(** * [map] and [mapi] *)

Fixpoint map (f:elt -> elt') (m:t elt) : t elt' :=
  match m with
   | nil => nil
   | (k,e)::m' => (k,f e) :: map f m'
  end.Fixpoint mapi (f: key -> elt -> elt') (m:t elt) : t elt' :=
  match m with
   | nil => nil
   | (k,e)::m' => (k,f k e) :: mapi f m'
  end.

Lemma mapi_lelistA : forall (m: t elt)(x:key)(e:elt)(f:key->elt->elt'), lelistA (@ltk elt) (x,e) m -> lelistA (@ltk elt') (x,f x e) (mapi f m).