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Proof step 4 from proof int2bytes-rec-neg-01 (previous step)

j % 2 ^ (i * 8) = 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(int2bits(j)) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').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) + 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, j % 2 ^ (i * 8) = 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

seq: ⊦ j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i = 0 → int2bits(j) = int2bits(j / 2 ^ i) + 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-01

Additional information

Used simplifier rules: ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i < j → ¬ j < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j * j0 = (i * j) * j0; Used terms: j, i * 8