proposition: Lemma subst_comp {ff : falsity_flag} (phi : form) sigma tau : phi[sigma][tau] = phi[sigma >> subst_term tau].
proof: Proof. induction phi in sigma, tau |- *; cbn. - reflexivity. - f_equal. rewrite map_map. apply map_ext. intros s. apply subst_term_comp. - now rewrite IHphi1, IHphi2. - rewrite IHphi. f_equal. now apply subst_ext, up_funcomp. 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