Inductive not_racy : option permission -> Prop :=
| empty : not_racy None.
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.