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Proof step 5 from proof afs-cons-rename-dentry (previous step)

old_dent.ino = dirs[old_parent_inode.ino].entries[old_dent.name], new_child_inode.ino = dirs[new_parent_inode.ino].entries[str], old_child_inode.ino = old_dent.ino, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, new_parent_inode.size = dirs[new_parent_inode.ino].size, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_child_inode.ino ∈ files ↔ old_dent.ino ∈ files, new_dent = mkdentry(str, new_child_inode.ino), old_dent.dentry?, new_parent_inode.directory, old_parent_inode.directory, afs-cons(dirs, files), str ∈ dirs[new_parent_inode.ino].entries, old_dent.name ∈ dirs[old_parent_inode.ino].entries, new_parent_inode.ino ∈ dirs, old_parent_inode.ino ∈ dirs, new_child_inode.ino ∈ dirs → new_child_inode.ino ≠ ROOT_INO ∧ dirs[new_child_inode.ino].entries = ∅, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, new_child_inode.ino ∈ dirs ∨ old_dent.ino ∈ files, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO, old_dent.ino ∈ dirs ∨ old_dent.ino ∈ files, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, new_child_inode.ino ∈ dirs ∧ new_child_inode.nlink = dirs[new_child_inode.ino].nlink ∧ new_child_inode.size = dirs[new_child_inode.ino].size ∧ new_child_inode.nsubdirs = dirs[new_child_inode.ino].nsubdirs ∧ new_child_inode.directory ∨ old_dent.ino ∈ files ∧ new_child_inode.nlink = files[new_child_inode.ino].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory, old_dent.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_dent.ino].nlink ∧ old_child_inode.size = dirs[old_dent.ino].size ∧ old_child_inode.nsubdirs = dirs[old_dent.ino].nsubdirs ∧ old_child_inode.directory ∨ old_dent.ino ∈ files ∧ old_child_inode.nlink = files[old_dent.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory ⊦ ⟪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 6:
old_child_inode.ino = m, new_child_inode.ino = dirs[new_parent_inode.ino].entries[str], old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, 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_child_inode.ino ∈ files ↔ m ∈ files, m = dirs[old_parent_inode.ino].entries[str0], new_dent = mkdentry(str, new_child_inode.ino), old_dent = mkdentry(str0, m), old_dent.dentry?, old_parent_inode.directory, new_parent_inode.directory, afs-cons(dirs, files), old_parent_inode.ino ∈ dirs, new_parent_inode.ino ∈ dirs, str0 ∈ dirs[old_parent_inode.ino].entries, str ∈ dirs[new_parent_inode.ino].entries, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, new_child_inode.ino ∈ dirs → new_child_inode.ino ≠ ROOT_INO ∧ dirs[new_child_inode.ino].entries = ∅, m ∈ dirs ∧ old_child_inode.nlink = dirs[m].nlink ∧ old_child_inode.size = dirs[m].size ∧ old_child_inode.nsubdirs = dirs[m].nsubdirs ∧ old_child_inode.directory ∨ m ∈ files ∧ old_child_inode.nlink = files[m].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory, new_child_inode.ino ∈ dirs ∧ new_child_inode.nlink = dirs[new_child_inode.ino].nlink ∧ new_child_inode.size = dirs[new_child_inode.ino].size ∧ new_child_inode.nsubdirs = dirs[new_child_inode.ino].nsubdirs ∧ new_child_inode.directory ∨ m ∈ files ∧ new_child_inode.nlink = files[new_child_inode.ino].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, m ∈ dirs ∨ m ∈ files, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO, new_child_inode.ino ∈ dirs ∨ m ∈ files ⊦ ⟪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

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent, str0, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent, str0, m