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Proof step 417 from proof refine-rename-dir-negdentry (previous step)

# links(entries1[str], cache_dirs) = cache_dirs[entries1[str]].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, # links(m3, cache_dirs) = cache_dirs[m3].nlink, asynced0 ↔ false, asynced1 ↔ false, entries1[str] = cache_dirs[m3].entries[str], cache_dirs[m3] = mkdir(cache_dirs[m3].size, md4, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries1), cache_dirs[m] = mkdir(cache_dirs[m].size, md3, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries0), cache_dirs[entries1[str]] = mkdir(cache_dirs[entries1[str]].size, md5, cache_dirs[entries1[str]].nlink, cache_dirs[entries1[str]].nsubdirs, entries2), dirs = dirs1[old_ino, dirs1[old_ino].nsubdirs:= (dirs1[old_ino].nsubdirs - 1)] [new_ino, dirs1[old_ino, dirs1[old_ino].nsubdirs:= (dirs1[old_ino].nsubdirs - 1)][new_ino] .entries:= dirs1[old_ino, dirs1[old_ino].nsubdirs:= (dirs1[old_ino].nsubdirs - 1)][new_ino].entries[str0, old_dent.ino] ], dirs0 = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str, entries1[str]).name)], dirs1 = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], new_dent = negdentry(str0), new_ino = m, old_dent = mkdentry(str, entries1[str]), old_ino = m3, old_dent.dentry?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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 ∈ cache_dirs[m3].entries, m ∈ cache_dirs, m3 ∈ cache_dirs, entries1[str] ∈ cache_dirs, str ∈ entries1, old_dent.ino ∈ dirs1, dirs1[old_ino].nsubdirs ≥ 1, dirs0[old_ino].size ≥ 1, ⌊err0⌋ , m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨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(m3, md0, true, # links(m3, cache_dirs), cache_dirs[m3].nsubdirs, cache_dirs[m3].size); dirs, afs_files); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size); dirs, afs_files); new_child_inode := new_child_inode0; 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 := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, afs_files[m3].meta, false, afs_files[m3].nlink, 0, afs_files[m3].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].size) ); err := ESUCCESS; asynced := ?⟩ ( mkinode(m3, md0, true, # links(m3, cache_dirs), cache_dirs[m3].nsubdirs, cache_dirs[m3].size) = old_parent_inode ∧ mkinode(m, md, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size) = new_parent_inode ∧ new_child_inode0 = new_child_inode ∧ mkdentry(str, entries1[str]) = old_dent ∧ negdentry(str0) = new_dent ∧ err0 = err ∧ dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced2)), ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), str0 ∈ entries0, str0 ∈ cache_dirs[m].entries

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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