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Proof step 95 from proof rightshift-8-01-01 (previous step)

0 ≤ b2i(firstn(# int2bytes(i) - i→n(j), int2bytes(i)).first), i < 0, i→n(j) < # int2bytes(i) ⊦ bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))) = bytes2int(mklist(i2b(~1), i→n(j)) + firstn(# int2bytes(i) - i→n(j), int2bytes(i))), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 96:
⊦ n ≠ 0 ∧ bytes ≠ [] → firstn(n, bytes).first = bytes.first

Rule argument

seq: ⊦ n ≠ 0 ∧ bytes ≠ [] → firstn(n, bytes).first = bytes.first subst: [bytes, n] → [int2bytes(i), # int2bytes(i) - i→n(j)] rotate: F spec: list-del inst: bytelist name: firstn-first

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];%int2bytes-empty: ⊦ int2bytes(i) ≠ [];%bytes2int-first-gez: ⊦ 0 ≤ b2i(int2bytes(i).first) ↔ 0 ≤ i;% ⊦ n < m → m - n ≠ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: int2bytes(i), # int2bytes(i) - i→n(j)