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Proof step 132 from proof int2bytes-rec-neg-02 (previous step)

# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 ≤ i ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 133:
⊦ bytes2int(bytes) = bits2int(bytes2bits(bytes))
Proof step 134:
# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 ≤ bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))), 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 ≤ i ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: bytes2int rotate: F subst: [bytes] → [bits2bytes(int2bits(j % 2 ^ (i * 8)))]

Additional information

Used terms: bits2bytes(int2bits(j % 2 ^ (i * 8)))