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Proof step 64 from proof int2bytes-rec-neg-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 66:
¬ # int2bits(j) % 8 ≠ 0, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ # bits2bytes(int2bits(j)) = i→n(i) + 1, j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + fix(i→n(i) + 1, bits2bytes(int2bits(j))).rest
Proof step 78:
# int2bits(j) % 8 ≠ 0, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ # int2bits(j) / 8 + 1 = i→n(i) + 1, j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + fix(i→n(i) + 1, bits2bytes(int2bits(j))).rest

Rule argument

name: bits2bytes-len-02 rotate: F subst: [bits] → [int2bits(j)]

Additional information

Used terms: int2bits(j)