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Proof step 8 from proof bytes2int-neg (previous step)

∀ bytes0. # bytes0 < #(by + bytes1) → true → bytes0 ≠ [] → (bytes2int(bytes0) < 0 ↔ b2i(bytes0.first) < 0) ⊦ bytes1 = [], band(255, b2i(bytes1.last)) + 256 * bytes2int(by ' + bytes1.butlast) < 0 ↔ ¬ 0 ≤ b2i(by)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
bytes1 = bytes + by0 ', ∀ bytes0. # bytes0 < #(by + bytes1) → true → bytes0 ≠ [] → (bytes2int(bytes0) < 0 ↔ b2i(bytes0.first) < 0) ⊦ bytes1 = [], band(255, b2i(by0)) + 256 * bytes2int(by ' + bytes) < 0 ↔ ¬ 0 ≤ b2i(by)

Rule argument

seq: bytes ≠ [] ⊦ by = bytes.last ∧ bytes0 = bytes.butlast ↔ bytes = bytes0 + by ' subst: [bytes, by, bytes0] → [bytes1, by0, bytes] 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: bytes1, by0, bytes