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Proof step 137 from proof int2bytes-rec-neg-02 (previous step)

# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) < 0, # bits2bytes(int2bits(j % 2 ^ (i * 8))) < i→n(i), 0 < i ⊦ i→n(i) = # bits2bytes(int2bits(j % 2 ^ (i * 8))), j % 2 ^ (i * 8) = 0, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 138:
⊦ # bits % 8 = 0 ∧ bits ≠ [] → # bits2bytes(bits) = # bits / 8

Rule argument

name: bits2bytes-len-01 rotate: F subst: [bits] → [int2bits(j % 2 ^ (i * 8))]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ int2bits(j) ≠ [];%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;%n ≠ 0 ⊦ (m * n) / n = m;% ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j); Used terms: int2bits(j % 2 ^ (i * 8))