(***************************************************)
(** * Applying functions to the elements of a list *)
(***************************************************)
(************)
(** ** Map  *)
(************)
Section Map.
Variables (A : Type) (B : Type).
Variable f : A -> B.
Local Notation map := (@map A B f).

Lemma map_eq_app  : forall l l1 l2,
map l = l1 ++ l2 -> exists l1' l2', l = l1' ++ l2' /\ map l1' = l1 /\ map l2' = l2.