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Proof step 42 from proof int2bytes-len-pos (previous step)

j < 2 ^ (n→i(m) * 8 + n→i(n) - 1), 2 ^ (n→i(m) * 8 + n→i(n) - 2) ≤ j, n < 8, 0 < j, j < 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 2 ^ (8 * i) ≤ j, n→i(m) * 8 + n→i(n) ≤ 8 * (i + 1), 0 ≤ j, 8 * i + 1 < n→i(m) * 8 + n→i(n), 1 < n→i(m) * 8 + n→i(n), 0 < n→i(m) * 8 + n→i(n), 8 * i + 1 < 8 * (i + 1), i ≤ n→i(m) ⊦ m * 8 + n = 0, m = i→n(i), 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), i + 1, 2] rotate: F spec: int-mult inst: name: modlsp-03

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ n→i(n);%0 ≤ i ⊦ n→i(n) < (* i) ↔ n < i→n(i);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * j0;% ⊦ i * j * j0 = (i * j) * j0; Used terms: 8, n→i(m), n→i(n), i + 1, 2