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Proof step 1 from proof keys-inodekey-in (conclusion)

⊦ inodekey(n) ∈ ns.keys ↔ n ∈ ns

User applied rule induction

And obtained the following new goals

Proof step 2:
∀ ns0, n. # ns0 < # ns → true → (inodekey(n) ∈ ns0.keys ↔ n ∈ ns0) ⊦ inodekey(n) ∈ ns.keys ↔ n ∈ ns

Rule argument

indvar: # ns wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # ns