proposition: Lemma midf_lt x y : x < y -> (x < mid x y) * (mid x y < y).
proof: Proof. move=> ltxy; rewrite ltr_pdivlMr ?ltr_pdivrMr ?ltr0Sn //. by rewrite !mulrDr !mulr1 !ltrD2. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)