Verify the statement made in the discussion of the Verhoeff check digit scheme based on D5 that a * σ(b) ≠ b * s(a) for distinct a and b. Use this to prove that σi(a) * σi+1(b) ≠ σi(b) * σi+1(a) for all i. Prove that this implies that all transposition errors involving adjacent digits are detected.
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