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Proof step 15 from proof int2bytes-index-rightshift (previous step)

j < n→i(# int2bytes(i)), 0 ≤ j, i→n(n→i(# int2bytes(i)) - j + 1) < # int2bytes(i) ⊦ int2bytes(i)[i→n(j)] = i2b(bytes2int(firstn(# int2bytes(i) - i→n(n→i(# int2bytes(i)) - j + 1), int2bytes(i))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ bytes ≠ [] → i2b(bytes2int(bytes)) = bytes.last
Proof step 17:
firstn(# int2bytes(i) - i→n(n→i(# int2bytes(i)) - j + 1), int2bytes(i)) ≠ [], j < n→i(# int2bytes(i)), 0 ≤ j, i→n(n→i(# int2bytes(i)) - j + 1) < # int2bytes(i) ⊦ int2bytes(i)[i→n(j)] = firstn(# int2bytes(i) - i→n(n→i(# int2bytes(i)) - j + 1), int2bytes(i)).last

Rule argument

name: bytes2int-i2b rotate: F subst: [bytes] → [firstn (# int2bytes(i) - i→n(n→i(# int2bytes(i)) - j + 1), int2bytes(i))]

Additional information

Used simplifier rules: ⊦ firstn(n, bytes) = [] ↔ n = 0;% ⊦ n < m → m - n ≠ 0; Used terms: firstn (# int2bytes(i) - i→n(n→i(# int2bytes(i)) - j + 1), int2bytes(i))