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Proof step 1 from proof cond (conclusion)

n ≠ 0 ⊦ m / n * n ≤ m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m < m / n * n ⊦ n = 0, m / n = 0

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat