Is there a general poset representation that specializes to power set lattices in case of finite boolean algebras?

Question

I read here that every finite, complemented, distributive lattice is isomorphic to a power set lattice.

Is there a general order preserving mapping from a poset $P$ to a set inclusion poset $S$, such that

1. When $P$ is a distributive lattice, the meet and join in $S$ are set intersection and union.
2. When $P$ is also complemented, $S$ is complemented by set complement.
3. When $P$ is also finite, $S$ is a power set?

Which is the more general construction of this kind?