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Proof step 53 from proof int2bytes-first-zerobyte-01 (previous step)

i ≤ i0, 2 ≤ j0 + 8 * i0, 2 ^ (j0 + 8 * i0 - 2) ≤ j, j < 2 ^ (j0 + 8 * i0 - 1), 0 < j0 + 8 * i0, j0 < 8, 0 ≤ j, 0 ≤ j0, 0 < i0, 2 ^ (8 * i - 1) ≤ j, j < 2 ^ (8 * i), j0 + 8 * i0 < 2 + 8 * i, 0 ≤ i, 8 * i < j0 + 8 * i0, 0 < i ⊦ i→n(j0) + 8 * i→n(i0) = 0, 8 * i→n(i0) = 1, i0 = 0, j0 = 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, i0, j0, i, 2] rotate: F spec: int-mult inst: name: modlsp-03

Additional information

Used simplifier rules: ⊦ i < j + i0 ∧ ¬ j0 < j → i < j0 + i0;% ⊦ i * j = j * i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j = j + i;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ 0 < j → (j < 2 ↔ j = 1); Used terms: 8, i0, j0, i, 2