proposition: Lemma real_leif_mean_square_scaled x y : x \is real -> y \is real -> x * y *+ 2 <= x ^+ 2 + y ^+ 2 ?= iff (x == y).
proof: Proof. move=> Rx Ry; rewrite -[_ *+ 2]add0r -leifBRL addrAC -sqrrB -subr_eq0. by rewrite -sqrf_eq0 eq_sym; apply: leif_eq; rewrite -realEsqr rpredB. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)