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Proof step 10 from proof bits2int-split-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1
Proof step 12:
bitsinvert(bits0) ≠ [], true ∈ bits0 ⊦ bits0 = [], bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bitsinvert(bits0) +1) + bits2uint(bitsinvert(bits0)) + 1 = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, bitsinvert(bits0) +1 = []

Rule argument

name: bits2uint-succ rotate: F subst: [bits] → [bitsinvert(bits0)]

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = []; Used terms: bitsinvert(bits0)