proposition: Lemma gt_1_mult_lt_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 (strictly_order_preserving_pos (.*.) y). Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps