proposition: Lemma sinE : sin = fun x => lim (pseries (fun n => (odd n)%:R * (-1) ^+ n.-1./2 * (n`!%:R)^-1) x @ \oo).
proof: Proof. by apply/funext => x; rewrite /pseries -sin_coeffE. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) reals ereal nsatz_realtype signed topology normedtype landau sequences derive realfun exp