User blog comment:LittlePeng9/FOOT is not as strong as I thought/@comment-5529393-20161225200516/@comment-1605058-20170127191948

We still need to prove theorems of the form "* implies ..." if we want S to interpret T+* - after all, "* implies ..." is also a theorem of T+*, if it's a theorem of T. Every theorem of T is a theorem of T+*, so it's not like we need less theorems when dealing with T+* than with T.

Quite the opposite, actually - to interpret T+* we have to prove *, which is a theorem of T+*, but not of T.