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Proof step 29 from proof refine-rename-dir-negdentry (previous step)

# links(m3, cache_dirs) = m9, # links(entries0[str], cache_dirs) = m1, # links(m, cache_dirs) = m12, asynced1 ↔ cache_asynced, cache_dirs[entries0[str]] = mkdir(m5, md2, # links(entries0[str], cache_dirs), m11, entries), cache_dirs[m] = mkdir(m4, md5, # links(m, cache_dirs), m6, entries2), cache_dirs[m3] = mkdir(m0, md3, # links(m3, cache_dirs), m7, entries0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dcache = cache_dcache, dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m6, m4), old_child_inode = mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m11, m5), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m3, md0, true, # links(m3, cache_dirs), m7, m0), 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), str ∈ entries0, entries0[str] ∈ cache_dirs, m3 ∈ cache_dirs, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [if pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) then let asynced0 = new_dent.dentry? in {afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1); if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if asynced0 then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, dcache)}} else abort] ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(cache_pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, cache_pcache) ∧ (cache_sync → synced(files, icache, cache_pcache)) → ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m12, m6, m4); old_parent_inode0 := mkinode(m3, md0, true, m9, m7, m0); old_child_inode0 := mkinode(entries0[str], md1, true, m1, m11, 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) ⊕ icache ∧ (afs_asynced ↔ asynced1))), str0 ∈ entries2

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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