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Proof step 158 from proof int2bytes-rec-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 159:
⊦ # bits ≤ 8 → bits2bytes(bits) = i2b(bits2int(bits)) '
Proof step 160:
# mklist(true, 8) ≤ 8, ((8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8))) % 8 = 0, 8 < (8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8, 0 < i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i) ⊦ j % 2 ^ (i * 8) = 0, mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), i = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = (i2b(bits2int(mklist(true, 8))) ' + bits2bytes(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)) - 8) + int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

name: bits2bytes-base rotate: F subst: [bits] → [mklist(true, 8)]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ m * n = n * m;% ⊦ # mklist(boolvar, n) = n; Used terms: mklist(true, 8)