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