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Proof step 13 from proof bytes2bytes-first-neg (previous step)

b2i(by) = 0, 0 ≤ b2i(bytes.first), b2i(int2bytes(bytes2int(by ' + bytes)).first) < 0, ∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
bytes = by0 + bytes1, b2i(by) = 0, 0 ≤ b2i(by0), b2i(int2bytes(bytes2int(by ' + bytes)).first) < 0, ∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = []

Rule argument

seq: ⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0) subst: [bytes, by, bytes0] → [bytes, by0, bytes1] rotate: T spec: list-data inst: bytelist name: elim-1

Additional information

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