unfold is_irreducible in |- *.
unfold equal in |- *.
intros.
generalize (irr_incl_irr_irr h).
generalize (irr_irr_incl_irr h).
tauto.
Qed.

(** if g ~ h and g is irreducible then g is included in h *)
Theorem equiv_irr_impl_incl :
forall g h : hedge, equiv_h g h -> is_irreducible g -> inclusion g h.