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Proof step 6 from proof mod-nle (previous step)

n1 < n0, n2 < n0, m0 < m, m * n0 + n2 ≤ m0 * n0 + n1 ⊦ m * n0 + n2 = m0 * n0 + n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m * n0 + n2 < m0 * n0 + n1, n1 < n0, n2 < n0, m0 < m ⊦ m * n0 + n2 = m0 * n0 + n1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)