:: MBOOLEAN semantic presentation
:: deftheorem Def1 defines bool MBOOLEAN:def 1 :
Lemma25:
for i, I, X being set
for M being ManySortedSet of I st i in I holds
dom (M +* (i .--> X)) = I
Lemma27:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(bool (A \/ B)) . i = bool ((A . i) \/ (B . i))
Lemma28:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(bool (A /\ B)) . i = bool ((A . i) /\ (B . i))
Lemma29:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(bool (A \ B)) . i = bool ((A . i) \ (B . i))
Lemma30:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(bool (A \+\ B)) . i = bool ((A . i) \+\ (B . i))
theorem Th1: :: MBOOLEAN:1
theorem Th2: :: MBOOLEAN:2
theorem Th3: :: MBOOLEAN:3
theorem Th4: :: MBOOLEAN:4
theorem Th5: :: MBOOLEAN:5
theorem Th6: :: MBOOLEAN:6
theorem Th7: :: MBOOLEAN:7
theorem Th8: :: MBOOLEAN:8
theorem Th9: :: MBOOLEAN:9
theorem Th10: :: MBOOLEAN:10
theorem Th11: :: MBOOLEAN:11
theorem Th12: :: MBOOLEAN:12
theorem Th13: :: MBOOLEAN:13
theorem Th14: :: MBOOLEAN:14
canceled;
theorem Th15: :: MBOOLEAN:15
theorem Th16: :: MBOOLEAN:16
theorem Th17: :: MBOOLEAN:17
theorem Th18: :: MBOOLEAN:18
theorem Th19: :: MBOOLEAN:19
theorem Th20: :: MBOOLEAN:20
:: deftheorem Def2 defines union MBOOLEAN:def 2 :
Lemma46:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(union (A \/ B)) . i = union ((A . i) \/ (B . i))
Lemma47:
for I being set
for A, B being ManySortedSet of I
for i being set st i in I holds
(union (A /\ B)) . i = union ((A . i) /\ (B . i))
theorem Th21: :: MBOOLEAN:21
theorem Th22: :: MBOOLEAN:22
theorem Th23: :: MBOOLEAN:23
theorem Th24: :: MBOOLEAN:24
theorem Th25: :: MBOOLEAN:25
theorem Th26: :: MBOOLEAN:26
theorem Th27: :: MBOOLEAN:27
theorem Th28: :: MBOOLEAN:28
theorem Th29: :: MBOOLEAN:29
theorem Th30: :: MBOOLEAN:30
theorem Th31: :: MBOOLEAN:31
theorem Th32: :: MBOOLEAN:32
theorem Th33: :: MBOOLEAN:33
theorem Th34: :: MBOOLEAN:34
theorem Th35: :: MBOOLEAN:35
theorem Th36: :: MBOOLEAN:36
theorem Th37: :: MBOOLEAN:37