Fixpoint Map_of_alist (l:alist) : Map A :=
match l with
| nil => M0 A
| (a, y) :: l' => MapPut A (Map_of_alist l') a y
end.

Lemma Map_of_alist_semantics :
forall l:alist, eqm A (alist_semantics l) (MapGet A (Map_of_alist l)).