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

Lemma not_racy_union :
forall p1 p2 (Hnot_racy: not_racy p1),
exists pu, perm_union p1 p2 = Some pu.