unfold equal in |- *.
intros.
unfold inclusion in |- *.
tauto.
Qed.

(* Specifications: *)
(** intersection is symmetric *)
Lemma inter_sym : forall g h : hedge, equal (inter g h) (inter h g).
unfold inter in |- *.
(** g is included in the union of g and h *)
Lemma hedge_left_union : forall g h : hedge, inclusion g (union g h).
unfold union in |- *.