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Proof step 32 from proof int2bytes-len-neg-01 (previous step)

i + 2 < n→i(n0), 0 ≤ i, 0 < j + 2 ^ (8 * (i + 1)), j + 2 ^ (8 * (i + 1) - 1) < 0, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0, n→i(n0) * 8 < 2 + 8 * (n→i(n0) - 1), 0 < j + 2 ^ (8 * (n→i(n0) - 1)) ⊦ n0 = 0, n0 * 8 = 1, n0 = 2 + i→n(i)

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i < j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [8, n→i(n0), n→i(n0) - 1, 2] rotate: F spec: int-mult inst: name: modlsp

Additional information

Used simplifier rules: ⊦ i < j + i0 ∧ ¬ j0 < j → i < j0 + i0;% ⊦ i * j = j * i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i ≥ 0 → ((* i) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m);% ⊦ m + m0 ≤ m ↔ m0 = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 8, n→i(n0), n→i(n0) - 1, 2