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Proof step 10 from proof crash-neutral-rmdir (previous step)

c_inode.ino = entries[str], c_inode.nlink = m3, c_inode.nsubdirs = m4, c_inode.size = m1, dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[entries[str]] = mkdir(m1, md1, m3, m4, entries0), dent = mkdentry(str, entries[str]), dirs0 = dirs \ orphans(dirs, files), entries0 = ∅, files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), c_inode.directory, afs-cons(dirs, files), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# links(entries[str], dirs) = c_inode.nlink, c_inode.ino = entries[str], dirs[entries[str]] = mkdir(c_inode.size, md1, c_inode.nlink, c_inode.nsubdirs, ∅), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dent = mkdentry(str, entries[str]), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), entries[str] ≠ ROOT_INO, c_inode.directory, afs-cons(dirs, files), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base