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Proof step 1 from proof mod-nle (conclusion)

⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m * n0 + n2 ≤ m0 * n + n1, m0 < m, n ≤ n0, n2 < n0, n1 < n, n1 < n0 ⊦ m = 0, n0 = 0, n = 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