proposition: Lemma lee_pemull x y : 0 <= y -> 1 <= x -> y <= x * y.
proof: Proof. move: x y => [x| |] [y| |] //; last by rewrite mulyy. - by rewrite -EFinM 3!lee_fin; exact: ler_peMl. - move=> _; rewrite lee_fin => x1. by rewrite mulr_infty gtr0_sg ?mul1e// (lt_le_trans _ x1). - rewrite lee_fin le_eqVlt => /predU1P[<- _|y0 _]; first by rewrite mule0. by rewrite mulr_infty gtr0_sg// mul1e leey. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed