simple induction n.
simpl in |- *.
intros.
unfold inclusion in |- *.
intros.
apply AnaInc; trivial.
intros.
simpl in |- *.
unfold inclusion in |- *.
intros.
apply AnaInc.
trivial.
Qed.

(** the n-th analysis of h is included in the (n+p)-th analysis of h *)
Lemma analysis_seq_grows :
forall (p n : nat) (h : hedge),
inclusion (analysis_seq h n) (analysis_seq h (p + n)).