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Proof step 6 from proof crash-neutral-link (previous step)

c_inode.ino = dirs[ino].entries[str], p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nlink = files[c_inode.ino].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = dirs[p_inode.ino].size, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), new_dent = negdentry(str0), p_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), ino ∈ dirs, str ∈ dirs[ino].entries, p_inode.ino ∈ dirs, c_inode.ino ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(c_inode.ino, dirs) ≠ ∅ ∨ c_inode.ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), c_inode.directory, str0 ∈ dirs[p_inode.ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
c_inode.ino = dirs[ino].entries[str], c_inode.nlink = files[c_inode.ino].nlink, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), new_dent = negdentry(str0), p_inode.directory, afs-cons(dirs, files), c_inode.ino ∈ files, p_inode.ino ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, ¬ c_inode.directory, ¬ str0 ∈ dirs[p_inode.ino].entries, links(c_inode.ino, dirs) ≠ ∅ ∨ c_inode.ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ negdentry(str).negdentry?; (s)