proposition: Lemma mult_apart_zero_l x y : x * y ≶ 0 -> x ≶ 0.
proof: Proof. intros. apply (strong_extensionality (.* y)). rewrite mult_0_l. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.apartness HoTT.Classes.theory.rings