proposition: Lemma from_alg_crealK (x : {alg {alg F}}) : (to_alg_creal (to_alg_creal (from_alg_creal x)) == x%:CR)%CR.
proof: Proof. apply: eq_crealP; exists_big_modulus m {alg {alg F}}. move=> e i e_gt0 hi; unlock from_alg_creal=> /=. by rewrite (@asympt1modP _ _ (asympt_approx2 x)). 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)