#[local]
Hint Resolve InA_eqke_eqk : ordered_type.
Definition MapsTo (k:key)(e:elt):= InA eqke (k,e).
Definition In k m := exists e:elt, MapsTo k e m.
Notation Sort := (sort ltk).
Notation Inf := (lelistA ltk).
#[local]
Hint Unfold MapsTo In : ordered_type.
(* An alternative formulation for [In k l] is [exists e, InA eqk (k,e) l] *)

(* Specifications: *)
Lemma In_alt : forall k l, In k l <-> exists e, InA eqk (k,e) l.
Proof with auto with ordered_type.