proposition: Lemma decides_in_to_run_true: forall p L i, Decides p L -> L i -> Run (p i) true.
proof: Proof. intros. apply decides_to_recognizes in H. apply recognizes_in_to_run_true with (L:=L); auto. Qed.
imports: Coq.Setoids.Setoid Coq.Bool.Bool Coq.Logic.Classical_Prop