Section NAT_AGEABLE.
Definition natLevel (x:nat) : nat := x.
Definition natAge1 (x:nat) : option nat :=
match x with
| 0 => None
| S n => Some n
end.
Definition natUnage (x:nat) : nat := S x.
Definition ag_nat : ageable nat :=
mkAgeable nat natLevel natAge1 ag_nat_facts.
End NAT_AGEABLE.

Lemma necR_nat {A} `{H : ageable A}:
forall {x y: A}, necR x y -> @necR nat ag_nat (level x) (level y).