Galois connections and complete lattices

Does anyone have a reference for the following fact? Consider posets P and Q which intersect in a complete lattice L. Let F:P-->L<=Q be the closure operator and G:Q-->L<=P be the kernel operator corresponding to L. Then F and G form an Galois connection. Moreover, every Galois connection is of this form (of course, the posets need not actually intersect in L, it is enough that they have subposets which are copies of L). Joshua Meyers [For admin and other information see: http://www.mta.ca/~cat-dist/ ]