Let D1 be the set of chickens pecked by the king, vk. Let D2 be the set of chickens virtually
pecked by the king, but not pecked directly. Thus, each chicken in D2 was pecked
by some chicken in D1. Since vk is a king, this accounts for all the chickens; that is, {vk},
D1, and D2 form a partition of the set of chickens {v1, . . . , vn}. The situation is represented
schematically below.