Module WP := WProperties_fun E M.  (* More useful stuff about maps *)
Print Module WF.
Print Module WP.
Check E.lt. (*   : positive -> positive -> Prop *)
(** [E.lt] is a comparison predicate on [positive] numbers.  It is _not_ the usual less-than operator; it is a different ordering that is more compatible with the order that a Positive Trie arranges its keys.  In the application of certain lemmas about maps and sets, we will need the facts that [E.lt] is a [StrictOrder] (irreflexive and transitive) and respects a congruence over equality (is [Proper] for [eq ==> eq ==> iff]).   As shown here, we just have to dig up these facts from a submodule of a submodule of a submodule of [M]. *)

Lemma lt_strict: StrictOrder E.lt.