End Dom.
Section InDom.
Variables A B : Type.

(* Specifications: *)
Lemma in_dom_restrto :
forall (m:Map A) (m':Map B) (a:ad),
in_dom A a (MapDomRestrTo A B m m') =
andb (in_dom A a m) (in_dom B a m').
Lemma in_dom_restrby :
forall (m:Map A) (m':Map B) (a:ad),
in_dom A a (MapDomRestrBy A B m m') =
andb (in_dom A a m) (negb (in_dom B a m')).