Fixpoint MapCard (m:Map) : nat :=
match m with
| M0 => 0
| M1 _ _ => 1
| M2 m m' => MapCard m + MapCard m'
end.
Fixpoint MapMerge (m:Map) : Map -> Map :=
match m with
| M0 => fun m':Map => m'
| M1 a y => fun m':Map => MapPut_behind m' a y
| M2 m1 m2 =>
fun m':Map =>
match m' with
| M0 => m
| M1 a' y' => MapPut m a' y'
| M2 m'1 m'2 => M2 (MapMerge m1 m'1) (MapMerge m2 m'2)
end
end.

Lemma MapMerge_semantics :
forall m m':Map,
eqm (MapGet (MapMerge m m'))
(fun a0:ad =>
match MapGet m' a0 with
| Some y' => Some y'
| None => MapGet m a0
end).