:: BINARI_4 semantic presentation
theorem Th1: :: BINARI_4:1
theorem Th2: :: BINARI_4:2
theorem Th3: :: BINARI_4:3
theorem Th4: :: BINARI_4:4
theorem Th5: :: BINARI_4:5
theorem Th6: :: BINARI_4:6
theorem Th7: :: BINARI_4:7
theorem Th8: :: BINARI_4:8
theorem Th9: :: BINARI_4:9
for
g,
h,
i being
Integer st
g <= h + i &
h < 0 &
i < 0 holds
(
g < h &
g < i )
theorem Th10: :: BINARI_4:10
theorem Th11: :: BINARI_4:11
theorem Th12: :: BINARI_4:12
theorem Th13: :: BINARI_4:13
theorem Th14: :: BINARI_4:14
theorem Th15: :: BINARI_4:15
theorem Th16: :: BINARI_4:16
theorem Th17: :: BINARI_4:17
theorem Th18: :: BINARI_4:18
theorem Th19: :: BINARI_4:19
theorem Th20: :: BINARI_4:20
:: deftheorem Def1 defines MajP BINARI_4:def 1 :
theorem Th21: :: BINARI_4:21
theorem Th22: :: BINARI_4:22
theorem Th23: :: BINARI_4:23
theorem Th24: :: BINARI_4:24
theorem Th25: :: BINARI_4:25
:: deftheorem Def2 defines 2sComplement BINARI_4:def 2 :
theorem Th26: :: BINARI_4:26
theorem Th27: :: BINARI_4:27
Lemma76:
for n being non empty Element of NAT
for k, l being Element of NAT st k mod n = l mod n & k > l holds
ex s being Integer st k = l + (s * n)
Lemma78:
for n being non empty Element of NAT
for k, l being Element of NAT st k mod n = l mod n holds
ex s being Integer st k = l + (s * n)
Lemma80:
for n being non empty Element of NAT
for k, l, m being Element of NAT st m < n & k mod (2 to_power n) = l mod (2 to_power n) holds
(k div (2 to_power m)) mod 2 = (l div (2 to_power m)) mod 2
Lemma82:
for n being non empty Element of NAT
for h, i being Integer st h mod (2 to_power n) = i mod (2 to_power n) holds
((2 to_power (MajP n,(abs h))) + h) mod (2 to_power n) = ((2 to_power (MajP n,(abs i))) + i) mod (2 to_power n)
Lemma83:
for n being non empty Element of NAT
for h, i being Integer st h >= 0 & i >= 0 & h mod (2 to_power n) = i mod (2 to_power n) holds
2sComplement n,h = 2sComplement n,i
Lemma84:
for n being non empty Element of NAT
for h, i being Integer st h < 0 & i < 0 & h mod (2 to_power n) = i mod (2 to_power n) holds
2sComplement n,h = 2sComplement n,i
theorem Th28: :: BINARI_4:28
theorem Th29: :: BINARI_4:29
theorem Th30: :: BINARI_4:30
theorem Th31: :: BINARI_4:31
theorem Th32: :: BINARI_4:32
theorem Th33: :: BINARI_4:33
theorem Th34: :: BINARI_4:34
theorem Th35: :: BINARI_4:35
theorem Th36: :: BINARI_4:36
theorem Th37: :: BINARI_4:37
theorem Th38: :: BINARI_4:38