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

(* Derivable from the Map interface *)
Theorem gsspec:
forall (A:Type)(i j: key) (x: A) (m: t A),
find i (add j x m) = if E.eq_dec i j then Some x else find i m.