Inductive not_racy : option permission -> Prop :=
  | empty : not_racy None.Inductive not_racy : option permission -> Prop :=
  | empty : not_racy None.Inductive racy : option permission -> Prop :=
  | freeable : racy (Some Freeable).Inductive racy : option permission -> Prop :=
  | freeable : racy (Some Freeable).

Lemma perm_order_incompatible: forall p p' (Hreadable: Mem.perm_order'' p (Some Readable)) (Hwritable: Mem.perm_order'' p' (Some Writable)), perm_union p p' = None.