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

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