5.3. The final steps🔗

The theorem eventual_sign_of_not_zerosAboveEveryHeight gives a constant sign beyond the zeros. The theorem tendsto_normalizedHardyIntegral proves the vanishing integral limit. The theorem not_positive_tail_of_vanishing_differences gives the integral contradiction. The theorem zerosAboveEveryHeight proves the existence of zeros above every height. The theorem hardy proves the exact infinitude statement.