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Proof step 39 from proof int2bytes-rec-neg-06 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i + 1 ≠ 0 → (~1 ≤ i ↔ 0 ≤ i) subst: [i] → [j] rotate: F spec: int-abs inst: name: mone-07

Additional information

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