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Proof step 38 from proof bytes2int-append (previous step)

bytes2bits(bytes).first, bytes2bits(bytes0).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 39:
⊦ bits ≠ [] ∧ bits.first → bits2uint(bitsinvert(bits)) = ~ bits2int(bits) - 1
Proof step 40:
bytes2bits(bytes0) ≠ [] ∧ bytes2bits(bytes0).first, bytes2bits(bytes).first, bytes2bits(bytes0).first ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], 256 ^ n→i(# bytes0) = 1 + (~ bits2int(bytes2bits(bytes0)) - 1) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

Rule argument

seq: ⊦ bits ≠ [] ∧ bits.first → bits2uint(bitsinvert(bits)) = ~ bits2int(bits) - 1 subst: [bits] → [bytes2bits(bytes0)] rotate: F spec: int2bits inst: name: bits2uint-inv-pos

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = []; Used terms: bytes2bits(bytes0)