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

Lemma erased_addThread:
forall tp tp' v arg v' arg' pmap pmap',
threadPool_erasure tp tp' ->
val_erasure v v' ->
val_erasure arg arg' ->
threadPool_erasure (addThread tp v arg pmap)
(addThread tp' v' arg' pmap').