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Proof step 34 from proof bytes2int-rec (previous step)

⊦ bytes2bits(bytes) + byte2bits(by) = [], bits2uint(bytes2bits(bytes) + byte2bits(by)) = bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255), bytes = [], (bytes2bits(bytes) + byte2bits(by)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 36:
¬(¬ bytes2bits(bytes).first ∧ bytes2bits(bytes) ≠ []) ⊦ bytes2bits(bytes) + byte2bits(by) = [], bits2uint(bytes2bits(bytes) + byte2bits(by)) = bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255), bytes = [], (bytes2bits(bytes) + byte2bits(by)).first
Proof step 39:
¬ bytes2bits(bytes).first ∧ bytes2bits(bytes) ≠ [] ⊦ bytes2bits(bytes) + byte2bits(by) = [], bits2uint(bytes2bits(bytes) + byte2bits(by)) = bits2uint(bytes2bits(bytes)) * 256 + band(b2i(by), 255), bytes = [], (bytes2bits(bytes) + byte2bits(by)).first

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [bytes2bits(bytes)] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used terms: bytes2bits(bytes)