proposition: Lemma flip_nonpos_negate x : x ≤ 0 <-> 0 ≤ -x.
proof: Proof. pattern x at 1;apply (transport _ (negate_involutive x)). split; intros; apply flip_nonneg_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