 states that the protocol solves the task if and only if there is a continuous  carried by  . The claim follows because  .  Applying the Discrete Protocol Complex Lemma (0.0.0):  Corollary 0.0.0  _The colorless task_   _has an_  - _resilient layered snapshot protocol if and only if there is a subdivision_   _of_   _and a simplicial map_  _carried by_  .  Theorem 0.0.0  _There is no_  - _