Show error correction ability of a code

Question

Let u ∈ F_2^n. A binary code C of length n is said to correct the error pattern u if and only if, for all c,c'∈ C with c \ne c', we have d(c, c+u) < d(c', c+u). Assume that u1, u2 ∈ F_2^n agree in at least the positions where 1 occurs in u1. Suppose that C corrects the error pattern u2. Prove that C also corrects the error pattern u1.