proposition: Lemma funcfree_bounded_func phi : funcfree phi -> forall x ar, bounded_func x ar phi.
proof: Proof. intros F. induction phi; intros x ar'; cbn. 1,3-6: firstorder. apply Forall_in. intros v H. apply funcfree_bounded_func_term. eapply Forall_in in F. apply F. easy. Qed.
imports: Undecidability.SOL.SOL Undecidability.Shared.Dec Undecidability.Shared.Libs.PSL(Vectors) Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) EqdepFacts Eqdep_dec