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Proof step 22 from proof int2bytes-rec-neg-04 (previous step)

i→n(i * 8) % 8 = 0, 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ j0 = 0, i = 0, bits2bytes(mklist(false, i→n(i * 8))) = fix(i→n(i) + 1, i2b(0) ').rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ n % 8 = 0 ∧ n ≠ 0 → bits2bytes(mklist(false, n)) = mklist(i2b(0), n / 8)
Proof step 24:
i→n(i * 8) % 8 = 0 ∧ i→n(i * 8) ≠ 0, i→n(i * 8) % 8 = 0, 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ j0 = 0, i = 0, mklist(i2b(0), i→n(i * 8) / 8) = fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

name: bits2bytes-mklist rotate: F subst: [n] → [i→n(i * 8)]

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i→n(i * 8)