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_of_Map :
forall m:Map A, eqmap A (Map_of_alist (alist_of_Map m)) m.