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Proof step 30 from proof int2bytes-rec-neg-02 (previous step)

2 ^ (i * 8) = 0, j < 0, 0 < i, # int2bits(j % 0) ≤ i→n(i * 8) + 1 ⊦ bits2bytes(int2bits(j / 0 - 1) + (mklist(¬ 0 < j % 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest) = bits2bytes(int2bits(j / 0 - 1)) + fix(i→n(i) + 1, int2bytes(j % 0)).rest, j % 0 = 0, # (mklist(¬ 0 < j % 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest % 8 = 0 ∧ (mklist(j % 0 < 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest ≠ []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ 0 < j → (i ^ j = 0 ↔ i = 0)

Rule argument

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

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i * 8, 2