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Proof step 5 from proof gcd-mod (previous step)

n0 < n ⊦ gcd(m0 * n + n0, n) = gcd(n, n0)

User applied rule structural induction

And obtained the following new goals

Proof step 6:
n0 < n ⊦ gcd(0 * n + n0, n) = gcd(n, n0)
Proof step 9:
n0 < n, ∀ n0, n. n0 < n → gcd(m * n + n0, n) = gcd(n, n0) ⊦ gcd(m +1 * n + n0, n) = gcd(n, n0)

Rule argument

indvar: m0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;