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Proof step 34 from proof int2bytes-fillsgn-rec (previous step)

0 ≤ b2i((int2bytes(i >> 8) + i2b(i) ').first), # int2bytes(i >> 8) < n, # int2bytes(i >> 8) + 1 < n, i < ~128, i >> 8 < 0, i < 0 ⊦ fillsgn(n, int2bytes(i >> 8) + i2b(i) ') = (mklist(i2b(~1), n - 1 - # int2bytes(i >> 8)) + int2bytes(i >> 8)) + i2b(i) ', n = # int2bytes(i >> 8) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ bytes ≠ [] → (bytes + bytes0).first = bytes.first

Rule argument

seq: ⊦ bytes ≠ [] → (bytes + bytes0).first = bytes.first subst: [bytes0, bytes] → [i2b(i) ', int2bytes(i >> 8)] rotate: F spec: list inst: bytelist name: first-01

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];%int2bytes-empty: ⊦ int2bytes(i) ≠ [];%bytes2int-first-gez: ⊦ 0 ≤ b2i(int2bytes(i).first) ↔ 0 ≤ i;% ⊦ i < 0 → ¬ 0 ≤ i >> j; Used terms: i2b(i) ', int2bytes(i >> 8)