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Proof step 7 from proof gcd-mod-one (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
m * m0 + 1 = n * n0, gcd(m, n) = 1 ⊦ n * n0 < m0, m = 0, n = 1, n = 0, (m * (n * n0 - m0)) % n = 1

Rule argument

fma: n * n0 < m0

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%ls-08: ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used formulas: n * n0 < m0