Prove that a comparison network with n inputs correctly sorts the input sequence n, n - 1,...,

Question:

Prove that a comparison network with n inputs correctly sorts the input sequence ⁪¬n, n - 1,..., 1¬ if and only if it correctly sorts the n - 1 zero-one sequences ⁪¬1, 0, 0,..., 0, 0⁪¬, ⁪¬1, 1, 0,..., 0, 0¬⁪,..., ¬⁪1, 1, 1,..., 1, 0¬⁪.