proposition: Lemma nonpos_plus_compat x y : x ≤ 0 -> y ≤ 0 -> x + y ≤ 0.
proof: Proof. intros. rewrite <-(plus_0_r 0). apply plus_le_compat;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