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Proof step 1 from proof keys-in (conclusion)

⊦ key ∈ ns.keys ↔ (∃ n. key = inodekey(n) ∧ n ∈ ns)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
key ∈ ns.keys ⊦ # ns.keys = 0, ns.keys = ∅, ∃ n. key = inodekey(n) ∧ n ∈ ns

Rule argument

Additional information

Used simplifier rules: keys-inodekey-in: ⊦ inodekey(n) ∈ ns.keys ↔ n ∈ ns;%size-zero-01: ⊦ ks ≠ ∅ → # ks ≠ 0; (forward) from specification set-basic[node-index]%ne-01: ⊦ key ∈ ks → ks ≠ ∅; (forward) from specification set-basic[node-index]