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Proof step 11 from proof mod-nle (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n < n0, m0 < m, m * n0 + n2 ≤ m0 * n + n1, n1 < n0, n1 < n, n2 < n0, n1 + 1 < n0 ⊦ n = 0, n0 = 0, m = 0, n = n0

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat