Error-correcting code proof

I can do examples fine to show that the following statement works, but I can't prove it for the life of me. If anyone is familiar in the area of Coding Theory, I would really appreciate some help. I am dealing with binary code.

Let $\displaystyle u_1$ and $\displaystyle u_2$ be error patterns of length $\displaystyle n$, and assume that $\displaystyle u_1$ and $\displaystyle u_2$ agree at least in the positions where a 1 occurs in $\displaystyle u_1$. Prove that if a code $\displaystyle C$ will correct $\displaystyle u_2$, then $\displaystyle C$ will also correct $\displaystyle u_1$.

Thanks for looking!