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Proof step 311 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(bits2uint(int2bits(j % 2 ^ (i * 8)))) = i2b(j % 2 ^ (i * 8)), bits2uint(int2bits(j % 2 ^ (i * 8))) = j % 2 ^ (i * 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j % 2 ^ (i * 8)] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i; Used terms: j % 2 ^ (i * 8)