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Proof step 308 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 ≤ b2i(i2b(j % 2 ^ (i * 8))) ⊦ i = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * (i→n(i) - 1)) + mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - 1 = 0, mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i2b(bits2int(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)))) = i2b(j % 2 ^ (i * 8)), bits2int(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = j % 2 ^ (i * 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≠ 0 → bits2int(mklist(false, n) + bits) = bits2int(false ' + bits) subst: [bits, n] → [int2bits(j % 2 ^ (i * 8)), 8 - # int2bits(j % 2 ^ (i * 8))] rotate: F spec: int2bits inst: name: bits2int-zeros

Additional information

Used simplifier rules: ⊦ n < m → m - n ≠ 0; Used terms: int2bits(j % 2 ^ (i * 8)), 8 - # int2bits(j % 2 ^ (i * 8))