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Proof step 4 from proof refine-renam (previous step)

p_inode1.ino = m, p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, p_inode.nlink = cache_dirs[p_inode.ino].nlink, p_inode0.nsubdirs = cache_dirs[p_inode0.ino].nsubdirs, p_inode.nsubdirs = cache_dirs[p_inode.ino].nsubdirs, p_inode0.size = cache_dirs[p_inode0.ino].size, p_inode.size = cache_dirs[p_inode.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m = cache_dirs[p_inode.ino].entries[str], new_child_inode = p_inode2, new_dent = old_dent1, new_parent_inode = p_inode0, old_child_inode = p_inode1, old_dent = old_dent0, old_dent0 = mkdentry(str, m), old_parent_inode = p_inode, old_dent0.dentry?, p_inode0.directory, 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_inode0.ino ∈ cache_dirs, str ∈ cache_dirs[p_inode.ino].entries, p_inode.ino ∈ cache_dirs, p_inode0.ino = p_inode.ino → p_inode0.meta = p_inode.meta, cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ p_inode1.nlink = cache_dirs[m].nlink ∧ p_inode1.size = cache_dirs[m].size ∧ p_inode1.nsubdirs = cache_dirs[m].nsubdirs ∧ p_inode1.directory ∨ m ∈ cache_files ∧ p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ p_inode1.nsubdirs = 0 ∧ ¬ p_inode1.directory, m ∈ cache_dirs ∨ m ∈ cache_files, links(p_inode.ino, cache_dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, (links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO) ∧ ¬ old_dent1.name ∈ cache_dirs[p_inode0.ino].entries ∧ old_dent1.negdentry? ∨ (links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO) ∧ (old_dent1.ino ∈ cache_dirs ∨ old_dent1.ino ∈ cache_files) ∧ old_dent1.name ∈ cache_dirs[p_inode0.ino].entries ∧ old_dent1.ino = cache_dirs[p_inode0.ino].entries[old_dent1.name] ∧ old_dent1.dentry? ∧ ( p_inode2.ino ∈ cache_dirs ∧ p_inode2.nlink = cache_dirs[p_inode2.ino].nlink ∧ p_inode2.size = cache_dirs[p_inode2.ino].size ∧ p_inode2.nsubdirs = cache_dirs[p_inode2.ino].nsubdirs ∧ p_inode2.directory ∨ p_inode2.ino ∈ cache_files ∧ p_inode2.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode2.ino].nlink ∧ p_inode2.nsubdirs = 0 ∧ ¬ p_inode2.directory) ∧ p_inode2.ino = old_dent1.ino ∧ (old_dent1.ino ∈ cache_files ↔ m ∈ cache_files) ∧ (old_dent1.ino ∈ cache_dirs → old_dent1.ino ≠ ROOT_INO ∧ cache_dirs[old_dent1.ino].entries = ∅) ⊦ ⟪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#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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