proposition: Lemma negate_zero_prod_l x y : -x * y = 0 <-> x * y = 0.
proof: Proof. split; intros E. - apply (injective (-)). rewrite negate_mult_distr_l, negate_0. trivial. - apply (injective (-)). rewrite negate_mult_distr_l, negate_involutive, negate_0. trivial. Qed.
imports: HoTT.Classes.theory.groups HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra