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Proof step 2 from proof int2bytes-len-le-neg-02 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ b2i(by) < 0 ∧ b2i(by) ≠ ~1 → bytes2int(by ' + bytes) < ~(2 ^ (8 * n→i(# bytes)))
Proof step 4:
b2i(int2bytes(i).first) < 0 ∧ b2i(int2bytes(i).first) ≠ ~1 → bytes2int(int2bytes(i).first ' + int2bytes(i).rest) < ~(2 ^ (8 * n→i(# int2bytes(i).rest))), i < 0 ⊦ int2bytes(i).first = i2b(~1), # int2bytes(i) ≤ n ↔ ¬ 2 ^ (8 * n→i(n)) + i < 0

Rule argument

name: bytes2int-size-06 subst: [by, bytes] → [int2bytes(i).first, int2bytes(i).rest]

Additional information

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