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Proof step 555 from proof refine-rename-file-dentry (previous step)

# links(m2, cache_dirs) = cache_dirs[m2].nlink, asynced1 ↔ true, asynced0 ↔ old_ino = new_ino ∧ mkdentry(str0, entries[str0]) = mkdentry(str0, entries[str0]), cache_dirs[m2] = mkdir(cache_dirs[m2].size, md3, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), entries[str0] = cache_dirs[m2].entries[str0], ¬ asynced0, dirs = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str0, entries[str0]).name)], new_ino = m2, old_dent = mkdentry(str0, entries[str0]), old_ino = m2, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons (cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons (cache_dcache[dentrykey(m2, str0), mkdentry(str0, entries[str0])], cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[m2, mkientry(false, mkinode(m2, md5, true, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, cache_dirs[m2].size))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, entries)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, cache_dirs[m2].size))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str0 ∈ entries, m2 ∈ cache_dirs, entries[str0] ∈ cache_files, str0 ∈ cache_dirs[m2].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, cache_dirs[m2].nlink, cache_dirs[m2].nsubdirs, cache_dirs[m2].size))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), old_ino = new_ino → str0 ∈ entries ∧ str0 ∈ entries, links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1; dirs[new_ino].entries[mkdentry(str0, entries[str0]).name] := old_dent.ino; new_dent := mkdentry(str0, entries[str0]); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, afs_files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m2, md5, true, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, cache_dirs[m2].size); dirs, afs_files); afs_inode_sync#(mkinode(m2, md5, true, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, cache_dirs[m2].size); dirs, afs_files); new_child_inode := mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, afs_files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, afs_files[new_child_inode.ino].meta, false, afs_files[new_child_inode.ino].nlink, 0, afs_files[new_child_inode.ino].size) )}; old_parent_inode := (m2 ∈ dirs ⊃ mkinode(m2, dirs[m2].meta, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size) ;mkinode(m2, afs_files[m2].meta, false, afs_files[m2].nlink, 0, afs_files[m2].size) ); new_parent_inode := (m2 ∈ dirs ⊃ mkinode(m2, dirs[m2].meta, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size) ;mkinode(m2, afs_files[m2].meta, false, afs_files[m2].nlink, 0, afs_files[m2].size) ); err := ESUCCESS; asynced := ?⟩ ( mkinode(m2, md5, true, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, cache_dirs[m2].size) = old_parent_inode ∧ mkinode(m2, md5, true, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, cache_dirs[m2].size) = new_parent_inode ∧ mkinode(entries[str0], md0, false, cache_files[entries[str0]].nlink, 0, m) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs[m2, mkdir(cache_dirs[m2].size, md5, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, entries)] ∧ afs_files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0] ⊕ cache_pcache) ⊕ cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), cache_dirs[m2].nsubdirs, cache_dirs[m2].size))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ] ∧ (asynced ↔ asynced2)), entries[str0] ∈ cache_dirs

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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