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Proof step 180 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes = 1 + # int2bytes(bytes2int(bytes.butlast)), band(b2i(bytes.last), 255) < 256, 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 0 ≤ band(b2i(bytes.last), 255), 0 ≤ bytes2int(bytes.butlast), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes(bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255)).last '

User applied rule insert elim lemma

And obtained the following new goals

Proof step 181:
bytes = bytes1 + by ', # bytes = 1 + # int2bytes(bytes2int(bytes1)), band(b2i(by), 255) < 256, 0 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 255 < bytes2int(bytes1) * 256 + band(b2i(by), 255), 0 ≤ band(b2i(by), 255), 0 ≤ bytes2int(bytes1), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes(bytes2int(bytes1)) + int2bytes(band(b2i(by), 255)).last '

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