proposition: Lemma alg_archi : Num.archimedean_axiom [numDomainType of {alg F}].
proof: Proof. move=> x; move: {x}`|x| (normr_ge0 x) => x x_ge0. pose a := approx x 1%:RA; exists (Num.bound (a + 1)). have := @archi_boundP _ (a + 1); rewrite -ltr_to_alg rmorph_nat. have := @approxP x _ _ ltr01 (lexx _); rewrite ltr_distl -/a => /andP [_ hxa]. rewrite -ler_to_alg rmorphD /= (le_trans _ (ltW hxa)) //. by move=> /(_ isT) /(lt_trans _)->. 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)