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Proof step 4 from proof int2bytes-rec-neg-05 (previous step)

0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ 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 5:
⊦ j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i ≠ 0 → int2bits(j) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest
Proof step 6:
¬(j ≤ ~(2 ^ (i * 8)) ∧ 0 < i * 8 ∧ j % 2 ^ (i * 8) ≠ 0), 0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ 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
Proof step 87:
j ≤ ~(2 ^ (i * 8)) ∧ 0 < i * 8 ∧ j % 2 ^ (i * 8) ≠ 0, 0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8) - 1) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest

Rule argument

seq: ⊦ j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i ≠ 0 → int2bits(j) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest subst: [j, i] → [j, i * 8] rotate: F spec: int2bits inst: name: int2bits-rec-2pot-neg-02

Additional information

Used terms: j, i * 8