proposition: Lemma flip_negate x y : -x = y <-> x = -y.
proof: Proof. split; intros E. - rewrite <-E, involutive. trivial. - rewrite E, involutive. trivial. Qed.
imports: HoTT.Classes.theory.groups HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra