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Proof step 8 from proof bytes2int-size-01 (previous step)

b2i(by) < 0, 256 * bytes2int(i2b(0) ' + by ' + bytes.butlast) + band(255, b2i(bytes.last)) < 2 ^ ((n→i(# bytes) + 1) * 8 - 1), ∀ by, bytes0. # bytes0 < # bytes → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦ bytes = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
bytes = bytes1 + by0 ', b2i(by) < 0, 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) < 2 ^ ((n→i(# bytes) + 1) * 8 - 1), ∀ by, bytes0. # bytes0 < # bytes → true → b2i(by) < 0 → 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ⊦ bytes = []

Rule argument

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