inversion H;simpl;try tauto.
case H0;try tauto.
right;auto.
Qed.

(** if x is in l, then there is l' such that (insertion x l' l) *)
Lemma in_insertion : forall (A:Set)(x:A)(l:list A),(In x l)->exists l':list A,(insertion A x l' l).
induction l;simpl;try tauto;intros.