proposition: Lemma capture_captures {ff:falsity_flag} n m l q phi : bounded n phi -> l >= n - m -> bounded l (capture q m phi).
proof: Proof. intros H Hl. induction m in l,Hl|-*; cbn. - rewrite Nat.sub_0_r in *. now eapply (@bounded_up _ n). - constructor. eapply bounded_up; [apply IHm |]. 2: apply le_n. lia. Qed.
imports: Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability(Shared.ListAutomation Shared.Dec) Coq(Eqdep_dec PeanoNat) Coq.Vectors.Vector Undecidability.Shared.Libs.PSL.Vectors(Vectors) EqdepFacts