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

Lemma remLock_updThread_comm:
forall ds,
forall i (cnti: containsThread ds i) c map l,
forall (cnti': containsThread (remLockSet ds l) i),
remLockSet
(updThread cnti c map)
l =
updThread cnti' c map.