inversion H;simpl;tauto.
inversion H;simpl.
split;intro.
case H5;intro.
eapply insertion_in;rewrite H6 in H4;apply H4.
elim (IHl l'0 H2 x);intros.
eapply insertion_inclusion;eauto.
case (in_insertion_inv A x a l'0 l' H4 H5);intro.
rewrite H6;tauto.
elim (IHl l'0 H2 x);intros.
right;auto.
Qed.

(* Specifications: *)
Lemma permutation_insertion_aux : forall (A:Set)(l l' l'':list A)(x:A),(insertion A x l l')->(insertion A x l l'')->(is_permutation A l' l'').
intros.