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Proof step 344 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(i2b(bits2int(firstn(n, int2bits(j % 2 ^ (i * 8))))) ' + bits2bytes(restn(n, int2bits(j % 2 ^ (i * 8))))), m * 8 + n < i→n(i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), n < 8, n < m * 8 + 7, n < 8 + m * 8, 8 < m * 8 + n, 1 < i, 0 < i, firstn(n, int2bits(j % 2 ^ (i * 8))).first ⊦ m * 8 = 1, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 * (i→n(i) - m + 1)) + 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, m = 0, n = 0, bits2uint(firstn(n, int2bits(j % 2 ^ (i * 8)))) = bits2int(firstn(n, int2bits(j % 2 ^ (i * 8)))), i2b(bits2uint(firstn(n, int2bits(j % 2 ^ (i * 8))))) = i2b(bits2int(firstn(n, int2bits(j % 2 ^ (i * 8)))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [int2bits(j % 2 ^ (i * 8)), n] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ int2bits(j) ≠ [];% ⊦ int2bits(j).first ↔ j < 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: int2bits(j % 2 ^ (i * 8)), n