Definition ag_prod :=
    mkAgeable (prod A B) levelAB age1AB ag_prod_facts.

(* Specifications: *)
Lemma prod_nec_split : forall n x n' x', @necR (prod A B) ag_prod (n,x) (n',x') <-> necR n n' /\ x = x'.
Lemma prod_later_split : forall n x n' x', @laterR (prod A B) ag_prod (n,x) (n',x') <-> laterR n n' /\ x = x'.
Lemma ag_prod'_facts : ageable_facts (prod A B) levelAB age1AB.