proposition: Lemma paddr_eq0 (x y : R) : 0 <= x -> 0 <= y -> (x + y == 0) = (x == 0) && (y == 0).
proof: Proof. rewrite le0r; case/orP=> [/eqP->|hx]; first by rewrite add0r eqxx. by rewrite (gt_eqF hx) /= => hy; rewrite gt_eqF // ltr_pwDl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)