proposition: Lemma subst_closed {ff : falsity_flag} phi sigma : closed phi -> phi[sigma] = phi.
proof: Proof. intros Hn. erewrite <- (@subst_id _ _ _ _ phi var) at 2. 2:easy. eapply bounded_subst. 1: apply Hn. lia. Qed.
imports: Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability(Shared.ListAutomation Shared.Dec) Coq(Eqdep_dec PeanoNat) Coq.Vectors.Vector Undecidability.Shared.Libs.PSL.Vectors(Vectors) EqdepFacts