proposition: Lemma nonneg_plus_lt_compat_l x y z : 0 ≤ z -> x < y -> x < z + y.
proof: Proof. intros. rewrite (commutativity (f:=plus)). apply nonneg_plus_lt_compat_r;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