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Proof step 16 from proof bits2int-split-01 (previous step)

⊦ bits2uint((false ' + bitsinvert(bits1))+1 + bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, bits0 = [], true ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 18:
# bits0 ≠ 0 ⊦ bits2uint((false ' + bitsinvert(bits1))+1) * 2 ^ n→i(# bits0) + bits2uint(bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, bits0 = [], true ∈ bits0

Rule argument

name: bits2uint-split rotate: F subst: [bits0, bits] → [bits0, (false ' + bitsinvert(bits1))+1]

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = []; Used terms: bits0, (false ' + bitsinvert(bits1))+1