End InDom.
Definition FSet := Map unit.
Section FSetDefs.
Variable A : Type.
Definition in_FSet : ad -> FSet -> bool := in_dom unit.
Fixpoint MapDom (m:Map A) : FSet :=
match m with
| M0 => M0 unit
| M1 a _ => M1 unit a tt
| M2 m m' => M2 unit (MapDom m) (MapDom m')
end.

Lemma MapDom_semantics_1 :
forall (m:Map A) (a:ad) (y:A),
MapGet A m a = Some y -> in_FSet a (MapDom m) = true.