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Proof step 2 from proof datalkeys-drop-orphans (previous step)

ro.inodes? ⊦ datakeys(key, n, ri ⊖ ro) = datakeys(key, n, ri), key ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 4:
ro.inodes? ⊦ key ∈ ro, ∀ key0. key0 ∈ datakeys(key, n, ri ⊖ ro) ↔ key0 ∈ datakeys(key, n, ri)

Rule argument

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

Additional information

Used terms: datakeys(key, n, ri), datakeys(key, n, ri ⊖ ro)