proposition: Lemma falsity_to_pred_subst {ff:falsity_flag} phi rho : falsity_to_pred (phi[rho]) = (falsity_to_pred phi)[rho].
proof: Proof. unfold falsity_to_pred. rewrite subst_falsity_comm. cbn. now rewrite atom_subst_comp. 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