intros.
apply cond_irr_impl_irreducible.
apply consistent_impl_cond_irr.
trivial.
Qed.

(* Specifications: *)
(** if g ~ h, g is consistent and h is consistent then g = h *)
Theorem equiv_consistent_consistent_equal :
forall g h : hedge,
equiv_h g h -> is_consistent g -> is_consistent h -> equal g h.