proposition: Theorem FSAT_FUNnREL1_ANY Σ n f r : ar_syms Σ f = n -> ar_rels Σ r = 1 -> FSAT (Σn1 n) ⪯ᵢ FSAT Σ.
proof: Proof. intros H1 H2. apply ireduces_dependent. intros A. exists (Σn1_Σ _ _ _ H1 H2 A). apply Σn1_Σ_correct. 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 )