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Verification (Continued)

By function definition, we have four cases:

• m = 0.

  By (3), we have n != 0 and, by definition of gcd and Euclid,

  gcd(m, n) = n = Euclid(m, n)

  which implies (4).
• m != 0 /\  n = 0.

  We have, by definition of gcd and Euclid,

  gcd(m, n) = m = Euclid(m, n)

  which implies (4).