Proof step 404 from proof refine-rename-dir-negdentry (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

• Proof step 405:

  cache_dirs[entries1[str]] = mkdir(m6, md5, # links(entries1[str], cache_dirs), m9, entries2), cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m2, entries0), cache_dirs[m3] = mkdir(m1, md4, # links(m3, cache_dirs), m5, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err1, files = afs_files, new_child_inode = new_child_inode0, new_child_inode1 = new_child_inode0, new_dent = new_dent0, new_dent0 = negdentry(str0), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), new_parent_inode1 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs), m9, m6), old_dent = old_dent0, old_dent0 = mkdentry(str, entries1[str]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), old_parent_inode1 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), 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, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries1, entries1[str] ∈ cache_dirs, m3 ∈ cache_dirs, m ∈ cache_dirs, ⌊err0⌋ , 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 ⊦ ⟨ let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; 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} or fail#(; ; err); asynced := ?⟩ ( old_parent_inode1 = old_parent_inode ∧ new_parent_inode1 = new_parent_inode ∧ mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs0), m9, m6) = old_child_inode ∧ new_child_inode1 = new_child_inode ∧ mkdentry(str, entries1[str]) = old_dent ∧ negdentry(str0) = new_dent ∧ err0 = err ∧ dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0)), str0 ∈ entries0

• Proof step 486:

  cache_dirs[entries1[str]] = mkdir(m6, md5, # links(entries1[str], cache_dirs), m9, entries2), cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m2, entries0), cache_dirs[m3] = mkdir(m1, md4, # links(m3, cache_dirs), m5, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err1, files = afs_files, new_child_inode = new_child_inode0, new_child_inode1 = new_child_inode0, new_dent = new_dent0, new_dent0 = negdentry(str0), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), new_parent_inode1 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs), m9, m6), old_dent = old_dent0, old_dent0 = mkdentry(str, entries1[str]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), old_parent_inode1 = mkinode(m3, md0, true, # links(m3, cache_dirs), m5, m1), 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 ∈ entries1, entries1[str] ∈ cache_dirs, m3 ∈ cache_dirs, m ∈ cache_dirs, ⌊err0⌋ , 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 ⊦ ⟨abort⟩ ( old_parent_inode1 = old_parent_inode ∧ new_parent_inode1 = new_parent_inode ∧ mkinode(entries1[str], md1, true, # links(entries1[str], cache_dirs0), m9, m6) = old_child_inode ∧ new_child_inode1 = new_child_inode ∧ mkdentry(str, entries1[str]) = old_dent ∧ negdentry(str0) = new_dent ∧ err0 = err ∧ dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0)), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), str0 ∈ entries0

Rule argument

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