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.

Lemma nec_nat : forall (n n':nat),
@necR _ ag_nat n n' <-> n' <= n.