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Proof step 39 from proof int2bytes-len-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
0 < i, 1 + i→n(i) * 8 < # int2bits(~1), 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1) ⊦ i = 0, # int2bits(~1) / 8 = i→n(i), # int2bits(~1) % 8 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ 2 ^ i = 1 ↔ i = 0;% ⊦ i - j = i0 ↔ i = i0 + j;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ ¬ i < j ↔ j ≤ i;