Definition MapsTo {elt} (k:key)(e:elt):= InA eqke (k,e).
Definition In {elt} k m := exists e:elt, MapsTo k e m.
#[global]
Hint Unfold MapsTo In : core.
(* Alternative formulations for [In k l] *)

Lemma In_alt2 {elt} k (l:list (key*elt)) :
In k l <-> Exists (fun p => D.eq k (fst p)) l.