proposition: Lemma atom_subst_comp {Σ_preds2} {ff:falsity_flag} s rho phi : @atom_subst_respects Σ_preds2 _ s -> phi[s/atom][rho] = phi[rho][s/atom].
proof: Proof. intros Hresp. induction phi in s,rho,Hresp|-*. - easy. - cbn. rewrite Hresp. easy. - cbn. rewrite IHphi1. 1: now rewrite IHphi2. easy. - cbn. now rewrite IHphi. Qed.
imports: Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability(Shared.ListAutomation Shared.Dec) Coq(Eqdep_dec) Coq.Vectors.Vector Undecidability.Shared.Libs.PSL.Vectors(Vectors) EqdepFacts