(** g is included in h iff whenever (M,N) is in g then (M,N) is in h *)
Definition inclusion (g h : hedge) := forall M N : Msg, g M N -> h M N.(** g = h iff g is included in h and h is included in g *)
Definition equal (g h : hedge) := inclusion g h /\ inclusion h g.

(* Specifications: *)
Lemma inclusion_refl : forall h : hedge, inclusion h h.
Lemma inclusion_trans : forall f g h : hedge, inclusion f g -> inclusion g h -> inclusion f h.
Lemma inclusion_antisym : forall f g : hedge, inclusion f g -> inclusion g f -> equal f g.
Lemma equal_refl : forall h : hedge, equal h h.
Lemma equal_sym : forall g h : hedge, equal g h -> equal h g.
Lemma equal_trans : forall f g h : hedge, equal f g -> equal g h -> equal f h.