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Proof step 234 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 235:
n ≠ 0 ⊦ (n - 1) + 1 = n
Proof step 236:
i→n(i) ≠ 0, # int2bits(j % 2 ^ (i * 8)) = (i→n(i) - 1) * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), n < 8, 0 < i ⊦ i = 0, bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - i→n(i)) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = (i→n(i) - 1) * 8 + n, (i→n(i) - 1) * 8 + n = 8 * i→n(i)

Rule argument

seq: n ≠ 0 ⊦ (n - 1) + 1 = n subst: [n] → [i→n(i)] rotate: F spec: nat inst: name: num-02

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0; Used terms: i→n(i)