Proof using.
intros.
apply locks_correct_implies_mutex.
auto using locks_correct_invariant.
Qed.

(* Specifications: *)
Lemma last_holder'_locked_some_eq :
forall tr h c n,
last_holder' h (tr ++ [(Client c, inr [Locked])]) = Some n ->
c = n.
Lemma last_holder'_locked_some_eq :
forall tr h c n,
last_holder' h (tr ++ [(Client c, inr [Locked])]) = Some n ->
c = n.