:: YELLOW13 semantic presentation
theorem Th1: :: YELLOW13:1
theorem Th2: :: YELLOW13:2
theorem Th3: :: YELLOW13:3
theorem Th4: :: YELLOW13:4
theorem Th5: :: YELLOW13:5
theorem Th6: :: YELLOW13:6
theorem Th7: :: YELLOW13:7
theorem Th8: :: YELLOW13:8
theorem Th9: :: YELLOW13:9
theorem Th10: :: YELLOW13:10
theorem Th11: :: YELLOW13:11
theorem Th12: :: YELLOW13:12
theorem Th13: :: YELLOW13:13
theorem Th14: :: YELLOW13:14
theorem Th15: :: YELLOW13:15
Lemma79:
for T being non empty TopStruct
for A being Subset of T
for p being Point of T st p in Cl A holds
for K being Basis of p
for Q being Subset of T st Q in K holds
A meets Q
Lemma80:
for T being non empty TopStruct
for A being Subset of T
for p being Point of T st ( for K being Basis of p
for Q being Subset of T st Q in K holds
A meets Q ) holds
ex K being Basis of p st
for Q being Subset of T st Q in K holds
A meets Q
Lemma81:
for T being non empty TopStruct
for A being Subset of T
for p being Point of T st ex K being Basis of p st
for Q being Subset of T st Q in K holds
A meets Q holds
p in Cl A
theorem Th16: :: YELLOW13:16
theorem Th17: :: YELLOW13:17
:: deftheorem Def1 defines basis YELLOW13:def 1 :
:: deftheorem Def2 defines basis YELLOW13:def 2 :
theorem Th18: :: YELLOW13:18
theorem Th19: :: YELLOW13:19
:: deftheorem Def3 defines correct YELLOW13:def 3 :
theorem Th20: :: YELLOW13:20
theorem Th21: :: YELLOW13:21
theorem Th22: :: YELLOW13:22
theorem Th23: :: YELLOW13:23
:: deftheorem Def4 defines basis YELLOW13:def 4 :
theorem Th24: :: YELLOW13:24
theorem Th25: :: YELLOW13:25
theorem Th26: :: YELLOW13:26
theorem Th27: :: YELLOW13:27
:: deftheorem Def5 defines topological_semilattice YELLOW13:def 5 :
theorem Th28: :: YELLOW13:28