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Proof step 5 from proof rounded-help (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
n ≠ 0 ⊦ m % n + 1 = n → (m + 1) / n = m / n + 1
Proof step 7:
m * (n0 + 1) / m + m ≤ n0 + 1, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ m = 0, m ≠ 0 ∧ n0 % m + 1 = m
Proof step 12:
n0 % m + 1 = m, m * (n0 / m + 1) + m ≤ n0 + 1, ∀ m. m * n0 / m + m ≤ n0 → m = 0 ⊦ m = 0

Rule argument

spec: nat-div name: div-succ seq: n ≠ 0 ⊦ m % n + 1 = n → (m + 1) / n = m / n + 1 subst: [n, m] → [m, n0] flags: <all paths>

Additional information

Used terms: m, n0