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Proof step 6 from proof afs-cons-rename-file-negdentry (previous step)

old_child_inode.ino = dirs[old_parent_inode.ino].entries[str], old_child_inode.nlink = files[old_child_inode.ino].nlink, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_child_inode.nsubdirs = 0, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_parent_inode.size = dirs[new_parent_inode.ino].size, new_dent = negdentry(str0), old_dent = mkdentry(str, old_child_inode.ino), old_parent_inode.directory, new_parent_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), new_parent_inode.ino ∈ dirs, old_child_inode.ino ∈ files, old_parent_inode.ino ∈ dirs, str ∈ dirs[old_parent_inode.ino].entries, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), old_child_inode.directory, str0 ∈ dirs[new_parent_inode.ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
old_child_inode.ino = dirs[old_parent_inode.ino].entries[str], new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, old_child_inode.nlink = files[old_child_inode.ino].nlink, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, old_child_inode.nsubdirs = 0, new_parent_inode.size = dirs[new_parent_inode.ino].size, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_dent = negdentry(str0), old_dent = mkdentry(str, old_child_inode.ino), new_parent_inode.directory, old_parent_inode.directory, afs-cons(dirs, files), str ∈ dirs[old_parent_inode.ino].entries, old_parent_inode.ino ∈ dirs, old_child_inode.ino ∈ files, new_parent_inode.ino ∈ dirs, ¬ old_child_inode.directory, ¬ str0 ∈ dirs[new_parent_inode.ino].entries, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Rule argument

Additional information

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