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Proof step 5 from proof gcd-alldiv-h (previous step)

m ≤ n, m < n, n0 | n, n0 | m, ∀ n1, m, n0. n1 < n → m < n1 ∧ n0 | n1 ∧ n0 | m → n0 | gcd(m, n1) ⊦ n = 0, n0 | gcd(m, n - m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
m < n, n0 | n, n0 | m, ∀ n1, m, n0. n1 < n → m < n1 ∧ n0 | n1 ∧ n0 | m → n0 | gcd(m, n1) ⊦ n = 0, n0 | gcd(m, n - m)

Rule argument

Additional information

Used simplifier rules: lels-03: ⊦ m < n → m ≤ n; from specification nat