[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 2 from proof refine-rename-dir-negdentry (previous step)

old_child_inode.ino = old_dent.ino, afs_asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, new_child_inode = new_child_inode0, new_dent = new_dent0, new_parent_inode = new_parent_inode0, old_child_inode = old_child_inode0, old_dent = old_dent0, old_parent_inode = old_parent_inode0, afs-cons(afs_dirs, afs_files), 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), valid-dentry(old_parent_inode.ino, old_dent, afs_dirs, afs_files), valid-dir-inode(old_child_inode, afs_dirs, afs_files), valid-dir-inode(new_parent_inode, afs_dirs, afs_files), valid-dir-inode(old_parent_inode, afs_dirs, afs_files), valid-negdentry(new_parent_inode.ino, new_dent, afs_dirs, afs_files), new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪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)⟫ ⟨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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
old_dent0.ino = cache_dirs[old_parent_inode0.ino].entries[old_dent0.name], old_child_inode0.ino = old_dent0.ino, old_child_inode0.nlink = cache_dirs[old_dent0.ino].nlink, new_parent_inode0.nlink = cache_dirs[new_parent_inode0.ino].nlink, old_parent_inode0.nlink = cache_dirs[old_parent_inode0.ino].nlink, old_child_inode0.nsubdirs = cache_dirs[old_dent0.ino].nsubdirs, new_parent_inode0.nsubdirs = cache_dirs[new_parent_inode0.ino].nsubdirs, old_parent_inode0.nsubdirs = cache_dirs[old_parent_inode0.ino].nsubdirs, old_child_inode0.size = cache_dirs[old_dent0.ino].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, new_child_inode = new_child_inode0, new_dent = new_dent0, new_parent_inode = new_parent_inode0, old_child_inode = old_child_inode0, old_dent = old_dent0, old_parent_inode = old_parent_inode0, old_dent0.dentry?, old_child_inode0.directory, new_parent_inode0.directory, old_parent_inode0.directory, new_dent0.negdentry?, 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), old_dent0.name ∈ cache_dirs[old_parent_inode0.ino].entries, old_dent0.ino ∈ cache_dirs, old_parent_inode0.ino ∈ cache_dirs, new_parent_inode0.ino ∈ cache_dirs, ¬ new_dent0.name ∈ cache_dirs[new_parent_inode0.ino].entries, 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(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)⟫ ⟨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))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)