generalize (insertion_length A l' l'' x H0);intro;congruence.
Qed.

(* Specifications: *)
Lemma insertion_permutation_eq : forall (A:Set)(l l':list A)(x:A),(insertion A x l' l)->forall (l'':list A),(insertion A x l'' l)->(is_permutation A l' l'').
induction l;intros;inversion H.