intros.
apply equiv_h_trans with (analysis_def h).
unfold equiv_h in |- *.
split.
apply h_le_h_ana_h.
apply cond_irr_impl_le_h_ana; trivial.
apply ana_h_equiv_irr_h.
Qed.

(** if h satisfies cond_irr then I(h) is included in h *)
Lemma cond_irr_impl_irr_incl_h :
forall h : hedge, cond_irr h -> inclusion (irreducible h) h.