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Proof step 65 from proof rightshift-8-01-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ 0 < i → (i * j < 0 ↔ j < 0)
Proof step 67:
¬ 0 < j0, 0 ≤ 2 ^ (8 * abs(j)) * (j0 + 1), 2 ^ (8 * abs(j) - 1) + j0 * 2 ^ (8 * abs(j)) < 0, j0 * 2 ^ (8 * abs(j)) < 0 ⊦ j0 = ~1, int2bytes(j0 * 2 ^ (8 * abs(j))).first = i2b(~1), j = 0, 2 ^ (8 * abs(j)) = 0

Rule argument

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

Additional information

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