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Proof step 8 from proof keys-inodekeys (previous step)

∀ ns0. # ns0 < # ns → true → ns0.keys.inodes? ⊦ # ns = 0, ns.keys.inodes?, ∀ n. n ∈ ns ↔ n ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n ∈ ns, ∀ ns0. # ns0 < # ns → true → ns0.keys.inodes? ⊦ # ns = 0, ns.keys.inodes?

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n ∈ ∅; (s)