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

Lemma xmap2_lr :
forall (A B : Type)(f g: option A -> option A -> option B)(m : t A),
(forall (i j : option A), f i j = g j i) ->
xmap2_l f m = xmap2_r g m.