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Proof step 146 from proof int2bytes-rec-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 147:
⊦ # bits % 8 = 0 ∧ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(8, bits)) + bits2bytes(restn(8, bits))
Proof step 148:
¬ ( #(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ 8 < #(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)))), # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8 ⊦ i = 0, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], j % 2 ^ (i * 8) = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest
Proof step 151:
#(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ 8 < #(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8 ⊦ i = 0, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], j % 2 ^ (i * 8) = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = ( bits2bytes(firstn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)))) ).rest

Rule argument

name: bits2bytes-rec-02 rotate: F subst: [bits] → [ mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))]

Additional information

Used terms: mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))