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Proof step 164 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8) ⊦ # int2bits(j % 2 ^ (i * 8)) % 8 = 0, i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + 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 165:
⊦ bytes ≠ [] → (bits2int(bytes2bits(bytes)) < 0 ↔ b2i(bytes.first) < 0)
Proof step 166:
bits2bytes(int2bits(j % 2 ^ (i * 8))) ≠ [], i→n(i * 8) % 8 = 0, b2i(bits2bytes(int2bits(j % 2 ^ (i * 8))).first) < 0, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8) ⊦ # int2bits(j % 2 ^ (i * 8)) % 8 = 0, i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: bits2int-zero-ls rotate: F subst: [bytes] → [bits2bytes(int2bits(j % 2 ^ (i * 8)))]

Additional information

Used simplifier rules: bits2bytes-empty: ⊦ bits2bytes(bits) ≠ []; Used terms: bits2bytes(int2bits(j % 2 ^ (i * 8)))