This paper studies, under substitutable and cardinal monotone preferences,
the lattice structure of the set S(P) of many-to-many pairwise-stable
matchings. It proves that the selection matchings are increasing functions on S(P).
This fact, along with a few auxiliary results, is then used to prove that SðPÞ is a
distributive lattice. The contribution of this paper is not new, but the alternative
proof is interesting as it avoids the use of abstract lattice theory.