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Proof step 35 from proof bytes2int-append (previous step)

bytes2bits(bytes).first ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], 256 ^ n→i(# bytes0) = 1 + bits2uint(bitsinvert(bytes2bits(bytes0))) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ bits ≠ [] ∧ ¬ bits.first → bits2uint(bitsinvert(bits)) = 2 ^ n→i(# bits) + ~ bits2int(bits) - 1
Proof step 37:
¬(bytes2bits(bytes0) ≠ [] ∧ ¬ bytes2bits(bytes0).first), bytes2bits(bytes).first ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], 256 ^ n→i(# bytes0) = 1 + bits2uint(bitsinvert(bytes2bits(bytes0))) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)
Proof step 50:
bytes2bits(bytes0) ≠ [] ∧ ¬ bytes2bits(bytes0).first, bytes2bits(bytes).first ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], 256 ^ n→i(# bytes0) = 1 + (2 ^ n→i(# bytes2bits(bytes0)) + ~ bits2int(bytes2bits(bytes0)) - 1) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

Rule argument

seq: ⊦ bits ≠ [] ∧ ¬ bits.first → bits2uint(bitsinvert(bits)) = 2 ^ n→i(# bits) + ~ bits2int(bits) - 1 subst: [bits] → [bytes2bits(bytes0)] rotate: F spec: int2bits inst: name: bits2uint-inv-neg

Additional information

Used terms: bytes2bits(bytes0)