proposition: Lemma flip_pos_negate x : 0 < x <-> -x < 0.
proof: Proof. split; intros E. - rewrite <- negate_0. apply flip_lt_negate. rewrite !involutive;trivial. - apply flip_lt_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