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.

Lemma safe_ksafe:
forall st,
(forall U : SCH, valid st U) ->
(forall U, safe st U) ->
(forall n U, ksafe st U n).