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Proof step 11 from proof inv-rmdir (previous step)

dirs[entries[str]] = mkdir(m0, md1, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(m1, md2, m3, m4, entries), c_inode = mkinode(entries[str], md, true, # links(entries[str], dirs), m2, m0), dent = mkdentry(str, entries[str]), p_inode = mkinode(m, md0, true, m3, m4, m1), 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)⟫ afs-cons(dirs, files), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
dirs[entries[str]] = mkdir(m0, md1, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries), c_inode = mkinode(entries[str], md, true, # links(entries[str], dirs), m2, m0), dent = mkdentry(str, entries[str]), p_inode = mkinode(m, md0, true, # links(m, dirs), m4, m1), entries[str] ≠ ROOT_INO, 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)⟫ 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