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Proof step 85 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, i→n(i) < # bits2bytes(int2bits(j % 2 ^ (i * 8))), 2 ^ (i * 8) ≤ j, 0 < i ⊦ int2bits(j % 2 ^ (i * 8)).rest = [], bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = lastn(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 86:
⊦ n = # bytes → lastn(n, bytes) = bytes
Proof step 87:
i→n(i) + 1 ≠ # bits2bytes(int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, i→n(i) < # bits2bytes(int2bits(j % 2 ^ (i * 8))), 2 ^ (i * 8) ≤ j, 0 < i ⊦ int2bits(j % 2 ^ (i * 8)).rest = [], bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = lastn(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest
Proof step 96:
i→n(i) + 1 = # bits2bytes(int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, i→n(i) < # bits2bytes(int2bits(j % 2 ^ (i * 8))), 2 ^ (i * 8) ≤ j, 0 < i ⊦ int2bits(j % 2 ^ (i * 8)).rest = [], bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = bits2bytes(int2bits(j % 2 ^ (i * 8))).rest

Rule argument

seq: ⊦ n = # bytes → lastn(n, bytes) = bytes subst: [bytes, n] → [bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1] rotate: F spec: list-del inst: bytelist name: lastN-all

Additional information

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