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Proof step 11 from proof crash-neutral-rmdir (previous step)

# links(entries[str], dirs) = c_inode.nlink, c_inode.ino = entries[str], dirs[entries[str]] = mkdir(c_inode.size, md1, c_inode.nlink, c_inode.nsubdirs, ∅), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dent = mkdentry(str, entries[str]), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), entries[str] ≠ ROOT_INO, c_inode.directory, afs-cons(dirs, files), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; 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 12:
# links(entries[str], dirs) = c_inode.nlink, c_inode.ino = entries[str], dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[entries[str]] = mkdir(c_inode.size, md1, c_inode.nlink, c_inode.nsubdirs, ∅), dent = mkdentry(str, entries[str]), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), c_inode.directory, afs-cons(dirs, files), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨if pre-rmdir(p_inode, c_inode, dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), entries[str] = ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: rmdir: ⊦ ;