proposition: Lemma eqr_sqrt a b : 0 <= a -> 0 <= b -> (sqrt a == sqrt b) = (a == b).
proof: Proof. move=> a_ge0 b_ge0; apply/eqP/eqP=> [HS|->] //. by move: (sqr_sqrtr a_ge0); rewrite HS (sqr_sqrtr b_ge0). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)