proposition: Lemma compose_lt x y z : 0 < z → y = x + z → x < y.
proof: Proof. intros E1 E2. rewrite E2. now apply pos_plus_lt_compat_r. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps