:: 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
Lemma11:
for b1 being non empty TopStruct
for b2 being Subset of b1
for b3 being Point of b1 holds
( b3 in Cl b2 implies for b4 being Basis of b3
for b5 being Subset of b1 holds
not ( b5 in b4 & not b2 meets b5 ) )
Lemma12:
for b1 being non empty TopStruct
for b2 being Subset of b1
for b3 being Point of b1 holds
not ( ( for b4 being Basis of b3
for b5 being Subset of b1 holds
not ( b5 in b4 & not b2 meets b5 ) ) & ( for b4 being Basis of b3 holds
ex b5 being Subset of b1 st
( b5 in b4 & not b2 meets b5 ) ) )
Lemma13:
for b1 being non empty TopStruct
for b2 being Subset of b1
for b3 being Point of b1 holds
( ex b4 being Basis of b3 st
for b5 being Subset of b1 holds
not ( b5 in b4 & not b2 meets b5 ) implies b3 in Cl b2 )
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