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Proof step 68 from proof rightshift-8-01-01 (previous step)

j0 < 0, 2 ^ (8 * abs(j) - 1) + j0 * 2 ^ (8 * abs(j)) < 0, 0 ≤ 2 ^ (8 * abs(j)) * (j0 + 1) ⊦ j0 = 0, 2 ^ (8 * abs(j)) = 0, j = 0, int2bytes(j0 * 2 ^ (8 * abs(j))).first = i2b(~1), j0 = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j)

Rule argument

seq: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j) subst: [j, i] → [j0 + 1, 2 ^ (8 * abs(j))] rotate: F spec: int-mult inst: name: zero-ge

Additional information

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