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Proof step 2 from proof ls-03 (previous step)

n0 / n + 1 < (n0 + n) / n ⊦ n = 0, (n0 + n) / n = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n
Proof step 4:
n ≠ 0 → (n0 + n) / n * n ≤ n0 + n ∧ n0 + n < ((n0 + n) / n)+1 * n, n0 / n + 1 < (n0 + n) / n ⊦ n = 0, (n0 + n) / n = 0

Rule argument

spec: nat-div inst: name: Divdef seq: ⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n subst: [n, m] → [n, n0 + n] flags: current, []

Additional information

Used terms: n, n0 + n