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Proof step 136 from proof int2bytes-rec-neg-02 (previous step)

# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0, # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 ≤ i ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j % 2 ^ (i * 8))) = (mklist(i2b(~1), 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 137:
# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0, # bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i), 0 < i ⊦ i→n(i) = # bits2bytes(int2bits(j % 2 ^ (i * 8))), j % 2 ^ (i * 8) = 0, i = 0

Rule argument

Additional information

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