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Proof step 9 from proof crash-neutral-mkdir (previous step)

dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), 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)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 10:
dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨if pre-mkdir(p_inode, dent, md, dirs, files) then { {choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs); afs_inode_sync#(p_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(dent.ino, dirs, files)} or fail#(; ; err); asynced := ?} else abort⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), str ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: mkdir: ⊦ ;