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Proof step 39 from proof int2bytes-len-pos (previous step)

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

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, i, 1, n→i(m), n→i(n)] rotate: F spec: int-mult inst: name: modlsp-03

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0;% ⊦ abs(n→i(n)) = n→i(n);%0 ≤ i ⊦ n→i(n) < (* i) ↔ n < i→n(i);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false); Used terms: 8, i, 1, n→i(m), n→i(n)