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Proof step 9 from proof new-inode-exists (previous step)

∀ ks0. # ks0 < # ks → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino) ⊦ ∃ ino. ∀ ino0. inodekey(ino0) ∈ ks → ino0 < ino

User applied rule cut formula

And obtained the following new goals

Proof step 10:
∀ ks0. # ks0 < # ks → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino) ⊦ ks = ∅, ∃ ino. ∀ ino0. inodekey(ino0) ∈ ks → ino0 < ino

Rule argument

fma: ks = ∅

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ∅; (s) Used formulas: ks = ∅