proposition: Lemma mult_apart_zero_r x y : x * y ≶ 0 → y ≶ 0.
proof: Proof. intros. apply (strong_extensionality (x *.)). now rewrite mult_0_r. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.theory.strong_setoids MathClasses.theory.rings