proposition: Lemma real_leif_mean_square x y : x \is real -> y \is real -> x * y <= mid (x ^+ 2) (y ^+ 2) ?= iff (x == y).
proof: Proof. move=> Rx Ry; rewrite -(mono_leif (ler_pM2r (ltr_nat F 0 2))). by rewrite divfK ?pnatr_eq0 // mulr_natr; apply: real_leif_mean_square_scaled. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)