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

Lemma no_race_racy : forall p1 p2 (Hracy: racy p1)
(Hnorace: exists pu, perm_union p1 p2 = Some pu),
not_racy p2.