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Proof step 1 from proof gcd-mult (conclusion)

⊦ gcd(n0 * m, n0 * n) = n0 * gcd(m, n)

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ n1, m1, n2. n1 * m1 + n1 * n2 < n0 * m + n0 * n → true → gcd(n1 * m1, n1 * n2) = n1 * gcd(m1, n2) ⊦ gcd(n0 * m, n0 * n) = n0 * gcd(m, n)

Rule argument

indvar: n0 * m + n0 * n wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: n0 * m + n0 * n