proposition: Lemma ge_1_mult_le_compat_r x y z : 1 ≤ z → 0 ≤ y → x ≤ y → x ≤ y * z.
proof: Proof. intros. transitivity y; [easy |]. rewrite <-(mult_1_r y) at 1. now apply (order_preserving_nonneg (.*.) y). Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps