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Proof step 284 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)) = (i→n(i) - 1) * 8 + n, 0 ≤ bytes2int(i2b(bits2int(firstn(n, int2bits(j % 2 ^ (i * 8))))) ' + bits2bytes(restn(n, int2bits(j % 2 ^ (i * 8))))), 0 < i, n < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, n < (i→n(i) - 1) * 8 + 7, n < 8 + (i→n(i) - 1) * 8, 8 < (i→n(i) - 1) * 8 + n ⊦ (i→n(i) - 1) * 8 = 1, i = 0, (i→n(i) - 1) * 8 + n = 8 * i→n(i), 1 + 8 * i→n(i) = (i→n(i) - 1) * 8 + n, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - 1 = 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: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [firstn(n, int2bits(j % 2 ^ (i * 8)))] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: firstn(n, int2bits(j % 2 ^ (i * 8)))