#[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).

Lemma In_inv_3 {elt} x x' (l:list (key*elt)) :
InA eqke x (x' :: l) -> ~ eqk x x' -> InA eqke x l.