proposition: Lemma lte_pmul2r z : z \is a fin_num -> 0 < z -> {mono *%E^~ z : x y / x < y}.
proof: Proof. move: z => [z| |] _ // z0 [x| |] [y| |] //. - by rewrite !lte_fin ltr_pM2r. - by rewrite mulr_infty gtr0_sg// mul1e 2!ltry. - by rewrite mulr_infty gtr0_sg// mul1e ltNge leNye ltNge leNye. - by rewrite mulr_infty gtr0_sg// mul1e ltNge leey ltNge leey. - by rewrite mulr_infty gtr0_sg// mul1e mulr_infty gtr0_sg// mul1e. - by rewrite mulr_infty gtr0_sg// mul1e 2!ltNyr. - by rewrite mulr_infty gtr0_sg// mul1e mulr_infty gtr0_sg// mul1e. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed