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Proof step 16 from proof crash-neutral-mkdir (previous step)

# links(m, dirs) = m1, dirs[m] = mkdir(m0, md1, m1, m2, entries), dirs[m] = mkdir(m0, md0, m1, m2, entries0), dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md2, true, m1, m2, m0), afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in afs_mkdir_ino#(m, md, ino; dent, err, dirs); afs_inode_sync#(p_inode; dirs, files); p_inode := (p_inode.ino ∈ dirs ⊃ mkinode(p_inode.ino, dirs[p_inode.ino].meta, true, dirs[p_inode.ino].nlink, dirs[p_inode.ino].nsubdirs, dirs[p_inode.ino].size) ;mkinode(p_inode.ino, files[p_inode.ino].meta, false, files[p_inode.ino].nlink, 0, files[p_inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), str ∈ entries0, str ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries0), dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md2, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), m ∈ dirs, ¬ str ∈ entries0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in afs_mkdir_ino#(m, md, ino; dent, err, dirs); afs_inode_sync#(p_inode; dirs, files); p_inode := (p_inode.ino ∈ dirs ⊃ mkinode(p_inode.ino, dirs[p_inode.ino].meta, true, dirs[p_inode.ino].nlink, dirs[p_inode.ino].nsubdirs, dirs[p_inode.ino].size) ;mkinode(p_inode.ino, files[p_inode.ino].meta, false, files[p_inode.ino].nlink, 0, files[p_inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)