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Proof step 50 from proof int2bytes-first-zerobyte-01 (previous step)

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, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
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, 2 ^ (8 * i - 1) ≤ j, j < 2 ^ (8 * i), j0 + 8 * i0 < 2 + 8 * i, 0 ≤ i, 8 * i < j0 + 8 * i0, 0 < i ⊦ i→n(j0) + 8 * i→n(i0) = 0, 8 * i→n(i0) = 1, i0 = 0, j0 = 1

Rule argument

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ 0 < i ∧ j < 0 → ((* j) < (* i) * i0 ↔ (j + 1 - i) / i < i0);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i - j < i0 ↔ i < j + i0;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ 2 ^ (i - 1) < 2 ^ i ↔ 0 ≤ i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i * j = j * i;