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Proof step 42 from proof refine-rmdir (previous step)

# links(m, cache_dirs) = m3, # links(entries[str], cache_dirs) = cache_dirs[entries[str]].nlink, cache_dirs[entries[str]].entries = ∅, cache_dirs[m] = mkdir(m0 + 1, md3, m3, m1 + 1, entries), cache_dirs[entries[str]] = mkdir(cache_dirs[entries[str]].size, md2, cache_dirs[entries[str]].nlink, cache_dirs[entries[str]].nsubdirs, ∅), entries[str] = entries0[str], cache_dirs[m] = mkdir(m2, md1, m3, m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, ((cache_dirs[m].entries:= (entries0 -- str)).size:= m0).nsubdirs:= m1], m2 = m0 + 1, m4 = m1 + 1, 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), entries[str] ∈ cache_dirs, str ∈ entries, m ∈ cache_dirs, str ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, cache_files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, m3, m1 + 1, m0 + 1); dirs, cache_files); afs_inode_sync# (mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), cache_dirs[entries[str]].nsubdirs, cache_dirs[entries[str]].size) ; dirs, cache_files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ); c_inode := getinode(entries[str], dirs, cache_files); err := ESUCCESS; 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, cache_files) ∧ dcache-cons(cache_dcache, dirs, cache_files) ∧ pcache-cons(cache_pcache, dirs, cache_files) ∧ synced(dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(dirs, cache_files) → ⟨dent0 := mkdentry(str, entries[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); p_inode1 := mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), cache_dirs[entries[str]].nsubdirs, cache_dirs[entries[str]].size); afs_rmdir#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (cache_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 simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nsubdirs:= m4 = mkdir(m, md, m0, m4, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base