Definition compatible m1 m2 := forall k v1 v2, m1 k = Some v1 -> m2 k = Some v2 -> v1 = v2.Global Instance compatible_refl : Reflexive compatible.Global Instance compatible_comm : Symmetric compatible.

Lemma map_incl_add : forall m1 m2, map_incl m1 (map_add m1 m2).