proposition: Lemma midf_le x y : x <= y -> (x <= mid x y) * (mid x y <= y).
proof: Proof. move=> lexy; rewrite ler_pdivlMr ?ler_pdivrMr ?ltr0Sn //. by rewrite !mulrDr !mulr1 !lerD2. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)