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Proof step 8 from proof rounded-help (previous step)

m * n0 / m + m ≤ n0 + 1, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ n0 % m + 1 = m, m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
n ≠ 0, m / n * n ≤ m ⊦ m % n = m - m / n * n
Proof step 10:
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

Rule argument

spec: nat-div name: rax seq: n ≠ 0, m / n * n ≤ m ⊦ m % n = m - m / n * n subst: [n, m] → [m, n0] flags: <all paths>

Additional information

Used simplifier rules: n ≠ 0 ⊦ m / n * n ≤ m; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, n0