:: WAYBEL33 semantic presentation
:: deftheorem defines lim_inf WAYBEL33:def 1 :
theorem :: WAYBEL33:1
:: deftheorem Def2 defines lim-inf WAYBEL33:def 2 :
theorem Th2: :: WAYBEL33:2
theorem Th3: :: WAYBEL33:3
theorem Th4: :: WAYBEL33:4
theorem Th5: :: WAYBEL33:5
theorem Th6: :: WAYBEL33:6
theorem Th7: :: WAYBEL33:7
Lm3:
for L1, L2 being up-complete /\-complete Semilattice st RelStr(# the carrier of L1,the InternalRel of L1 #) = RelStr(# the carrier of L2,the InternalRel of L2 #) holds
the topology of (ConvergenceSpace (lim_inf-Convergence L1)) c= the topology of (ConvergenceSpace (lim_inf-Convergence L2))
theorem :: WAYBEL33:8
theorem Th9: :: WAYBEL33:9
theorem Th10: :: WAYBEL33:10
:: deftheorem Def3 defines Xi WAYBEL33:def 3 :
theorem Th11: :: WAYBEL33:11
theorem Th12: :: WAYBEL33:12
theorem Th13: :: WAYBEL33:13
Lm4:
for L being LATTICE
for F being non empty Subset of (BoolePoset ([#] L)) holds { [a,f] where a is Element of L, f is Element of F : a in f } c= [:the carrier of L,(bool the carrier of L):]
theorem Th14: :: WAYBEL33:14
theorem Th15: :: WAYBEL33:15
theorem Th16: :: WAYBEL33:16
theorem Th17: :: WAYBEL33:17
theorem Th18: :: WAYBEL33:18
theorem Th19: :: WAYBEL33:19
theorem Th20: :: WAYBEL33:20
theorem Th21: :: WAYBEL33:21
theorem Th22: :: WAYBEL33:22
theorem Th23: :: WAYBEL33:23
theorem Th24: :: WAYBEL33:24
theorem Th25: :: WAYBEL33:25
theorem Th26: :: WAYBEL33:26
theorem :: WAYBEL33:27