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Proof step 211 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - # bits2bytes(int2bits(j % 2 ^ (i * 8)))) + bits2bytes(int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 212:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 213:
# int2bits(j % 2 ^ (i * 8)) % 8 ≠ 0, i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), # int2bits(j % 2 ^ (i * 8)) / 8 + 1 ≤ i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - # int2bits(j % 2 ^ (i * 8)) / 8 + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)) % 8 = 0

Rule argument

name: bits2bytes-len-02 rotate: F subst: [bits] → [int2bits(j % 2 ^ (i * 8))]

Additional information

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