# Proof of Small-Step Semantics property

I'm trying to solve the exercise 2.20 from the book "Semantics with Applications" by Nielson & Nielson. The request is the following:

Exercise 2.20 Suppose that (S1;S2,s) =>* (S2,s'). Show that is not necessarily the case that (S1,s) =>* s'.

I suppose that the proof should use induction on the length of the derivation sequence, but I don't even know where to start.

I attach here the table defining the semantics used.

• How is $\Rightarrow *$ defined? Is it transitive reflective closure of $\Rightarrow$ relation? – Apoorv Feb 21 at 2:46