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Proof step 58 from proof abs-nlinks-h (previous step)

ispath(p, ino0, dirs, files) ↔ p ∈ tree, dirs[m] = mkdir(m0, md, m1, m2, entries), abs(tree, ino0)(dirs), ispath(p, ino0, m, dirs, files), entries[str] ∈ files, ino0 ∈ dirs, m ∈ dirs, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
dirs[m] = mkdir(m0, md, m1, m2, entries), abs(tree, ino0)(dirs), ispath(p, ino0, m, dirs, files), str ∈ entries, m ∈ dirs, ino0 ∈ dirs, entries[str] ∈ files, p ∈ tree, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

Rule argument

Additional information

Used simplifier rules: ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)