:: FIB_NUM2 semantic presentation
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theorem :: FIB_NUM2:1
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theorem Th2: :: FIB_NUM2:2
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theorem Th3: :: FIB_NUM2:3
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theorem Th4: :: FIB_NUM2:4
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theorem Th5: :: FIB_NUM2:5
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theorem Th6: :: FIB_NUM2:6
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theorem Th7: :: FIB_NUM2:7
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theorem Th8: :: FIB_NUM2:8
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theorem Th9: :: FIB_NUM2:9
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theorem Th10: :: FIB_NUM2:10
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theorem Th11: :: FIB_NUM2:11
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theorem Th12: :: FIB_NUM2:12
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theorem Th13: :: FIB_NUM2:13
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theorem Th14: :: FIB_NUM2:14
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theorem Th15: :: FIB_NUM2:15
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:: deftheorem defines Prefix FIB_NUM2:def 1 :
theorem Th16: :: FIB_NUM2:16
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for
m,
n,
k being
Nat st
k <> 0 &
k + m <= n holds
m < n
theorem Th17: :: FIB_NUM2:17
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theorem Th18: :: FIB_NUM2:18
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theorem Th19: :: FIB_NUM2:19
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theorem Th20: :: FIB_NUM2:20
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theorem Th21: :: FIB_NUM2:21
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theorem Th22: :: FIB_NUM2:22
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theorem Th23: :: FIB_NUM2:23
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theorem Th24: :: FIB_NUM2:24
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theorem Th25: :: FIB_NUM2:25
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theorem Th26: :: FIB_NUM2:26
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theorem Th27: :: FIB_NUM2:27
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theorem Th28: :: FIB_NUM2:28
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theorem Th29: :: FIB_NUM2:29
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Lm1:
for k being Nat holds Fib ((2 * (k + 2)) + 1) = (Fib ((2 * k) + 3)) + (Fib ((2 * k) + 4))
theorem Th30: :: FIB_NUM2:30
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theorem Th31: :: FIB_NUM2:31
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theorem Th32: :: FIB_NUM2:32
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theorem Th33: :: FIB_NUM2:33
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theorem :: FIB_NUM2:34
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theorem Th35: :: FIB_NUM2:35
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theorem Th36: :: FIB_NUM2:36
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theorem Th37: :: FIB_NUM2:37
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theorem Th38: :: FIB_NUM2:38
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theorem Th39: :: FIB_NUM2:39
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theorem :: FIB_NUM2:40
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theorem :: FIB_NUM2:41
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theorem Th42: :: FIB_NUM2:42
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theorem Th43: :: FIB_NUM2:43
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theorem Th44: :: FIB_NUM2:44
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theorem Th45: :: FIB_NUM2:45
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theorem Th46: :: FIB_NUM2:46
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theorem :: FIB_NUM2:47
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theorem Th48: :: FIB_NUM2:48
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theorem Th49: :: FIB_NUM2:49
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for
k being
Nat holds
(
Fib k = 1 iff (
k = 1 or
k = 2 ) )
theorem Th50: :: FIB_NUM2:50
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for
k,
n being
Nat st
n > 1 &
k <> 0 &
k <> 1 & ( (
k <> 1 &
n <> 2 ) or (
k <> 2 &
n <> 1 ) ) holds
(
Fib k = Fib n iff
k = n )
theorem Th51: :: FIB_NUM2:51
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theorem :: FIB_NUM2:52
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:: deftheorem Def2 defines FIB FIB_NUM2:def 2 :
:: deftheorem defines EvenNAT FIB_NUM2:def 3 :
:: deftheorem defines OddNAT FIB_NUM2:def 4 :
theorem Th53: :: FIB_NUM2:53
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theorem Th54: :: FIB_NUM2:54
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:: deftheorem defines EvenFibs FIB_NUM2:def 5 :
:: deftheorem defines OddFibs FIB_NUM2:def 6 :
theorem Th55: :: FIB_NUM2:55
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theorem :: FIB_NUM2:56
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theorem Th57: :: FIB_NUM2:57
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theorem :: FIB_NUM2:58
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theorem Th59: :: FIB_NUM2:59
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theorem Th60: :: FIB_NUM2:60
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theorem Th61: :: FIB_NUM2:61
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theorem Th62: :: FIB_NUM2:62
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theorem Th63: :: FIB_NUM2:63
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theorem Th64: :: FIB_NUM2:64
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theorem Th65: :: FIB_NUM2:65
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theorem Th66: :: FIB_NUM2:66
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theorem :: FIB_NUM2:67
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theorem :: FIB_NUM2:68
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theorem Th69: :: FIB_NUM2:69
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theorem Th70: :: FIB_NUM2:70
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theorem :: FIB_NUM2:71
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theorem :: FIB_NUM2:72
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