proposition: Lemma ltr_sqrt a b : 0 < b -> (sqrt a < sqrt b) = (a < b).
proof: Proof. move=> b_gt0; have [a_le0|a_gt0] := ler0P a; last first. by rewrite (leW_mono_in ler_psqrt)//; apply: ltW. by rewrite ler0_sqrtr // sqrtr_gt0 b_gt0 (le_lt_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)