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Proof step 87 from proof int2bytes-rec-neg-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 88:
⊦ # bytes ≥ n → fix(n, bytes) = lastn(n, bytes)
Proof step 89:
¬ # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≥ i→n(i) + 1, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = []
Proof step 92:
# bits2bytes(int2bits(j % 2 ^ (i * 8))) ≥ i→n(i) + 1, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = lastn(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = []

Rule argument

name: fix-longer rotate: F subst: [bytes, n] → [bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1]

Additional information

Used terms: bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1