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Proof step 54 from proof int2bytes-len-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
n < 8, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, m * 8 + n ≤ i→n(8 * (i + 1)) + 1, 0 ≤ i, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, 8 * (i + 1) < n→i(m) * 8 + n→i(n) ⊦ m * 8 + n = 0, j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0, m = 0 ∧ n = 1

Rule argument

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i - j < i0 ↔ i < j + i0;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 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;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ n→i(m * n) = n→i(m) * n→i(n);% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);