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Proof step 8 from proof subdirs-delete-orphans (previous step)

dirs[ino] = mkdir(m, md, m0, m1, entries), entries[str] ∈ dirs, str ∈ entries, ino ∈ dirs, entries[str] ∈ orphans(dirs, files) ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅, ino ∈ orphans(dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [files, dirs, entries[str]] flags: <all paths>

Additional information

Used simplifier rules: links-nonempty: ⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; Used terms: files, dirs, entries[str]