proposition: Lemma pmulrn_rle0 x n : 0 < x -> x *+ n <= 0 = (n == 0)%N.
proof: Proof. by move=> x_gt0; rewrite -(mulr0n x) ler_pMn2l ?leqn0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)