Remark poffset_monotone:
  forall p q, pge p q -> pge (poffset p) (poffset q).Remark provenance_monotone:
  forall x y, vge x y -> pge (provenance x) (provenance y).

Lemma vnormalize_monotone: forall chunk x y, vge x y -> vge (vnormalize chunk x) (vnormalize chunk y).