proposition: Lemma flip_nonneg_negate x : 0 ≤ x <-> -x ≤ 0.
proof: Proof. split; intros E. - rewrite <-negate_0. apply flip_le_negate. rewrite !involutive. trivial. - apply flip_le_negate. rewrite negate_0. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings