I find that when proving a theorem by the method of contradiction, some authors start by saying "assume to the contrary" while some use "assume on the contrary". According to this post, it seems that "to the contrary" and "on the contrary" have subtle differences. So my question is which one should I use, "assume to the contrary" or "assume on the contrary"?
Below is an example.
Theorem. A is equal to B.
Proof: Assume on/to the contrary that A does not equal B. ...