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Proof step 29 from proof refine-rmdir (previous step)

# links(entries[str], cache_dirs) = m8, # links(m, cache_dirs) = m5, cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m4, entries), cache_dirs[entries[str]] = mkdir(m3, md2, # links(entries[str], cache_dirs), m6, ∅), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m6, m3), dent = mkdentry(str, entries[str]), dirs = cache_dirs, err = err0, files = cache_files, p_inode = mkinode(m, md, true, # links(m, cache_dirs), m4, m0), 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), pre-rmdir(p_inode, c_inode, dent, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), entries[str] ∈ cache_dirs, str ∈ entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [ let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?; if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, cache_icache); icache_set#(p_inode, asynced; err, cache_icache); dcache_delete#(p_inode.ino, dent.name; err, cache_dcache)}] ( icache-cons(cache_icache, dirs, files) ∧ dcache-cons(cache_dcache, dirs, files) ∧ pcache-cons(cache_pcache, dirs, files) ∧ synced(dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) ∧ afs-cons(dirs, files) → ⟨dent0 := mkdentry(str, entries[str]); p_inode0 := mkinode(m, md, true, m5, m4, m0); p_inode1 := mkinode(entries[str], md0, true, m8, m6, m3); afs_rmdir#(; p_inode0, p_inode1, dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = dent0 ∧ err = err0)), entries[str] = ROOT_INO

Heuristic conditional right split applied rule or split right

And obtained the following new goals

Rule argument

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