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Proof step 2 from proof gcd-le-both-h (previous step)

m < n ⊦ m = 0, n = 0, ¬ m < gcd(m, n) ∧ ¬ n < gcd(m, n)

User applied rule induction

And obtained the following new goals

Proof step 3:
m < n, ∀ n0, m. n0 < n → m < n0 → m = 0 ∨ n0 = 0 ∨ ¬ m < gcd(m, n0) ∧ ¬ n0 < gcd(m, n0) ⊦ m = 0, n = 0, ¬ m < gcd(m, n) ∧ ¬ n < gcd(m, n)

Rule argument

indvar: n wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: n