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Proof step 61 from proof int2bytes-len-neg-01 (previous step)

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), n < 8, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, m * 8 + n ≤ 9 + 8 * i→n(i), n→i(m) * 8 + n→i(n) < 2 ⊦ m * 8 + n = 0, j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0, n = 1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i + j0 < j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [8, n→i(m), n→i(n), 0, 2] rotate: F spec: int-mult inst: name: modlsp-03

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ 0 ≤ n→i(n);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ n→i(n) ≤ 0 ↔ n = 0;% ⊦ n ≠ 1 → (n < 2 ↔ n = 0);% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = n + m;% ⊦ m * n = n * m;%0 ≤ i ⊦ (* i) ≤ n→i(n) ↔ i→n(i) ≤ n;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n;% ⊦ m ≤ m;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;%0 ≤ i ⊦ n→i(n) < (* i) ↔ n < i→n(i); Used terms: 8, n→i(m), n→i(n), 0, 2