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Proof step 35 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), 0 ≤ j, 0 ≤ i, 0 < i, 2 ^ (i * 8) ≤ j, 0 < j, i→n(i * 8) ≤ 8 * i→n(i) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 8 * i→n(i) - i→n(i * 8)) + int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, i→n(i * 8) % 8 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n - n + n1 = m - n1;