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Proof step 14 from proof int2bytes-rec-pos-any (previous step)

0 < j, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 1 + 8 * i→n(i), 0 ≤ i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(1 + 8 * i→n(i), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ 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: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [int2bits(j % 2 ^ (i * 8)), i→n(i * 8 + 1)] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used terms: int2bits(j % 2 ^ (i * 8)), i→n(i * 8 + 1)