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Proof step 5 from proof keys-inodekeys (previous step)

∀ ns0. # ns0 < # ns → true → ns0.keys.inodes? ⊦ ns = ∅, ns.keys.inodes?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ ns0. # ns0 < # ns → true → ns0.keys.inodes? ⊦ # ns = 0, ns = ∅, ns.keys.inodes?

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ns ≠ 0 → ns ≠ ∅; (forward) from specification set-basic[nat-set]%size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]