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Proof step 8 from proof gcd-mod (previous step)

∀ n0, n. n0 < n → gcd(m * n + n0, n) = gcd(n, n0), n0 < n ⊦ gcd(m +1 * n + n0, n) = gcd(n, n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n0 < n, ∀ n0, n. n0 < n → gcd(m * n + n0, n) = gcd(n, n0) ⊦ gcd((n * m + n) + n0, n) = gcd(n, n0)

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%rsucc-02: ⊦ m * (n + 1) = m * n + m; from specification nat-mult%succ: ⊦ m +1 = m + 1; from specification nat-basic2