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Proof step 29 from proof bytes2bytes-length (previous step)

1 + # bytes1 < # int2bytes(bytes2int(i2b(~1) ' + bytes1)), b2i(bytes1.first) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + bytes1) → # bytes0 < # int2bytes(bytes2int(bytes0)) → bytes0 = [] ⊦ bytes1 = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
bytes1 = by + bytes, 1 + # bytes1 < # int2bytes(bytes2int(i2b(~1) ' + bytes1)), b2i(by) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + bytes1) → # bytes0 < # int2bytes(bytes2int(bytes0)) → bytes0 = [] ⊦ bytes1 = []

Rule argument

seq: ⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0) subst: [bytes, by, bytes0] → [bytes1, by, bytes] 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: bytes1, by, bytes