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Proof step 3 from proof one (previous step)

⊦ n / n = 1, n = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: Divdef seq: ⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n subst: [n, m] → [n, n]

Additional information

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