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

Lemma finite_Ssafe_safe': (forall P : Prop, P \/ ~ P) -> (forall P : ST -> Prop, finite P -> finite (SST_step P)) -> forall P, (finite P) -> ( forall n : nat, safeN (ST -> Prop) SST_step n P) -> Ssafe P.