Cauchy integral theorem and complex integral several equivalence relations

By document method, we get that Cauchy integral theorem actually is residue theorem that integrand functions as analytic function in integration region; Cauchy integral formula actually is the residue theorem that integrand has first order pole in integration region; derivatives of high order formula actually is the residue theorem that integrand has order pole in integration region. Make comparison summary on it, and effective combine with other documents, utilize Cauchy integral theorem to prove Cauchy integral formula, derivatives of high order formula, residue theorem, and find out their inner equivalence relations.