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Proof step 66 from proof int2bytes-rec-pos-any (previous step)

# fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, 0 < i, 2 ^ (i * 8) ≤ j, 2 ^ (i * 8) ≤ j % 2 ^ (i * 8), 0 < j % 2 ^ (i * 8) ⊦ bits2bytes(fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j → ¬ j ≤ i % j subst: [i, j] → [j, 2 ^ (i * 8)] rotate: F spec: int-div inst: name: mod-les

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; Used terms: j, 2 ^ (i * 8)