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Proof step 3 from proof afs-cons-rename-dir-negdentry (previous step)

old_dent.ino = dirs[old_parent_inode.ino].entries[old_dent.name], old_child_inode.ino = old_dent.ino, old_child_inode.nlink = dirs[old_dent.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, old_child_inode.nsubdirs = dirs[old_dent.ino].nsubdirs, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, old_child_inode.size = dirs[old_dent.ino].size, new_parent_inode.size = dirs[new_parent_inode.ino].size, old_parent_inode.size = dirs[old_parent_inode.ino].size, old_dent.dentry?, old_child_inode.directory, new_parent_inode.directory, old_parent_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), old_dent.name ∈ dirs[old_parent_inode.ino].entries, old_dent.ino ∈ dirs, old_parent_inode.ino ∈ dirs, new_parent_inode.ino ∈ dirs, ¬ new_dent.name ∈ 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
old_child_inode.ino = m, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_child_inode.nlink = dirs[m].nlink, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_child_inode.nsubdirs = dirs[m].nsubdirs, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_parent_inode.size = dirs[new_parent_inode.ino].size, old_child_inode.size = dirs[m].size, m = dirs[old_parent_inode.ino].entries[str], old_dent = mkdentry(str, m), old_dent.dentry?, old_parent_inode.directory, new_parent_inode.directory, old_child_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), new_parent_inode.ino ∈ dirs, old_parent_inode.ino ∈ dirs, m ∈ 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), new_dent.name ∈ dirs[new_parent_inode.ino].entries

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent, str, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent, str, m