#[local]
Hint Immediate eqk_sym eqke_sym : core.
Global Instance eqk_equiv : Equivalence eqk.
#[local]
Hint Resolve InA_eqke_eqk : core.

Lemma InA_eqk : forall p q m, eqk p q -> InA eqk p m -> InA eqk q m.
Definition MapsTo (k:key)(e:elt):= InA eqke (k,e).