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Proof step 46 from proof int2bytes-len-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, # int2bits(j) ≤ i→n(8 * (i + 1)) + 1, 0 ≤ i ⊦ j + 2 ^ (8 * (i + 1)) = 0, # int2bits(j) / 8 + 1 = i→n(i + 2), # 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)% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ~ i = j ↔ i + j = 0;