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Proof step 161 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 162:
# int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), 0 < i, i→n(i) ≤ # int2bits(j % 2 ^ (i * 8)) / 8 ⊦ bits2bytes(mklist(false, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, mklist(false, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), i = 0, # int2bits(j % 2 ^ (i * 8)) % 8 = 0

Rule argument

Additional information

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