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Proof step 19 from proof int2bytes-rec-neg-03 (previous step)

0 ≤ j0, 2 ^ (i * 8) * (j0 + 1) < 0, 0 < i ⊦ int2bytes(j0) = int2bytes((j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8)), 2 ^ (i * 8) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 < i → (i * j < 0 ↔ j < 0)

Rule argument

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

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);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j0 + 1, 2 ^ (i * 8)