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Proof step 104 from proof bytes2int-append (previous step)

0 ≤ bits2int(bytes2bits(bytes0)) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = bits2int(bytes2bits(bytes0)) % 2 ^ (8 * n→i(# bytes0)), bytes2bits(bytes).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 105:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 106:
¬ bytes2bits(bytes0).first ∧ bytes2bits(bytes0) ≠ [], 0 ≤ bits2uint(bytes2bits(bytes0)) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bits2uint(bytes2bits(bytes0)) = bits2uint(bytes2bits(bytes0)) % 2 ^ (8 * n→i(# bytes0)), bytes2bits(bytes).first

Rule argument

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

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];%bits ≠ [] ⊦ 0 ≤ bits2int(bits) → ¬ bits.first; Used terms: bytes2bits(bytes0)