Proof using.
unfold locks_correct.
intros.
destruct (Name_eq_dec (Client c) (Client n)); rewrite_update; try find_inversion; auto.
Qed.

(* Specifications: *)
Lemma locks_correct_locked_at_head :
forall sigma p c,
pDst p = Client c ->
pBody p = Locked ->
locks_correct_locked sigma p ->
at_head_of_queue sigma c.
Lemma locks_correct_locked_at_head :
forall sigma p c,
pDst p = Client c ->
pBody p = Locked ->
locks_correct_locked sigma p ->
at_head_of_queue sigma c.