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Proof step 207 from proof int2bytes-rec-neg-05 (previous step)

# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, 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 208:
⊦ # bytes < n ∧ bytes2int(bytes) < 0 → fix(n, bytes) = mklist(i2b(~1), n - # bytes) + bytes
Proof step 209:
¬(# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0), # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, 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
Proof step 217:
# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0, # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, j % 2 ^ (i * 8) < 0, 0 ≤ i ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j % 2 ^ (i * 8))) = (mklist(i2b(~1), i→n(i) + 1 - # bits2bytes(int2bits(j % 2 ^ (i * 8)))) + bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: fix-neg rotate: F subst: [bytes, n] → [bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1]

Additional information

Used terms: bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1