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Proof step 201 from proof int2bytes-rec-pos-any (previous step)

0 ≤ i ∧ 0 ≤ 8, (i→n(i) * i→n(8)) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = n * 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, n * 8 < i→n(i) * i→n(8) ⊦ i = 0, n * 8 = i→n(i) * i→n(8), i→n(i) * i→n(8) + 1 = n * 8, mklist(false, i→n(i) * i→n(8) - n * 8) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, i→n(i) * i→n(8) - n * 8) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, ¬ i→n(i) < n ∧ ¬ bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 202:
# int2bits(j % 2 ^ (i * 8)) = n * 8, bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0, n < i→n(i), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), 0 < i ⊦ bits2bytes(mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = n * 8, n = i→n(i), i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ m < n → ¬ n < m;% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;% ⊦ i * j = j * i;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m * n) % n = 0;