u r } are (2n + 5)-scattered wrt. Im(g) 2. ?j, k > i, let a j ? {x j , x j }. Then dist Ti (g(a j ), g(x k )) ? min ,

,

, Let them be such that dist T0 (g(x j ), g(x k )) ? 2n + 5, and let's prove that dist W0 (g(x j ), g(x k )) ? dist T0 (g(x j ), g(x k )). it goes through at least one S-edge: the first time it does

,