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Proof step 7 from proof int2bytes-rec-neg-05 (previous step)

0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8) ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j)) = int2bytes(j / 2 ^ (i * 8) - 1) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
0 < j, i < 0, abs(i) < j ⊦ i / j = 0
Proof step 9:
0 < 2 ^ (i * 8) ∧ j < 0 ∧ abs(j) < 2 ^ (i * 8), 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8) ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j)) = int2bytes(0 - 1) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest

Rule argument

seq: 0 < j, i < 0, abs(i) < j ⊦ i / j = 0 subst: [j, i] → [2 ^ (i * 8), j] rotate: F spec: int-div inst: name: div-zero-01

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