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Proof step 10 from proof rounded-help (previous step)

m * n0 / m + m ≤ n0 + 1, n0 / m * m ≤ n0, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ (n0 - n0 / m * m) + 1 = m, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
m * n0 / m + m ≤ n0, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ n0 + 1 = n0 / m * m + m, m = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ m / n * n ≤ m; (s)