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Proof step 16 from proof int2bytes-rec-neg-05 (previous step)

# bits2bytes(int2bits(j)) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + bits2bytes(int2bits(j)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ # bits % 8 ≠ 0 ∧ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits % 8, bits)) + bits2bytes(restn(# bits % 8, bits))
Proof step 18:
¬(# int2bits(j) % 8 ≠ 0 ∧ 8 < # int2bits(j)), # bits2bytes(int2bits(j)) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + bits2bytes(int2bits(j)).rest
Proof step 50:
# int2bits(j) % 8 ≠ 0 ∧ 8 < # int2bits(j), #(bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + bits2bytes(restn(# int2bits(j) % 8, int2bits(j)))) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + bits2bytes(restn(# int2bits(j) % 8, int2bits(j))) = i2b(~1) ' + (bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + bits2bytes(restn(# int2bits(j) % 8, int2bits(j)))).rest

Rule argument

name: bits2bytes-rec-01 rotate: F subst: [bits] → [int2bits(j)]

Additional information

Used terms: int2bits(j)