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Proof step 12 from proof mod-nle (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
n < n0, n1 < n, n2 < n0, m0 < m, n1 < n0, n1 + 1 < n0, m * n0 + n2 ≤ m0 * n + n1 ⊦ n = n0

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%trans-01: ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)