End FSubsetOrder.
Section MapSubsetExtra.
Variables A B : Type.

Lemma MapSubset_Put_behind_mono :
forall (m:Map A) (m':Map B) (a:ad) (y:A) (y':B),
MapSubset A B m m' ->
MapSubset A B (MapPut_behind A m a y) (MapPut_behind B m' a y').