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 Ssafe_safe: forall st_init,
(forall U, valid st_init U) ->
Ssafe (@P_init st_init) -> forall U, safe st_init U.