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Proof step 1 from proof datakeys-set-add (conclusion)

⊦ datakeys(ks ++ key, ri) = datakeys(ks, ri) ∪ datakeys(key, ri)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 3:
⊦ ∀ key0. key0 ∈ datakeys(ks ++ key, ri) ↔ key0 ∈ datakeys(ks, ri) ∪ datakeys(key, ri)

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [datakeys(ks, ri) ∪ datakeys(key, ri), datakeys(ks ++ key, ri)] flags: <all paths>

Additional information

Used terms: datakeys(ks, ri) ∪ datakeys(key, ri), datakeys(ks ++ key, ri)