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Proof step 9 from proof inv-rmdir (previous step)

dirs[dirs[m].entries[str]] = mkdir(m0, md1, m1, m2, entries), c_inode = mkinode(dirs[m].entries[str], md, true, m1, m2, m0), dent = mkdentry(str, dirs[m].entries[str]), entries = ∅, p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries, dirs[m].entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), dirs[m].entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
dirs[dirs[m].entries[str]] = mkdir(m0, md1, # links(dirs[m].entries[str], dirs), m2, ∅), c_inode = mkinode(dirs[m].entries[str], md, true, # links(dirs[m].entries[str], dirs), m2, m0), dent = mkdentry(str, dirs[m].entries[str]), p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), dirs[m].entries[str] ≠ ROOT_INO, afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries, dirs[m].entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(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