hep-lat/0408047 and references

Theorem 1. (Grätzer and Knapp [1], [2]) Each finite slim planar semimodular lattice can be obtained from a cover-preserving join-homomorphic image of two finite chains. Proof. It is a trivial remark that every finite lattice L is the join-homomorphic image of a disztributive lattice B, ϕ(B) = L: ineed the free kommutative, idempotent semilattices are the finite Boolean lattices. If L is semimodular then ϕ is ”semimodular-preseving”. This is just the cover-preserving property, We have now a distributive lattice B and a cover-preserving join-homomorphism such that ϕ(B) = L. A short trivial discussion shows that B is planar