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Proof step 13 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes = # int2bytes(bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)), bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255) ≤ 255, ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = int2bytes(bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)), # bytes = 1, bytes = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
bytes = bytes1 + by ', # bytes = # int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), bytes2int(bytes1) * 256 + band(b2i(by), 255) ≤ 255, ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = int2bytes(bytes2int(bytes1) * 256 + band(b2i(by), 255)), # bytes = 1, bytes = []

Rule argument

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