proposition: Lemma real_leif_AGM2_scaled x y : x \is real -> y \is real -> x * y *+ 4 <= (x + y) ^+ 2 ?= iff (x == y).
proof: Proof. move=> Rx Ry; rewrite sqrrD addrAC (mulrnDr _ 2) -leifBLR addrK. exact: 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)