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Proof step 2 from proof datakeys-set-empty (previous step)

⊦ # datakeys(∅, ri) = 0, datakeys(∅, ri) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)

Rule argument

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

Additional information

Used simplifier rules: datakeys-set: ⊦ key ∈ datakeys(ks, ri) ↔ key ∈ ri ∧ key.data? ∧ inodekey(key.ino) ∈ ks;% ⊦ ¬ key ∈ ∅; (s) Used terms: ∅, datakeys(∅, ri)