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Proof step 76 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 78:
¬ # int2bits(j % 2 ^ (i * 8)) % 8 ≠ 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, 0 < i, 2 ^ (i * 8) ≤ j, # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≤ i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, int2bits(j % 2 ^ (i * 8)).rest = []
Proof step 81:
# int2bits(j % 2 ^ (i * 8)) % 8 ≠ 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, 0 < i, 2 ^ (i * 8) ≤ j, # int2bits(j % 2 ^ (i * 8)) / 8 + 1 ≤ i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, int2bits(j % 2 ^ (i * 8)).rest = []

Rule argument

name: bits2bytes-len-02 rotate: F subst: [bits] → [int2bits(j % 2 ^ (i * 8))]

Additional information

Used terms: int2bits(j % 2 ^ (i * 8))