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Proof step 52 from proof abs-nlinks-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
dirs[m] = mkdir(m0, md, m1, m2, entries), abs(tree, ino0)(dirs), str ∈ entries, m ∈ dirs, ino0 ∈ dirs, entries[str] ∈ files, ∀ 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: size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)