#[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_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.