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

Thanks for looking!