for L1, L2 being complete LATTICE st RelStr(# the carrier of L1, the InternalRel of L1 #) = RelStr(# the carrier of L2, the InternalRel of L2 #) holds
for X1 being non empty Subset of L1
for X2 being non empty Subset of L2
for F1 being Filter of (BoolePoset X1)
for F2 being Filter of (BoolePoset X2) st F1 = F2 holds
lim_inf F1 = lim_inf F2