unfold remLockSet, updThread; simpl; intros.
f_equal.
Qed.

(* Specifications: *)
Lemma remLock_updThreadC_comm :
forall ds i (cnti: containsThread ds i) c l
(cnti': containsThread (remLockSet ds l) i),
remLockSet (updThreadC cnti c) l = updThreadC cnti' c.