Notation eqke := (@eq_key_elt elt).
Notation eqk := (@eq_key elt).
Instance eqk_equiv : Equivalence eqk.
(** Complements about InA, NoDupA and findA *)

(* Specifications: *)
Lemma InA_eqke_eqk : forall k1 k2 e1 e2 l,
E.eq k1 k2 -> InA eqke (k1,e1) l -> InA eqk (k2,e2) l.
Lemma NoDupA_eqk_eqke : forall l, NoDupA eqk l -> NoDupA eqke l.
Lemma findA_rev : forall l k, NoDupA eqk l ->
findA (eqb k) l = findA (eqb k) (rev l).