Definition no_preds (r: resource) :=
match r with NO => True | YES _ _ pp => pp=NoneP | PURE _ pp => pp=NoneP end.

Lemma ageN_resource_at_eq:
forall phi1 phi2 loc n phi1' phi2',
level phi1 = level phi2 ->
phi1 @ loc = phi2 @ loc ->
ageN n phi1 = Some phi1' ->
ageN n phi2 = Some phi2' ->
phi1' @ loc = phi2' @ loc.