proposition: Lemma ltr_pmul_le_r R (x1 y1 x2 y2 : R) : 0 < x1 -> 0 < x2 -> x1 < y1 -> x2 <= y2 -> x1 * x2 < y1 * y2.
proof: Proof. move=> Hx1 Hx2 Hx1y1 Hx2y2; rewrite mulrC [y1*y2]mulrC; exact: ltr_pmul_le_l. Qed.
imports: mathcomp(all_ssreflect all_algebra all_field) mathcomp(bigenough)