proposition: Lemma translate_form_bounded {ff:falsity_flag} n phi : bounded n phi <-> bounded n (translate_form phi).
proof: Proof. Proof using sig_funcs_dec sig_preds_dec. rewrite <- ! bounded_comp_eq. destruct (translate_bounded_full phi n) as [[H _] _]. symmetry. apply H. Qed.
imports: Vector Undecidability.FOL(Syntax.Facts) Undecidability.FOL.Semantics.Tarski(FullFacts FragmentFacts) Undecidability.FOL.Semantics.FiniteTarski(Full Fragment) Undecidability.Shared(Dec) Undecidability.Shared.Libs.PSL(Numbers) Coq(Arith Lia List) Undecidability.Shared.Libs.DLW.Wf(wf_finite) Undecidability.Synthetic(Definitions)