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Proof step 38 from proof int2bytes-len-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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