proposition: Lemma to_alg_crealP (x : creal F) : creal_axiom (fun i => to_alg F (x i)).
proof: Proof. exists_big_modulus m (alg F). move=> e i j e_gt0 hi hj. rewrite -rmorphB -normr_to_alg (lt_trans _ (inf_lt_alg _)) //. by rewrite ltr_to_alg cauchymodP ?inf_alg_gt0. 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)