Proof of Lemma 1
If (i1, i2, ..., in) = (0, 0, ..., 0) => decision is 0.
If (i1, i2, ..., in) = (1, 1, ..., 1) => decision is 1.
Assume that each vector (i1, i2, ..., in) is univalent.
from all the above, there exists two starting vectors that are identical except of one entry for some processor p, where v0 is 0-valent and v1 is 1-valent.
Kill p at the beginning to reach a contradiction.