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Proof step 4 from proof keys-inodekeys (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 5:
∀ ns0. # ns0 < # ns → true → ns0.keys.inodes? ⊦ ns = ∅, ns.keys.inodes?

Rule argument

fma: ns = ∅

Additional information

Used simplifier rules: keys-base: ⊦ ∅.keys = ∅;% ⊦ ∅.inodes?; (s) Used formulas: ns = ∅