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Proof step 46 from proof int2bytes-first-zerobyte-01 (previous step)

0 ≤ j0 + 8 * i0 - 2, 0 ≤ j0, 0 ≤ j, j0 < 8, 0 < j0 + 8 * i0, j0 + 8 * i0 - 2 < j0 + 8 * i0 - 1, j < 2 ^ (j0 + 8 * i0 - 1), 2 ^ (j0 + 8 * i0 - 2) ≤ j, 0 < i0 ⊦ i0 = 0, 8 * i→n(i0) = 1, i→n(j0) + 8 * i→n(i0) = 0, j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
2 ≤ j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) ≤ j, j < 2 ^ (j0 + 8 * i0 - 1), 0 < j0 + 8 * i0, j0 < 8, 0 ≤ j, 0 ≤ j0, 0 < i0 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j), i→n(j0) + 8 * i→n(i0) = 0, 8 * i→n(i0) = 1, i0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * 0 = 0;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;