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Proof step 128 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 129:
⊦ # bits % 8 = 0 ∧ bits ≠ [] → # bits2bytes(bits) = # bits / 8
Proof step 130:
# int2bits(j % 2 ^ (i * 8)) % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)) ≠ [], i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0, # int2bits(j % 2 ^ (i * 8)) / 8 < i→n(i), 0 ≤ j % 2 ^ (i * 8), 0 < i, 2 ^ (i * 8) ≤ j ⊦ i→n(i) = # int2bits(j % 2 ^ (i * 8)) / 8, i = 0

Rule argument

name: bits2bytes-len-01 rotate: F subst: [bits] → [int2bits(j % 2 ^ (i * 8))]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j % 2 ^ (i * 8))