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Proof step 67 from proof bytes2int-append (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 69:
¬ bytes2bits(bytes).first ∧ bytes2bits(bytes) ≠ [] ⊦ bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes) + bytes2bits(bytes0)) = bits2uint(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1), bytes = [], bytes0 = [], bytes2bits(bytes).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 simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = []; Used terms: bytes2bits(bytes)