proposition: Lemma eval_encoding alpha rho p : @eval _ _ (M_domain Standard_Model) _ ⟨alpha, get_func rho, get_pred rho⟩ (encode_polynomial p) = dp_eval_pfree alpha p.
proof: Proof. induction p; cbn. - induction n. reflexivity. cbn. now repeat f_equal. - reflexivity. - destruct d; cbn; now repeat f_equal. Qed.
imports: PeanoNat Lia Vector List Undecidability.SOL(SOL PA2) Undecidability.Shared.Libs.PSL(Vectors) Undecidability.SOL.Util(Syntax Subst Tarski PA2_facts PA2_categoricity) Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability.H10(H10p) Undecidability.Shared.Dec