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Proof step 43 from proof int2bytes-rec-neg-02 (previous step)

0 ≤ i ∧ 0 ≤ 8, i→n(i) * i→n(8) + 1 = # int2bits(j % 2 ^ (i * 8)), 0 < i, j + 2 ^ (i * 8) < 0, j < 0, j % 2 ^ (i * 8) < 0 ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + int2bits(j % 2 ^ (i * 8)).rest) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, 2 ^ (i * 8) = 0, j % 2 ^ (i * 8) = 0, (i→n(i) * i→n(8)) % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)).rest ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
int2bits(j % 2 ^ (i * 8)).rest = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest = []

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes = bytes + bytes0 ↔ bytes0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ i * j = j * i;