proposition: Lemma real_exprn_even_le0 n x : x \is real -> ~~ odd n -> (x ^+ n <= 0) = (n != 0) && (x == 0).
proof: Proof. move=> xR n_even; rewrite !real_leNgt ?rpred0 ?rpredX //. by rewrite real_exprn_even_gt0 // negb_or negbK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)