theorem Th4: :: WAYBEL33:4

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
for N1 being net of L1
for N2 being net of L2 st RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of N2, the InternalRel of N2 #) & the mapping of N1 = the mapping of N2 holds
lim_inf N1 = lim_inf N2