simple induction p.
simpl in |- *.
intros.
apply inclusion_refl.
intros.
replace (S n + n0) with (S (n + n0)); try auto with arith.
apply inclusion_trans with (analysis_seq h (n + n0)); trivial.
apply analysis_seq_grow_S.
Qed.

(** if n <= m then the n-th analysis of h is included in the m-th analysis of h *)
Lemma analysis_seq_increase :
forall (n m : nat) (h : hedge),
n <= m -> inclusion (analysis_seq h n) (analysis_seq h m).