Proof via induction for small-step semantics

Question

I'm doing a course in Computer Programming Languages and I'm trying to prove the following (roughly following Pierce's Types and Programming Languages book):

if $t \rightarrow^* t'$ then $if\; t\; then \; t2 \; else \; t3 \rightarrow^* if\; t'\; then \; t2 \; else \; t3$

I'm a little confused about where to start; as far as I know, I'm supposed to define a base case, then prove it via induction.

I've started my proof by assuming these base cases:

$P(\frac{}{true \rightarrow^* true})$ and $P(\frac{}{false \rightarrow^* false})$.

I'm stuck at this point, and I don't really how know to proceed.

edit: I've added the syntax in an effort to clear things up.