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Proof step 6 from proof refine-unlink (previous step)

c_inode.ino = m, c_inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, p_inode.nlink = cache_dirs[p_inode.ino].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = cache_dirs[p_inode.ino].nsubdirs, p_inode.size = cache_dirs[p_inode.ino].size, dent = mkdentry(str, m), m = cache_dirs[p_inode.ino].entries[str], dent.dentry?, p_inode.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), p_inode.ino ∈ cache_dirs, str ∈ cache_dirs[p_inode.ino].entries, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode.ino, cache_dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ c_inode.nlink = cache_files[m].nlink, c_inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
c_inode.ino = cache_dirs[p_inode.ino].entries[str], p_inode.nlink = cache_dirs[p_inode.ino].nlink, c_inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[c_inode.ino].nlink, p_inode.nsubdirs = cache_dirs[p_inode.ino].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = cache_dirs[p_inode.ino].size, p_inode.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), c_inode.ino ∈ cache_files, str ∈ cache_dirs[p_inode.ino].entries, p_inode.ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode.ino, cache_dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ c_inode.nlink = cache_files[c_inode.ino].nlink, c_inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)