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Proof step 222 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), n < 8 ⊦ mklist(false, 8 * (i→n(i) -1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, bits2bytes(mklist(false, 8 * (i→n(i) -1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 223:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 224:
¬ ( #(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ mklist(false, 8 * (i→n(i) -1 - m)) ≠ [] ∧ mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) ≠ []), i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), n < 8 ⊦ mklist(false, 8 * (i→n(i) -1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, bits2bytes(mklist(false, 8 * (i→n(i) -1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0
Proof step 289:
#(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ mklist(false, 8 * (i→n(i) -1 - m)) ≠ [] ∧ mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) ≠ [], i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), n < 8 ⊦ mklist(false, 8 * (i→n(i) -1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, bits2bytes(mklist(false, 8 * (i→n(i) -1 - m))) + bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * (i→n(i) -1 - m))]

Additional information

Used terms: mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)), mklist(false, 8 * (i→n(i) -1 - m))