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Proof step 238 from proof int2bytes-rec-neg-05 (previous step)

8 ≤ 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)), ((8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8))) % 8 = 0, 8 < (8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8, 0 < i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i) ⊦ j % 2 ^ (i * 8) = 0, mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), i = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = (bits2bytes(mklist(true, 8)) + bits2bytes(restn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)))) + int2bits(j % 2 ^ (i * 8)))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 239:
⊦ n % 8 = 0 ∧ n ≠ 0 → bits2bytes(mklist(true, n)) = mklist(i2b(~1), n / 8)
Proof step 240:
8 % 8 = 0 ∧ 8 ≠ 0, 8 ≤ 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)), ((8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8))) % 8 = 0, 8 < (8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8, 0 < i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i) ⊦ j % 2 ^ (i * 8) = 0, mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), i = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = (mklist(i2b(~1), 8 / 8) + bits2bytes(restn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)))) + int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: bits2bytes-mklist-02 rotate: F subst: [n] → [8]

Additional information

Used simplifier rules: ⊦ i * j = j * i;%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, n -1);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m ≤ n → restn(m, mklist(boolvar, n)) = mklist(boolvar, n - m);% ⊦ m * n = n * m;% ⊦ m + n = n + m;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ m < n → m ≤ n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 8