If a man sees his wife committing zina and does not establish the evidence

Question:
Honorable Shaykh, what do you say if a man sees with his own eyes that his wife is committing zina and he is unable to establish the evidence? Is it permissible for him to remain with her while he knows in the depths of his heart that she committed zina?

Answer:
And between two matters: either he files a claim against her before the judge and li'an (mutual oath-swearing) is performed between them, as the Prophet (peace and blessings be upon him) did, or he divorces her. Allah made divorce your number, so let the Muslim look, let him look, let him decide.
But if, when he divorces her, he fears that the child will be attributed to him, and he is performing li'an for the sake of the child's lineage, whereas if there is no child, he divorces her and is relieved of her and is safe from, I mean, the establishment of li'an and these difficult procedures; he divorces her and is relieved. And if there is a child and he sees that the child is from him, he does not get rid of it except through li'an.