End filtered_konig.
Section Safety.
Context (ST:Type)(SCH:Type).
Context (STEP:ST->SCH->ST->SCH-> Prop).
Context (valid: ST-> SCH -> Prop).
Hypothesis em: forall P, P \/ ~ P.

(* This is too weak... but is a good example*)
Lemma SsafeN_Ssafe:
(forall P: Prop, P \/ ~ P) ->
forall P,
(forall P, finite (SST_step P)) ->
(forall n, SsafeN n P) ->
Ssafe P.