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Proof step 16 from proof int2bytes-len-le-neg (previous step)

# int2bytes(i) < n, 1 ≤ # int2bytes(i), i < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i + 2 ^ (8 * (n→i(n) - 1)) < 0 ⊦ int2bytes(i).first = i2b(~1), b2i(int2bytes(i).first) = ~1, n = 1

User applied rule insert lemma

And obtained the following new goals

Proof step 17:
⊦ b2i(by) < 0 → ~(2 ^ ((n→i(# bytes) + 1) * 8 - 1)) ≤ bytes2int(by ' + bytes)
Proof step 18:
b2i(int2bytes(i).first) < 0 → ~(2 ^ ((n→i(# int2bytes(i).rest) + 1) * 8 - 1)) ≤ bytes2int(int2bytes(i).first ' + int2bytes(i).rest), # int2bytes(i) < n, 1 ≤ # int2bytes(i), i < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i + 2 ^ (8 * (n→i(n) - 1)) < 0 ⊦ int2bytes(i).first = i2b(~1), b2i(int2bytes(i).first) = ~1, n = 1

Rule argument

name: bytes2int-size-04 subst: [by, bytes] → [int2bytes(i).first, int2bytes(i).rest]

Additional information

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