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Proof step 8 from proof bytes2int-append (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 10:
¬(¬ (bytes2bits(bytes) + bytes2bits(bytes0)).first ∧ bytes2bits(bytes) + bytes2bits(bytes0) ≠ []) ⊦ bytes0 = [], bytes = [], bits2int(bytes2bits(bytes) + bytes2bits(bytes0)) = bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)
Proof step 63:
¬ (bytes2bits(bytes) + bytes2bits(bytes0)).first ∧ bytes2bits(bytes) + bytes2bits(bytes0) ≠ [] ⊦ bytes0 = [], bytes = [], bits2uint(bytes2bits(bytes) + bytes2bits(bytes0)) = bits2int(bytes2bits(bytes)) * 256 ^ n→i(# bytes0) + band(bits2int(bytes2bits(bytes0)), 256 ^ n→i(# bytes0) - 1)

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [bytes2bits(bytes) + bytes2bits(bytes0)] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used terms: bytes2bits(bytes) + bytes2bits(bytes0)