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Proof step 7 from proof inv-mkdir (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), m ∈ dirs, ¬ str ∈ entries, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_mkdir#(md; 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