proposition: Lemma asympt_approx2 x : { asympt e : i / `|(approx2 x i)%:RA%:RA - x| < e }.
proof: Proof. exists_big_modulus m {alg {alg F}}. move=> e i e_gt0 hi; rewrite distrC /approx2. rewrite (@split_dist_add _ (approx x (2%:R ^- i))%:RA) //. rewrite approxP ?gtr0E // ltW //. by rewrite upper_nthrootVP ?divrn_gt0 ?ltr_to_alg. rewrite (lt_trans _ (inf_lt_alg _)) ?divrn_gt0 //. rewrite -rmorphB -normr_to_alg ltr_to_alg approxP ?gtr0E // ltW //. by rewrite upper_nthrootVP ?divrn_gt0 ?inf_alg_gt0 ?ltr_to_alg. by close. 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)