intro.
generalize (analysis_is_analysis (irreducible h)).
unfold is_analysis in |- *.
unfold analysis_cond in |- *.
intros.
elim H.
intros.
apply H1.
split.
unfold irreducible in |- *.
apply red_incl_h.
generalize (analysis_is_analysis h).
unfold is_analysis in |- *.
unfold analysis_cond in |- *.
tauto.
Qed.

(** I(I(h)) is included in I(h) *)
Lemma irr_irr_incl_irr :
forall h : hedge, inclusion (irreducible (irreducible h)) (irreducible h).