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Proof step 1 from proof bits2int-split (conclusion)

⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 3:
¬ (bits + bits0).first ∧ bits + bits0 ≠ [] ⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)

Rule argument

name: bits2int-pos-02 rotate: F subst: [bits] → [bits + bits0]

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = []; Used terms: bits + bits0