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Proof step 4 from proof ls (previous step)

m = m0 * n + n1 ∧ n1 < n, m0 < m / n0, n ≤ n0 ⊦ n = 0, m / n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n1 < n0, n ≤ n0, m0 < (m0 * n + n1) / n0, n1 < n ⊦ (m0 * n + n1) / n0 = 0, n = 0, n0 = 0

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1