inversion H;rewrite <- H3 in H0;inversion H0.
simpl in H7;trivial.
intro.
case H10;intro.
apply H9;rewrite H11;eapply insertion_in;apply H5.
elim (IHl l'0 x H5 H8 H11).
Qed.

(** if l is a set, x not in l and (insertion x l l') then l' is a set *)
Lemma insertion_is_set : forall (A:Set)(l:list A),(is_set _ l)->forall (x:A),~(In x l)->forall (l':list A),(insertion _ x l l')->(is_set _ l').
induction 1.