#[global]
 Instance MapsTo_compat {elt} :
   Proper (D.eq==>Logic.eq==>equivlistA eqke==>iff) (@MapsTo elt).#[global]
 Instance In_compat {elt} : Proper (D.eq==>equivlistA eqk==>iff) (@In elt).

(* Specifications: *)
Lemma MapsTo_eq {elt} (l:list (key*elt)) x y e : D.eq x y -> MapsTo x e l -> MapsTo y e l.
Lemma In_eq {elt} (l:list (key*elt)) x y : D.eq x y -> In x l -> In y l.
Lemma In_inv {elt} k k' e (l:list (key*elt)) : In k ((k',e) :: l) -> D.eq k k' \/ In k l.
Lemma In_inv_2 {elt} k k' e e' (l:list (key*elt)) : InA eqk (k, e) ((k', e') :: l) -> ~ D.eq k k' -> InA eqk (k, e) l.
Lemma In_inv_3 {elt} x x' (l:list (key*elt)) : InA eqke x (x' :: l) -> ~ eqk x x' -> InA eqke x l.