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Proof step 7 from proof bytes2int-size-06 (previous step)

0 ≤ 2 ^ (8 * n→i(# bytes)) + band(255, b2i(bytes.last)) + 256 * bytes2int(by ' + bytes.butlast), b2i(by) < 0, ∀ by, bytes0. # bytes0 < # bytes → 0 ≤ bytes2int(by ' + bytes0) + 2 ^ (8 * n→i(# bytes0)) ∧ b2i(by) < 0 → b2i(by) = ~1 ⊦ bytes = [], b2i(by) = ~1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
bytes = bytes1 + by0 ', 0 ≤ 2 ^ (8 * n→i(# bytes)) + band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes1), b2i(by) < 0, ∀ by, bytes0. # bytes0 < # bytes → 0 ≤ bytes2int(by ' + bytes0) + 2 ^ (8 * n→i(# bytes0)) ∧ b2i(by) < 0 → b2i(by) = ~1 ⊦ bytes = [], b2i(by) = ~1

Rule argument

seq: bytes ≠ [] ⊦ by = bytes.last ∧ bytes0 = bytes.butlast ↔ bytes = bytes0 + by ' subst: [bytes, by, bytes0] → [bytes, by0, bytes1] rotate: T spec: list-last inst: bytelist name: last-elim

Additional information

Used simplifier rules: bytes ≠ [] ⊦ by = bytes.last ∧ bytes0 = bytes.butlast ↔ bytes = bytes0 + by '; (elim) Used terms: bytes, by0, bytes1