proposition: Lemma flip_neg_negate x : x < 0 <-> 0 < -x.
proof: Proof. pattern x at 1;apply (transport _ (negate_involutive x)). split; intros; apply flip_pos_negate;trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings