apply le_h_trans with (analysis_def h).
apply h_le_h_ana_h.
generalize (ana_h_equiv_irr_h h).
unfold equiv_h in |- *.
tauto.
Qed.

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