proposition: Lemma nonneg_plus_le_compat_r x z : 0 ≤ z <-> x ≤ x + z.
proof: Proof. pattern x at 1. apply (transport _ (plus_0_r x)). split; intros. - apply (order_preserving _). trivial. - apply (order_reflecting (x+)). trivial. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps