proposition: Lemma to_domain_mul x y : to_domain (x * y) = to_domain x i⊗ to_domain y.
proof: Proof. Proof using M_correct. revert y. induction x; intros; cbn. - symmetry. apply mul_zero. - rewrite mul_rec. rewrite to_domain_add. now repeat f_equal. Qed.
imports: PeanoNat Lia Vector Undecidability.SOL(SOL PA2) Undecidability.Shared.Libs.PSL(Vectors) Undecidability.SOL.Util(Syntax Subst Tarski) Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability.Shared.Dec