proposition: Lemma pos_plus_lt_compat_r x z : 0 < z <-> x < x + z.
proof: Proof. pattern x at 1;apply (transport _ (plus_0_r x)). split; intros. - apply (strictly_order_preserving _);trivial. - apply (strictly_order_reflecting (x+));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