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Proof step 244 from proof int2bytes-rec-pos-any (previous step)

i→n(i) = m + 1 ∧ i→n(i) ≠ 0, m = 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 245:
0 ≤ bytes2int(bits2bytes(int2bits(j % 256))), 0 ≤ j, 0 < j, 256 ≤ j, # int2bits(j % 256) < 8 ⊦ bits2bytes(mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256)) = bits2bytes(int2bits(j % 256)), mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256) = [], 9 = # int2bits(j % 256), # int2bits(j % 256) = 8

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j;% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i = 1 → i * j = j;%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ i ≠ j → (i ≤ j ↔ i < j);