Corollary SsafeN_ksafe: forall n st,
      SsafeN n (@P_init st) -> forall U, valid st U -> ksafe st U n.

Lemma SsafeN_Ssafe: (forall P: Prop, P \/ ~ P) -> forall P, (forall P, finite (SST_step P)) -> (forall n, SsafeN n P) -> Ssafe P.