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Proof step 11 from proof gcd-mod-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
m * (n * n0 - m0) = m1 * n + n1, m * m0 + 1 = n * n0, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ m = 0, n = 1, n1 = 1

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)