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Proof step 27 from proof int2bytes-len-pos-01 (previous step)

n→i(m) ≤ i + 1, i < n→i(m), j < 2 ^ (n→i(m) * 8 + n→i(n) - 1), 2 ^ (n→i(m) * 8 + n→i(n) - 2) ≤ j, n < 8, 0 ≤ i, j < 2 ^ (8 * (i + 1)), 2 ^ (8 * (i + 1) - 1) ≤ j, n→i(m) * 8 + n→i(n) < 2 + 8 * (i + 1), 0 ≤ j, 8 * (i + 1) < n→i(m) * 8 + n→i(n), 0 < n→i(m) * 8 + n→i(n) ⊦ m = 0, m * 8 + n = 0, n = 0, m + 1 = i→n(i + 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
n→i(m) = i + 1, 0 ≤ i, j < 2 ^ (8 * (i + 1)), 2 ^ (8 * (i + 1) - 1) ≤ j, 0 ≤ j, j < 2 ^ ((i + 1) * 8), 2 ^ ((i + 1) * 8 - 1) ≤ j ⊦ m = 0, m + 1 = i→n(i + 2)

Rule argument

Additional information

Used simplifier rules: ⊦ i + 0 = i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m ≤ m;% ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i ≤ i;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ m ≠ 0 → (m < 2 ↔ m = 1);%0 ≤ i ⊦ n→i(n) < (* i) ↔ n < i→n(i);% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ i * (j + i0) < i * (j0 + i0) + j1 ↔ i * j < i * j0 + j1;% ⊦ i + (j - i) = j;% ⊦ i - j < i0 ↔ i < j + i0;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1);% ⊦ i + j = j + i;% ⊦ i * j = j * i;