I'm trying to solve a proof problem related to Frege's construction of number. The problem is:
Show that, for any numbers x and y, if S*xy, z is the successor of x and w is the successor of y, then S*zw. [Hint. Given an S-hereditary concept F that holds of z, define an S-hereditary concept that holds of x. Be careful to be explicit on how you’re using the fact that S is one-one.]
If anyone could solve this or give me some direction I'd appreciate it.