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Proof step 5 from proof mod-once (previous step)

(m + n) / n * n ≤ m + n ⊦ m + n - (m + n) / n * n = m % n, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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