for L being lower-bounded LATTICE holds
( ( L is algebraic implies ex X being non empty set ex S being full SubRelStr of BoolePoset X st
( S is infs-inheriting & S is directed-sups-inheriting & L,S are_isomorphic ) ) & ( ex X being set ex S being full SubRelStr of BoolePoset X st
( S is infs-inheriting & S is directed-sups-inheriting & L,S are_isomorphic ) implies L is algebraic ) )