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Proof step 17 from proof int2bytes-len-le (previous step)

2 ^ ((n→i(n) - 1) * 8) ≤ i, # int2bytes(i) < n, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, 0 ≤ i ⊦ int2bytes(i).first = i2b(0)

User applied rule insert lemma

And obtained the following new goals

Proof step 18:
⊦ 0 < b2i(by) → bytes2int(by ' + bytes) < 2 ^ ((n→i(# bytes) + 1) * 8 - 1)
Proof step 19:
0 < b2i(int2bytes(i).first) → bytes2int(int2bytes(i).first ' + int2bytes(i).rest) < 2 ^ ((n→i(# int2bytes(i).rest) + 1) * 8 - 1), 2 ^ ((n→i(n) - 1) * 8) ≤ i, # int2bytes(i) < n, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, 0 ≤ i ⊦ int2bytes(i).first = i2b(0)

Rule argument

name: bytes2int-size-02 subst: [by, bytes] → [int2bytes(i).first, int2bytes(i).rest]

Additional information

Used terms: int2bytes(i).first, int2bytes(i).rest