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Proof step 7 from proof bits2int-split-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 9:
# bitsinvert(bits0) +1 ≠ 0, 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

Rule argument

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

Additional information

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