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Proof step 133 from proof int2bytes-rec-pos-any (previous step)

# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), 0 ≤ j % 2 ^ (i * 8), 0 < i, 2 ^ (i * 8) ≤ j, # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8))) = (mklist(i2b(0), i→n(i) + 1 - # bits2bytes(int2bits(j % 2 ^ (i * 8)))) + bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 134:
# int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) % 8 = 0, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), 2 ^ (i * 8) ≤ j, 0 < i, 0 ≤ j % 2 ^ (i * 8), # bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) ⊦ i→n(i) = # bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ m ≠ n → (m < n + 1 ↔ m < n);% ⊦ m ≤ n → (n - m = 0 ↔ n = m);% ⊦ mklist(by, m) = [] ↔ m = 0;% ⊦ bytes = bytes0 + bytes ↔ bytes0 = [];% ⊦ (by ' + bytes).rest = bytes;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ mklist(by, n) + by ' = by ' + mklist(by, n);% ⊦ mklist(by, 1) = by ';% ⊦ mklist(by, m + n) = mklist(by, m) + mklist(by, n);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ i * j = j * i;