# A Post production system

1. Aug 2, 2011

### roam

I want to write a Post production system if we have the set of symbols {A,B} where all strings are wffs, and the set of theorems is $\{A^nB^{3n} : n\geq 1\}$. Would it the following system be correct:

• Alphabet is {A,B}

• The only Axiom is AB3.

• Rules of inference:
1. From x infer xAB3

For example, A2B6 is a theorem. To see this, we can provide the following derivation:

1. AB3 (Axiom)
2. AB3AB3 = A2B6 (From 1 by rule 2)

So, is my system correct? Are there better ways to make the rules as simple as possible?