Please help me prove the following problem:
A unary function $f(x)$ is said to be partially $n$-computable if it is computed by some $\mathcal{S}$ program $\mathcal{P}$ such that $\mathcal{P}$ has no more than $n$ instructions, every variable in $\mathcal{P}$ is among $X, Y, Z_1, . . . , Z_n$ and every label in $\mathcal{P}$ is among $A_1,...,A_n,E$. Prove that if a unary function $f : N \rightarrow N$ is computed by a program with no more than $n$ instructions, then $f$ is partially $n$-computable.
This problem is in Chapter 2, Section 4 of Computability, Complexity, and Languages by M.Davis.
I am quite confused by this problem because the statement at the beginning and the question that needs to be proved are just two ways of saying the same thing. The statement is "q if p" and the question is "if p then q" which both mean "p implies q". So I totally don't understand what is asked to be proved here.