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Proof step 52 from proof refine-rename-dir-dentry (previous step)

# links(entries1[str], cache_dirs) = m16, # links(m, cache_dirs) = m9, # links(entries[str0], cache_dirs) = m1, # links(m3, cache_dirs) = m12, asynced1 ↔ new_dent.dentry?, asynced0 ↔ old_ino = new_ino ∧ new_dent = old_dent, cache_dirs[entries[str0]] = mkdir(m5, md3, # links(entries[str0], cache_dirs), m14, entries2), cache_dirs[entries1[str]] = mkdir(m2, md6, # links(entries1[str], cache_dirs), m13, ∅), cache_dirs[m] = mkdir(m4, md7, # links(m, cache_dirs), m7, entries1), cache_dirs[m3] = mkdir(m6, md4, # links(m3, cache_dirs), m11, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = dirs0[old_ino, dirs0[old_ino].entries:= (dirs0[old_ino].entries -- old_dent.name)], dirs0 = cache_dirs, err = err0, files = cache_files, new_child_inode = mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs), m13, m2), new_dent = mkdentry(str, entries1[str]), new_ino = new_parent_inode.ino, new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m7, m4), old_child_inode = mkinode(entries[str0], md2, true, # links(entries[str0], cache_dirs), m14, m5), old_dent = mkdentry(str0, entries[str0]), old_ino = old_parent_inode.ino, old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m11, m6), 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), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs0, files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries1, str0 ∈ entries, entries1[str] ∈ cache_dirs, entries[str0] ∈ cache_dirs, m ∈ cache_dirs, m3 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [if ¬ asynced0 then {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[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, 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#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS; asynced := ?; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries1[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, dirs, files) ∧ dcache-cons(cache_dcache, dirs, files) ∧ pcache-cons(cache_pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries1[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m, md, true, m9, m7, m4); old_parent_inode0 := mkinode(m3, md0, true, m12, m11, m6); new_child_inode0 := mkinode(entries1[str], md1, true, m16, m13, m2); old_child_inode0 := mkinode(entries[str0], md2, true, m1, m14, m5); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))), entries1[str] = ROOT_INO

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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