(* Disribuitivity of box over various connectives *)

(* Specifications: *)
Lemma box_and {A} `{ageable A}: forall R (P Q:pred A),
box R (P && Q) = box R P && box R Q.
Lemma box_all {A} `{ageable A} : forall B R (F:B -> pred A),
box R (allp F) = ALL x:B, box R (F x).
Lemma box_ex {A} `{ageable A} : forall B R (F:B->pred A),
EX x:B, box R (F x) |-- box R (exp F).
Lemma box_or {A} `{ageable A} : forall R (P Q:pred A),
box R P || box R Q |-- box R (P || Q).