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Proof step 51 from proof int2bytes-first-zerobyte-01 (previous step)

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

Proof step 52:
j * i < j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0
Proof step 53:
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

Rule argument

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

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: 8, i, i0, j0