Thurs Sotah 3

Tosfos quotes the Yerushalmi that there is an argument there if Kinoy is a permission or an obligation. R' Yehoshouh holds that he's permitted to Mikana but he's not obligated, while R' Eliezer holds he's obligated.

The Yerushalmi wants to say the argument depends on the argument what is grounds for divorce. R' Yehoshua holds like Bais Hillel that even burning his food is grounds for divorce. Therefore he's not obligated to Mikana her, since he has an option to just divorce her. However, R' Eliezer holds like Bais Shamai, the only grounds for divorce is that she definitely committed adultery (i.e., you have witnesses to the effect.) Here you don't have witnesses, so you don't have grounds for divorce, so you must Mikana her to permit her to you.

Tosfos asks: our Gemara says that R' Akiva holds it's an obligation to be Mikana, despite being the most lenient Shita about grounds for divorce. (He holds you may divorce a wife if you found a prettier woman.) So we see that the two arguments cannot be interdependent.