unfold inclusion in |- *.
tauto.
Qed.

(* Specifications: *)
(** h is included in the union of g and h *)
Lemma hedge_right_union : forall g h : hedge, inclusion h (union g h).
unfold union in |- *.
(** the intersection of g and h is included in g *)
Lemma inter_hedge_left : forall g h : hedge, inclusion (inter g h) g.
unfold inter in |- *.
(** the intersection of g and h is included in h *)
Lemma inter_hedge_right : forall g h : hedge, inclusion (inter g h) h.
unfold inter in |- *.
(** if f is included in h and g is included in h then the union of f and g is included in h *)
Lemma union_intro :
forall f g h : hedge,
inclusion f h -> inclusion g h -> inclusion (union f g) h.