(* Box and diamond are positive modal operators *)

(* Specifications: *)
Lemma box_positive {A} `{ageable A} : forall M (P Q:pred A),
P |-- Q ->
box M P |-- box M Q.
Lemma diamond_positive {A} `{ageable A} : forall M (P Q:pred A),
P |-- Q ->
diamond M P |-- diamond M Q.
Lemma box_refl_trans {A} `{ageable A}: forall (m:modality) p,
reflexive _ m ->
transitive _ m ->
box m (box m p) = box m p.