Definition bytes_writable (loc: address) (size: Z) (phi: rmap) : Prop :=
  forall i, (0 <= i < size) -> writable (adr_add loc i) phi.Definition bytes_readable (loc: address) (size: Z) (phi: rmap) : Prop :=
  forall i, (0 <= i < size) -> readable (adr_add loc i) phi.

Lemma writable_dec: forall loc phi, {writable loc phi}+{~writable loc phi}.