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Proof step 9 from proof gcd-mod-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
m * m0 + 1 = n * n0, gcd(m, n) = 1, m0 ≤ n * n0 ⊦ (m * (n * n0 - m0)) % n = 1, m = 0, n = 1, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)