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Proof step 365 from proof refine-rename-file-negdentry (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, # links(m3, cache_dirs) = cache_dirs[m3].nlink, asynced0 ↔ false, asynced1 ↔ false, entries0[str] = cache_dirs[m3].entries[str], cache_dirs[m3] = mkdir(cache_dirs[m3].size, md5, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, # links(entries0[str], cache_dirs), content), cache_dirs[m] = mkdir(cache_dirs[m].size, md4, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_files[entries0[str]] = mkfile(m1, md3, # links(entries0[str], cache_dirs), content0), dirs = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], dirs0 = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str, entries0[str]).name)], new_ino = m, old_dent = mkdentry(str, entries0[str]), old_ino = m3, 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 ∈ cache_dirs[m3].entries, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, dirs0[old_ino].size ≥ 1, ⌊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 ⊦ ⟨if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1; dirs[new_ino].entries[str0] := old_dent.ino; new_dent := negdentry(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(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, entries0[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 ∈ entries, str0 ∈ cache_dirs[m].entries

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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