:: WAYBEL19 semantic presentation
:: deftheorem Def1 defines lower WAYBEL19:def 1 :
theorem Th1: :: WAYBEL19:1
theorem Th2: :: WAYBEL19:2
:: deftheorem Def2 defines omega WAYBEL19:def 2 :
theorem Th3: :: WAYBEL19:3
theorem Th4: :: WAYBEL19:4
theorem Th5: :: WAYBEL19:5
theorem Th6: :: WAYBEL19:6
theorem Th7: :: WAYBEL19:7
theorem Th8: :: WAYBEL19:8
theorem Th9: :: WAYBEL19:9
theorem Th10: :: WAYBEL19:10
theorem Th11: :: WAYBEL19:11
theorem Th12: :: WAYBEL19:12
theorem Th13: :: WAYBEL19:13
theorem Th14: :: WAYBEL19:14
Lemma98:
for L1, L2 being non empty RelStr st RelStr(# the carrier of L1,the InternalRel of L1 #) = RelStr(# the carrier of L2,the InternalRel of L2 #) holds
for x1 being Element of L1
for x2 being Element of L2 st x1 = x2 holds
( uparrow x1 = uparrow x2 & downarrow x1 = downarrow x2 )
by WAYBEL_0:13;
theorem Th15: :: WAYBEL19:15
theorem Th16: :: WAYBEL19:16
theorem Th17: :: WAYBEL19:17
theorem Th18: :: WAYBEL19:18
theorem Th19: :: WAYBEL19:19
theorem Th20: :: WAYBEL19:20
theorem Th21: :: WAYBEL19:21
theorem Th22: :: WAYBEL19:22
theorem Th23: :: WAYBEL19:23
theorem Th24: :: WAYBEL19:24
theorem Th25: :: WAYBEL19:25
theorem Th26: :: WAYBEL19:26
theorem Th27: :: WAYBEL19:27
theorem Th28: :: WAYBEL19:28
:: deftheorem Def3 defines Lawson WAYBEL19:def 3 :
theorem Th29: :: WAYBEL19:29
theorem Th30: :: WAYBEL19:30
theorem Th31: :: WAYBEL19:31
theorem Th32: :: WAYBEL19:32
:: deftheorem Def4 defines lambda WAYBEL19:def 4 :
theorem Th33: :: WAYBEL19:33
theorem Th34: :: WAYBEL19:34
Lemma148:
for T being LATTICE
for F being Subset-Family of T st ( for A being Subset of T st A in F holds
A has_the_property_(S) ) holds
union F has_the_property_(S)
Lemma150:
for T being LATTICE
for A1, A2 being Subset of T st A1 has_the_property_(S) & A2 has_the_property_(S) holds
A1 /\ A2 has_the_property_(S)
Lemma153:
for T being LATTICE holds [#] T has_the_property_(S)
theorem Th35: :: WAYBEL19:35
theorem Th36: :: WAYBEL19:36
theorem Th37: :: WAYBEL19:37
theorem Th38: :: WAYBEL19:38
theorem Th39: :: WAYBEL19:39
theorem Th40: :: WAYBEL19:40
theorem Th41: :: WAYBEL19:41
theorem Th42: :: WAYBEL19:42
theorem Th43: :: WAYBEL19:43