intros.
apply le_h_trans with (analysis_def h).
apply le_h_trans with (analysis_def g).
generalize (ana_h_equiv_irr_h g).
unfold equiv_h in |- *; tauto.
apply le_h_ana_le_h; trivial.
generalize (ana_h_equiv_irr_h h).
unfold equiv_h in |- *; tauto.
Qed.

(* Specifications: *)
(** if g ~ h then I(g) = I(h) *)
Theorem equiv_h_impl_irr_unique :
forall g h : hedge, equiv_h g h -> equal (irreducible g) (irreducible h).