(*+ Collection of disjoint maps *)
(** For the proof of composition of safety, we need to maintain the invariants "all the maps are disjoint*" which is why we need this section.  * pairwise-disjointness is equivalent to arbitrary disjointness because the permissions are "set-theoretical" *)
Definition sameperms (m n : map) := forall x, m x = None <-> n x = None.

Lemma sameperms_trans m n o : sameperms m n -> sameperms n o -> sameperms m o.
Hint Resolve sameperms_refl sameperms_sym sameperms_trans.