proposition: Lemma up_decompose {ff : falsity_flag} sigma phi : phi[up (S >> sigma)][(sigma 0)..] = phi[sigma].
proof: Proof. rewrite subst_comp. apply subst_ext. intros []. - reflexivity. - apply subst_term_shift. Qed.
imports: Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability(Shared.ListAutomation Shared.Dec) Coq(Eqdep_dec PeanoNat Nat) Coq.Vectors.Vector Undecidability.Shared.Libs.PSL.Vectors(Vectors) EqdepFacts