Proof using.
intros.
apply last_holder'_unlock_none. auto.
Qed.

(* Specifications: *)
Lemma last_holder_some_unlock_inv :
forall tr h c n,
last_holder' h (tr ++ [(Client c, inl Unlock)]) = Some n ->
last_holder' h tr = Some n.
Lemma last_holder_some_unlock_inv :
forall tr h c n,
last_holder' h (tr ++ [(Client c, inl Unlock)]) = Some n ->
last_holder' h tr = Some n.