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Proof step 78 from proof int2bytes-rec-neg-02 (previous step)

# (mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0 ⊦ (mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = [], j % 2 ^ (i * 8) = 0, bits2bytes((mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = 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 79:
⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0
Proof step 80:
¬ mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) ≠ [], # (mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0 ⊦ (mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = [], j % 2 ^ (i * 8) = 0, bits2bytes((mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest
Proof step 119:
mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) ≠ [], #(mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))).rest + int2bits(j % 2 ^ (i * 8))) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 0 < i, j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0 ⊦ mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))).rest + int2bits(j % 2 ^ (i * 8)) = [], j % 2 ^ (i * 8) = 0, bits2bytes(mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))).rest + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

seq: ⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0 subst: [bits0, bits] → [int2bits(j % 2 ^ (i * 8)), mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))] rotate: F spec: list inst: bitlista name: rest-01

Additional information

Used terms: int2bits(j % 2 ^ (i * 8)), mklist(true, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))