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Proof step 49 from proof int2bytes-rec-neg-03 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
j = i0 * 2 ^ (i * 8) + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 2 ^ (i * 8) ∧ i0 ≤ 0 ∧ 0 < 2 ^ (i * 8), 0 < i, j + 2 ^ (i * 8) < 0, j < ~1, j < 0 ⊦ 2 ^ (i * 8) = 0, j0 = 0, int2bytes(i0 - 1) = int2bytes((j + 1) / 2 ^ (i * 8) - 1)

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [j, 2 ^ (i * 8), i0, j0] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

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