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 power_set_finite {X}:
(forall P : Prop, P \/ ~ P) ->
forall P: X-> Prop, finite P ->
finite (fun A => subset A P).