#[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 {elt} k k' e (l:list (key*elt)) : In k ((k',e) :: l) -> D.eq k k' \/ In k l.