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Proof step 4 from proof short-2bytes (previous step)

⊦ s2i(i2s(bytes2int(by ' + by0 '))) = bytes2int(by ' + by0 '), ¬ bytes2int(by ' + by0 ') < ~32768 ∧ ¬ 32767 < bytes2int(by ' + by0 ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 6:
by ' ≠ [] ⊦ s2i(i2s(bytes2int(by ') * 256 + band(b2i(by0), 255))) = bytes2int(by ') * 256 + band(b2i(by0), 255), ¬ bytes2int(by ') * 256 + band(b2i(by0), 255) < ~32768 ∧ ¬ 32767 < bytes2int(by ') * 256 + band(b2i(by0), 255)

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by0, by ']

Additional information

Used simplifier rules: ⊦ by ' ≠ []; Used terms: by0, by '