proposition: Lemma mult_apart_zero_r x y : x * y ≶ 0 -> y ≶ 0.
proof: Proof. intros. apply (strong_extensionality (x *.)). rewrite mult_0_r. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.apartness HoTT.Classes.theory.rings