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Proof step 18 from proof int2bytes-len-le-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1
Proof step 20:
int2bytes(i) ≠ [], int2bytes(i).first = i2b(~1), 2 ^ (8 * (1 + n→i((# int2bytes(i))-1 - 1)) - 1) + i < 0, 0 ≤ 2 ^ (8 * (1 + n→i((# int2bytes(i))-1 - 1))) + i, 0 ≤ b2i(int2bytes(i).rest.first) ⊦ int2bytes(i).rest = [], # int2bytes(i) ≤ n ↔ ¬ 2 ^ (8 * n→i(n) - 1) + i < 0

Rule argument

seq: ⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1 subst: [bytes] → [int2bytes(i)] rotate: F spec: list-data inst: bytelist name: length-rest

Additional information

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