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Proof step 5 from proof refine-rename-dir-dentry (previous step)

cache_dirs[new_child_inode0.ino].entries = ∅, old_child_inode0.ino = old_dent0.ino, new_child_inode0.ino = cache_dirs[new_parent_inode0.ino].entries[str], old_dent0.ino = cache_dirs[old_parent_inode0.ino].entries[old_dent0.name], old_parent_inode0.nlink = cache_dirs[old_parent_inode0.ino].nlink, new_parent_inode0.nlink = cache_dirs[new_parent_inode0.ino].nlink, old_child_inode0.nlink = cache_dirs[old_dent0.ino].nlink, new_child_inode0.nlink = cache_dirs[new_child_inode0.ino].nlink, old_parent_inode0.nsubdirs = cache_dirs[old_parent_inode0.ino].nsubdirs, new_parent_inode0.nsubdirs = cache_dirs[new_parent_inode0.ino].nsubdirs, old_child_inode0.nsubdirs = cache_dirs[old_dent0.ino].nsubdirs, new_child_inode0.nsubdirs = cache_dirs[new_child_inode0.ino].nsubdirs, old_parent_inode0.size = cache_dirs[old_parent_inode0.ino].size, new_parent_inode0.size = cache_dirs[new_parent_inode0.ino].size, old_child_inode0.size = cache_dirs[old_dent0.ino].size, new_child_inode0.size = cache_dirs[new_child_inode0.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = new_child_inode0, new_dent = mkdentry(str, new_child_inode0.ino), new_parent_inode = new_parent_inode0, old_child_inode = old_child_inode0, old_dent = old_dent0, old_parent_inode = old_parent_inode0, new_child_inode0.ino ≠ ROOT_INO, old_dent0.dentry?, old_parent_inode0.directory, new_parent_inode0.directory, old_child_inode0.directory, new_child_inode0.directory, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), old_parent_inode0.ino ∈ cache_dirs, new_parent_inode0.ino ∈ cache_dirs, old_dent0.ino ∈ cache_dirs, new_child_inode0.ino ∈ cache_dirs, old_dent0.name ∈ cache_dirs[old_parent_inode0.ino].entries, str ∈ cache_dirs[new_parent_inode0.ino].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), new_parent_inode0.ino = old_parent_inode0.ino → new_parent_inode0.meta = old_parent_inode0.meta, links(old_parent_inode0.ino, cache_dirs) ≠ ∅ ∨ old_parent_inode0.ino = ROOT_INO, links(new_parent_inode0.ino, cache_dirs) ≠ ∅ ∨ new_parent_inode0.ino = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, new_child_inode0.ino); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
cache_dirs[new_child_inode0.ino].entries = ∅, new_child_inode0.ino = cache_dirs[new_parent_inode0.ino].entries[str], old_child_inode0.ino = m, new_child_inode0.nlink = cache_dirs[new_child_inode0.ino].nlink, old_child_inode0.nlink = cache_dirs[m].nlink, new_parent_inode0.nlink = cache_dirs[new_parent_inode0.ino].nlink, old_parent_inode0.nlink = cache_dirs[old_parent_inode0.ino].nlink, new_child_inode0.nsubdirs = cache_dirs[new_child_inode0.ino].nsubdirs, old_child_inode0.nsubdirs = cache_dirs[m].nsubdirs, new_parent_inode0.nsubdirs = cache_dirs[new_parent_inode0.ino].nsubdirs, old_parent_inode0.nsubdirs = cache_dirs[old_parent_inode0.ino].nsubdirs, new_child_inode0.size = cache_dirs[new_child_inode0.ino].size, old_child_inode0.size = cache_dirs[m].size, new_parent_inode0.size = cache_dirs[new_parent_inode0.ino].size, old_parent_inode0.size = cache_dirs[old_parent_inode0.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m = cache_dirs[old_parent_inode0.ino].entries[str0], new_child_inode = new_child_inode0, new_dent = mkdentry(str, new_child_inode0.ino), new_parent_inode = new_parent_inode0, old_child_inode = old_child_inode0, old_dent = old_dent0, old_dent0 = mkdentry(str0, m), old_parent_inode = old_parent_inode0, old_dent0.dentry?, new_child_inode0.directory, old_child_inode0.directory, new_parent_inode0.directory, old_parent_inode0.directory, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ cache_dirs[new_parent_inode0.ino].entries, str0 ∈ cache_dirs[old_parent_inode0.ino].entries, new_child_inode0.ino ∈ cache_dirs, m ∈ cache_dirs, new_parent_inode0.ino ∈ cache_dirs, old_parent_inode0.ino ∈ cache_dirs, new_parent_inode0.ino = old_parent_inode0.ino → new_parent_inode0.meta = old_parent_inode0.meta, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(new_parent_inode0.ino, cache_dirs) ≠ ∅ ∨ new_parent_inode0.ino = ROOT_INO, links(old_parent_inode0.ino, cache_dirs) ≠ ∅ ∨ old_parent_inode0.ino = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, new_child_inode0.ino); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)), new_child_inode0.ino = ROOT_INO

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent0, str0, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent0, str0, m