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

n ≤ (n * m + n) + n0, n0 < n, ∀ n0, n. n0 < n → gcd(m * n + n0, n) = gcd(n, n0) ⊦ gcd((n * m + n) + n0 - n, n) = gcd(n, n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n0 < n, ∀ n0, n. n0 < n → gcd(m * n + n0, n) = gcd(n, n0) ⊦ gcd(n * m + n0, n) = gcd(n, n0)

Rule argument

Additional information

Used simplifier rules: lep: ⊦ m ≤ m + n; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq-01: ⊦ m + n - m = n; from specification nat