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

m * n0 + n2 ≤ m0 * n0 + n1, m0 < m, n2 < n0, n1 < n0 ⊦ m * n0 + n2 = m0 * n0 + n1, m = 0, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
m0 < m, n2 < n0, n1 < n0, m * n0 + n2 < m0 * n0 + n1 ⊦ m * n0 + n2 = m0 * n0 + n1, m = 0, n0 = 0, m0 * n0 + n1 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat