Proof step 33 from proof refine-unlink (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 34:

  p_inode1.ino = cache_dirs[m].entries[str], p_inode1.nlink = cache_files[p_inode1.ino].nlink, p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode1.ino].nlink, p_inode1.nsubdirs = 0, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, dent = mkdentry(str, p_inode1.ino), err = err0, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m2 = cache_dirs[m].size, p_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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), m ∈ cache_dirs, str ∈ cache_dirs[m].entries, p_inode1.ino ∈ cache_files, ¬ p_inode1.directory, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [cache_unlink#(; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨dent0 := mkdentry(str, p_inode1.ino); p_inode0 := mkinode(m, md, true, m0, m1, m2); afs_unlink#(; p_inode0, p_inode1, dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = dent0 ∧ err = err0))

Rule argument

Additional information