Let me corroborate the above question with an example:

input -> output
---------------
    2 -> 4
    4 -> 8
    8 -> 16
   16 -> 32

generated theorem, given that we already know how to handle multiplication:
*output = f(input) = input * 2*

This example coves only a specific set of integer inputs/outputs. The question 
is what is a common name for an app that generates theorems not only for 
integer inputs/outputs, but also theorems for data of any form, possibly 
ordered streams of bytes.

I assume that a theorem or a set of theorems  (possibly axioms) can describe 
any connection between a set of input and output streams of bytes.
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