proposition: Lemma to_alg_creal_repr (x : {alg F}) : (to_alg_creal (repr x) == x%:CR)%CR.
proof: Proof. apply: eq_crealP; exists_big_modulus m {alg F}. move=> e i e_gt0 hi /=; rewrite (le_lt_trans _ (inf_lt_alg _)) //. rewrite -{2}[x]reprK !piE sub_pi norm_pi. rewrite -(rwP (le_algP _ _)) norm_algcrealE /=; pose_big_enough j. apply: (@le_crealP _ j)=> k hk /=. by rewrite ltW // cauchymodP ?inf_alg_gt0. by close. 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)