for L1, L2 being non empty reflexive antisymmetric up-complete RelStr st RelStr(# the carrier of L1, the InternalRel of L1 #) = RelStr(# the carrier of L2, the InternalRel of L2 #) & L1 is satisfying_axiom_K & ( for x being Element of L1 holds
( not compactbelow x is empty & compactbelow x is directed ) ) holds
L2 is satisfying_axiom_K