proposition: Lemma real_exprn_even_ge0 n x : x \is real -> ~~ odd n -> 0 <= x ^+ n.
proof: Proof. move=> xR even_n; have [/exprn_ge0 -> //|x_lt0] := real_ge0P xR. rewrite -[x]opprK -mulN1r exprMn -signr_odd (negPf even_n) expr0 mul1r. by rewrite exprn_ge0 ?oppr_ge0 ?ltW. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)