proposition: Lemma plus_lt_compat_l x y z : 0 < z -> x < y -> x < z + y.
proof: Proof. rewrite (commutativity (f:=plus)). apply plus_lt_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