proposition: Lemma FSAT_REL_BOUNDED_ONE_REL Σ n : (syms Σ -> False) -> (forall r : rels Σ, ar_rels _ r <= n) -> finite_t (rels Σ) -> discrete (rels Σ) -> FSAT Σ ⪯ᵢ FSAT (Σrel (S n)).
proof: Proof. intros H1 H2 H3 H4. eapply ireduces_transitive; [ apply FSAT_UNIFORM, H2 | ]. eapply ireduces_transitive; [ apply FSAT_ONE_REL; simpl; trivial | ]. apply FSAT_NOCST; simpl; auto. Qed.
imports: List Arith Bool Lia Eqdep_dec Undecidability.Synthetic.Definitions Undecidability.Synthetic.ReducibilityFacts Undecidability.Synthetic.InformativeDefinitions Undecidability.Synthetic.InformativeReducibilityFacts Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.Shared.Libs.DLW.Wf(wf_finite) Undecidability.FOL.TRAKHTENBROT(notations utils decidable bpcp fo_sig fo_terms fo_logic fo_sat red_utils Sig_discrete BPCP_SigBPCP Sig_rem_syms Sig_uniform Sig_one_rel Sig_rem_cst Sign_Sig2 Sig2_Sign Sign_Sig Sig_Sig_fin Sig2_SigSSn1 Sign1_Sig )