proposition: Lemma ler_sqrt a b : 0 <= b -> (sqrt a <= sqrt b) = (a <= b).
proof: Proof. move=> b_ge0; have [a_le0|a_gt0] := ler0P a; last first. by rewrite ler_psqrt // nnegrE ltW. by rewrite ler0_sqrtr // sqrtr_ge0 (le_trans a_le0). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)