proposition: Lemma alg_to_crealP (x : algdom) : creal_axiom (to_algcreal_of (annul_algdom x) (center_alg x) (radius_alg x)).
proof: Proof. pose_big_modulus m F. exists m=> e i j e_gt0 hi hj. wlog leij : i j {hi} hj / (j <= i)%N. move=> hwlog; case/orP: (leq_total i j)=> /hwlog; last exact. by rewrite distrC; apply. rewrite (le_lt_trans (to_algcreal_ofP _ _ _ _)) ?radius_alg_ge0 //. rewrite ltr_pdivr_mulr ?gtr0E // -ltr_pdivr_mull //. by rewrite upper_nthrootP. 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)