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!