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_3 : forall x x' l,
InA eqke x (x' :: l) -> ~ eqk x x' -> InA eqke x l.