CFCONT_1:51
theorem :: CFCONT_1:52
theorem :: CFCONT_1:53
theorem Th54: :: CFCONT_1:54
theorem Th55: :: CFCONT_1:55
theorem Th56: :: CFCONT_1:56
theorem :: CFCONT_1:57
theorem Th58: :: CFCONT_1:58
theorem :: CFCONT_1:59
:: deftheorem Def5 defines is_continuous_on CFCONT_1:def 5 :
theorem Th60: :: CFCONT_1:60
theorem Th61: :: CFCONT_1:61
theorem Th62: :: CFCONT_1:62
theorem Th63: :: CFCONT_1:63
theorem :: CFCONT_1:64
theorem Th65: :: CFCONT_1:65
theorem :: CFCONT_1:66
theorem Th67: :: CFCONT_1:67
theorem :: CFCONT_1:68
theorem Th69: :: CFCONT_1:69
theorem :: CFCONT_1:70
theorem :: CFCONT_1:71
theorem :: CFCONT_1:72
:: deftheorem Def6 defines compact CFCONT_1:def 6 :
theorem Th73: :: CFCONT_1:73
theorem :: CFCONT_1:74