End PositiveMap.
(** Here come some additional facts about this implementation. Most are facts that cannot be derivable from the general interface. *)
Module PositiveMapAdditionalFacts.

Theorem map2_commut:
forall (A B: Type) (f g: option A -> option A -> option B),
(forall (i j: option A), f i j = g j i) ->
forall (m1 m2: t A),
_map2 f m1 m2 = _map2 g m2 m1.