proposition: Lemma upper_nthrootVP (F : archiFieldType) (x : F) (i : nat) : 0 < x -> (Num.bound (x ^-1) <= i)%N -> 2%:R ^- i < x.
proof: Proof. move=> x_gt0 hx; rewrite -ltf_pinv -?topredE //= ?gtr0E //. by rewrite invrK upper_nthrootP. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrnum ssrint rat poly polydiv polyorder) mathcomp(perm matrix mxpoly polyXY binomial generic_quotient) mathcomp(cauchyreals separable zmodp bigenough)