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' (x,n) (x',n') <-> necR n n' /\ x = x'.
Lemma prod'_later_split : forall n x n' x', @laterR (prod A B) ag_prod' (x,n) (x',n') <-> laterR n n' /\ x = x'.