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Proof step 4 from proof new-inode-exists (previous step)

inodekey(ino) ∈ ks, ∀ ino0. inodekey(ino0) ∈ ks → ino0 < ino ⊦ ∃ ino. ¬ inodekey(ino) ∈ ks

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
inodekey(ino) ∈ ks, ∀ ino0. inodekey(ino0) ∈ ks → ino0 < ino ⊦ # ks = 0, ks = ∅, ∃ ino. ¬ inodekey(ino) ∈ ks

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ks ≠ ∅ → # ks ≠ 0; (forward) from specification set-basic[node-index]%ne-01: ⊦ key ∈ ks → ks ≠ ∅; (forward) from specification set-basic[node-index]