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Proof step 7 from proof bits2int-ones-02 (previous step)

bits.first ⊦ bits + bits0 = [], bits = [], bits2uint((false ' + bitsinvert(bits0))+1) = bits2uint((bitsinvert(bits) + bitsinvert(bits0))+1), false ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ false ∈ bits0 → (bits + bits0)+1 = bits + bits0 +1
Proof step 9:
¬ false ∈ bitsinvert(bits0), bits.first ⊦ bits + bits0 = [], bits = [], bits2uint((false ' + bitsinvert(bits0))+1) = bits2uint((bitsinvert(bits) + bitsinvert(bits0))+1), false ∈ bits
Proof step 17:
false ∈ bitsinvert(bits0), bits.first ⊦ bits + bits0 = [], bits = [], bits2uint((false ' + bitsinvert(bits0))+1) = bits2uint(bitsinvert(bits) + bitsinvert(bits0) +1), false ∈ bits

Rule argument

seq: ⊦ false ∈ bits0 → (bits + bits0)+1 = bits + bits0 +1 subst: [bits0, bits] → [bitsinvert(bits0), bitsinvert(bits)] rotate: F spec: bitopsaux inst: name: succ-zero-01

Additional information

Used terms: bitsinvert(bits0), bitsinvert(bits)