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Proof step 10 from proof new-inode-exists (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ ks0. # ks0 < # ks → true → (∃ ino. ∀ ino0. inodekey(ino0) ∈ ks0 → ino0 < ino) ⊦ # ks = 0, ks = ∅, ∃ ino. ∀ ino0. inodekey(ino0) ∈ ks → ino0 < ino

Rule argument

Additional information

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