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Proof step 45 from proof abs-nlinks-h (previous step)

abs(tree, ino0)(dirs), ino1 ∈ files, ino0 ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ links(ino1, dirs) = ∅, ⌜ino1⌝ ∈ tree.fids

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
abs(tree, ino0)(dirs), ino1 ∈ files, ino0 ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # links(ino1, dirs) = 0, links(ino1, dirs) = ∅, ⌜ino1⌝ ∈ tree.fids

Rule argument

Additional information

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