proposition: Lemma subst_falsity_comm {ff1 ff2} (phi : @form _ _ _ ff1) (psi : @form _ _ _ ff2) rho : phi[psi/⊥][rho] = phi[rho][psi[rho]/⊥].
proof: Proof. induction phi in rho,psi|-*. - easy. - easy. - cbn. rewrite IHphi1. rewrite IHphi2. easy. - cbn. f_equal. rewrite IHphi. f_equal. apply up_form. 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