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Proof step 19 from proof bytes2int-rec (previous step)

bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], ~1 = bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(bits) +1)
Proof step 21:
bytes2bits(bytes).first ∧ bytes2bits(bytes) ≠ [], bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], ~1 = bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + ~ bits2uint(bitsinvert(bytes2bits(bytes)) +1) * 256 + band(b2i(by), 255)

Rule argument

seq: ⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(bits) +1) subst: [bits] → [bytes2bits(bytes)] rotate: F spec: int2bits inst: name: bits2int-neg-03

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = []; Used terms: bytes2bits(bytes)