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 laterR_level' {A} `{H : ageable A}: forall {w1 w2: A}, laterR w1 w2 -> @laterR _ ag_nat (level w1) (level w2).