Definition In k m := exists e:elt, MapsTo k e m.
#[local]
Hint Unfold MapsTo In : core.
(* An alternative formulation for [In k l] is [exists e, InA eqk (k,e) l] *)

Lemma In_inv_2 : forall k k' e e' l,
InA eqk (k, e) ((k', e') :: l) -> ~ eq k k' -> InA eqk (k, e) l.