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Proof step 1 from proof mod-nle-01 (conclusion)

⊦ n0 < m0 ∧ n ≤ m ∧ n0 ≠ 0 → ¬ m0 * m + n0 ≤ m0 * n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m0 * m + n0 ≤ m0 * n, n0 < m0, n ≤ m ⊦ n0 = 0, m0 = 0

Rule argument

Additional information

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