Section Elt.
Variable elt:Type.
Definition Add x (e:elt) m m' := forall y, find y m' = find y (add x e m).
Notation eqke := (@eq_key_elt elt).
Notation eqk := (@eq_key elt).
Instance eqk_equiv : Equivalence eqk.
(** Complements about InA, NoDupA and findA *)

Lemma InA_eqke_eqk : forall k1 k2 e1 e2 l,
E.eq k1 k2 -> InA eqke (k1,e1) l -> InA eqk (k2,e2) l.