induction H;simpl;tauto.
Qed.

(* Specifications: *)
(** if (insertion x l l') then l is included in l' *)
Lemma insertion_inclusion : forall (A:Set)(x:A)(l l':list A),(insertion A x l l')->forall (y:A),(In y l)->(In y l').
induction l;simpl;try tauto;intros.