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Proof step 32 from proof bits2bytes-mklist (previous step)

bits2bytes(mklist(false, n - 8)) = mklist(i2b(0), (n - 8) / 8), n % 8 = 0, 8 < n, ∀ n0. n0 < n → n0 % 8 = 0 → n0 = 0 ∨ bits2bytes(mklist(false, n0)) = mklist(i2b(0), n0 / 8) ⊦ i2b(0) ' + mklist(i2b(0), (n - 8) / 8) = mklist(i2b(0), n / 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
n ≠ 0 ⊦ n ≤ m → m / n = (m - n) / n + 1

Rule argument

seq: n ≠ 0 ⊦ n ≤ m → m / n = (m - n) / n + 1 subst: [n, m] → [8, n] rotate: F spec: nat-div inst: name: rec

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ mklist(by, m + n) = mklist(by, m) + mklist(by, n);% ⊦ mklist(by, 1) = by ';% ⊦ mklist(by, n) + by ' = by ' + mklist(by, n);% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ bytes + bytes0 = bytes + bytes1 ↔ bytes0 = bytes1; Used terms: 8, n