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Proof step 16 from proof gcd-mod-one (previous step)

m0 * m = n * n0 - 1, m * m0 + 1 = n * n0, (n * n0) * m - (n * n0 - 1) = m1 * n + n1, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ m = 0, n = 1, n1 = 1

User applied rule cut formula

And obtained the following new goals

Proof step 17:
m0 * m = n * n0 - 1, m * m0 + 1 = n * n0, n * (n0 * m - n0) + 1 = (n * n0) * m - (n * n0 - 1), (n * n0) * m - (n * n0 - 1) = m1 * n + n1, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ m = 0, n = 1, n1 = 1
Proof step 20:
m0 * m = n * n0 - 1, m * m0 + 1 = n * n0, (n * n0) * m - (n * n0 - 1) = m1 * n + n1, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ n * (n0 * m - n0) + 1 = (n * n0) * m - (n * n0 - 1), m = 0, n = 1, n1 = 1

Rule argument

fma: n * (n0 * m - n0) + 1 = (n * n0) * m - (n * n0 - 1)

Additional information

Used formulas: n * (n0 * m - n0) + 1 = (n * n0) * m - (n * n0 - 1)