(** We define an infinite sequence (analysis_seq h n) where the n-th term
    is the n-th analysis of h *)
Fixpoint analysis_seq (h : hedge) (n : nat) {struct n} : hedge :=
  match n with
  | O => h
  | S n => analysis (analysis_seq h n)
  end.

(* Specifications: *)
Lemma analysis_seq_grow_S : forall (n : nat) (h : hedge), inclusion (analysis_seq h n) (analysis_seq h (S n)).
Lemma analysis_seq_grows : forall (p n : nat) (h : hedge), inclusion (analysis_seq h n) (analysis_seq h (p + n)).
Lemma analysis_seq_increase : forall (n m : nat) (h : hedge), n <= m -> inclusion (analysis_seq h n) (analysis_seq h m).