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Proof step 16 from proof abs-delorphans (previous step)

links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p, ROOT_INO, ino, dirs, files), p ∈ tree, ino ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅, p = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, p ∈ tree, ROOT_INO ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅, p = ε

Rule argument

Additional information

Used simplifier rules: path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base