Proof with eauto with val_erasure erased.
destruct c; simpl...
Qed.

Lemma erased_updThreadC:
forall tp tp' i (cnti: containsThread tp i)
(cnti': containsThread tp' i) c c',
threadPool_erasure tp tp' ->
ctl_erasure c c' ->
threadPool_erasure (updThreadC cnti c)
(updThreadC cnti' c').