intros.
apply equiv_irr_impl_incl.
apply equiv_h_sym.
apply cond_irr_impl_equiv_h_irr.
trivial.
apply irreducible_is_irreducible.
Qed.

(* Specifications: *)
Lemma cond_irr_impl_stable_reduce :
forall h : hedge, cond_irr h -> equal h (reduce h).