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Proof step 26 from proof int2bytes-len-neg (previous step)

¬(j < 0 ∧ 0 ≤ 8 * i ∧ ~ j ≠ 2 ^ (8 * i)), j + 2 ^ (8 * i) ≤ 0, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, 0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1) ⊦ # int2bits(j) % 8 = 0, # int2bits(j) / 8 = i→n(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
j + 2 ^ (8 * i) = 0, j < 0, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j ⊦ # int2bits(j) / 8 = i→n(i), # int2bits(j) % 8 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ i + j ≤ i ↔ j ≤ 0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ ~ i = j ↔ i + j = 0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;