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Proof step 4 from proof bits2int-split-01 (previous step)

⊦ bits0 = [], bits2uint((false ' + 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 5:
⊦ ¬ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits +1 + bits0
Proof step 6:
¬ ¬ true ∈ bits0 ⊦ bits0 = [], bits2uint((false ' + bitsinvert(bits1) + bitsinvert(bits0))+1) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1
Proof step 15:
¬ true ∈ bits0 ⊦ bits0 = [], bits2uint((false ' + bitsinvert(bits1))+1 + bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1

Rule argument

seq: ⊦ ¬ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits +1 + bits0 subst: [bits0, bits] → [bits0, false ' + bitsinvert(bits1)] rotate: F spec: bitopsaux inst: name: succ-zeros

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits0, false ' + bitsinvert(bits1)