Is it permissible for a husband to divorce his wife if he is certain of her betrayal, but he does not possess conclusive proof of it?

The fundamental principle is that a person is innocent and pure. It is obligatory to have a good opinion and not to spy. However, if strong indications emerge pointing to wrongdoing, and suspicion recurs, then caution and prudence must be exercised, and avenues of corruption must be cut off. If the matter reaches a strong indication of corruption, then divorce is preferable. In such a case, it is not obligatory to obey the father in not divorcing.