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Proof step 52 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ int2bytes(i) = bits2bytes(int2bits(i))
Proof step 54:
# fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8))) + bits2bytes(fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = bits2bytes(int2bits(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 = []

Rule argument

name: int2bytes rotate: F subst: [i] → [j / 2 ^ (i * 8)]

Additional information

Used terms: j / 2 ^ (i * 8)