(** Useful tactic for simplifying expressions like [In y (add x e (remove z m))] *)

Ltac map_iff :=
 repeat (progress (
  rewrite add_mapsto_iff || rewrite add_in_iff ||
  rewrite remove_mapsto_iff || rewrite remove_in_iff ||
  rewrite empty_mapsto_iff || rewrite empty_in_iff ||
  rewrite map_mapsto_iff || rewrite map_in_iff ||
  rewrite mapi_in_iff)).

Lemma map2_1bis : forall (m: t elt)(m': t elt') x (f:option elt->option elt'->option elt''), f None None = None -> find x (map2 f m m') = f (find x m) (find x m').