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Proof step 14 from proof bytes2int-append (previous step)

(bytes2bits(bytes) + bytes2bits(bytes0)).first ⊦ bytes2bits(bytes) + bytes2bits(bytes0) = [], bytes0 = [], bytes = [], bits2uint((bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)))+1) + bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 16:
bytes2bits(bytes) ≠ [], bytes2bits(bytes).first ⊦ bytes2bits(bytes) + bytes2bits(bytes0) = [], bytes0 = [], bytes = [], bits2uint((bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)))+1) + bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1) = 0

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [bytes2bits(bytes0), bytes2bits(bytes)] rotate: F spec: list inst: bitlista name: first-01

Additional information

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