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Proof step 122 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), 0 ≤ j % 2 ^ (i * 8), 0 < i, 2 ^ (i * 8) ≤ j, # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i) ⊦ 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 123:
⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fix(n, bytes) = mklist(i2b(0), n - # bytes) + bytes
Proof step 124:
¬(# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8))))), i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), 0 ≤ j % 2 ^ (i * 8), 0 < i, 2 ^ (i * 8) ≤ j, # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest
Proof step 133:
# bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i) + 1 ∧ 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), 0 ≤ j % 2 ^ (i * 8), 0 < i, 2 ^ (i * 8) ≤ j, # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8))) = (mklist(i2b(0), i→n(i) + 1 - # bits2bytes(int2bits(j % 2 ^ (i * 8)))) + bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: fix-pos 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