proposition: Lemma nonneg_plus_le_compat_l x z : 0 ≤ z <-> x ≤ z + x.
proof: Proof. rewrite (commutativity (f:=plus)). apply nonneg_plus_le_compat_r. 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