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Proof step 19 from proof int2bytes-len-le-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bytes ≠ [] → bytes.first ' + bytes.rest = bytes
Proof step 21:
int2bytes(i) ≠ [], 0 ≤ 2 ^ ((n→i(# int2bytes(i).rest) + 1) * 8 - 1) + bytes2int(int2bytes(i)), i + 2 ^ (8 * (n→i(n) - 1)) < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i < 0, 1 ≤ # int2bytes(i), # int2bytes(i) < n ⊦ n = 1, b2i(int2bytes(i).first) = ~1, int2bytes(i).first = i2b(~1)

Rule argument

seq: ⊦ bytes ≠ [] → bytes.first ' + bytes.rest = bytes subst: [bytes] → [int2bytes(i)] rotate: F spec: list inst: bytelist name: fr

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ []; Used terms: int2bytes(i)