proposition: Lemma mid_between (a b: R): a < b -> a < half (a + b) < b.
proof: Proof. move => h. rewrite - half_lin - {1} (double_half a) - {3} (double_half b). by rewrite ltr_add2l ltr_add2r ltr_pmul2r ?h //invr_gt0 ltr0n. Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly ssrnum ssrint rat polyrcf) mathcomp(polyorder polydiv)