(*Lemma permDisjoint_sub: forall r1 r2 p,
      join_sub r2 r1 ->
      permDisjoint (perm_of_res r1) p ->
      permDisjoint (perm_of_res r2) p.
  Proof.*)

  (*Lemma join_permDisjoint: forall r1 r2 r3 p,
      join r1 r2 r3 ->
      permDisjoint (perm_of_res r1) p ->
      permDisjoint (perm_of_res r2) p ->
      permDisjoint (perm_of_res r3) p.
Proof.*)

  Definition permMapsDisjoint (pmap1 pmap2 : access_map) : Prop :=
    forall b ofs, exists pu,
      perm_union ((Maps.PMap.get b pmap1) ofs)
                 ((Maps.PMap.get b pmap2) ofs) = Some pu.

Lemma permMapsDisjoint2_comm: forall pmaps pmaps', permMapsDisjoint2 pmaps pmaps' <-> permMapsDisjoint2 pmaps' pmaps.