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Proof step 819 from proof refine-rename-file-dentry (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, # links(m3, cache_dirs) = cache_dirs[m3].nlink, asynced0 ↔ old_ino = new_ino ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0]), asynced1 ↔ true, entries0[str0] = cache_dirs[m3].entries[str0], entries[str] = cache_dirs[m].entries[str], cache_files[entries0[str0]] = mkfile(m0, md6, # links(entries0[str0], cache_dirs), content3), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, # links(entries0[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, # links(entries[str], cache_dirs), content), cache_dirs[m3] = mkdir(cache_dirs[m3].size, md8, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries0), cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), asynced0, dirs = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str0, entries0[str0]).name)], new_ino = m, old_dent = mkdentry(str0, entries0[str0]), 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), str0 ∈ cache_dirs[m3].entries, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, str ∈ entries, str0 ∈ entries0, ⌊err0⌋ , old_ino = new_ino → str ∈ entries ∧ str0 ∈ entries0, 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 ⊦ ⟨dirs[new_ino].entries[mkdentry(str, entries[str]).name] := old_dent.ino; new_dent := mkdentry(str, entries[str]); 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 := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); 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 ∧ mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10) = new_child_inode ∧ mkdentry(str0, entries0[str0]) = old_dent ∧ mkdentry(str, entries[str]) = new_dent ∧ err0 = err ∧ dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced2)), ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), entries[str] ∈ cache_dirs

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 820:
# links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, asynced1 ↔ true, asynced0 ↔ old_ino = new_ino ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0]), cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), cache_dirs[m3] = mkdir(cache_dirs[m3].size, md8, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, # links(entries[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, # links(entries0[str0], cache_dirs), content0), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_files[entries0[str0]] = mkfile(m0, md6, # links(entries0[str0], cache_dirs), content3), entries[str] = cache_dirs[m].entries[str], entries0[str0] = cache_dirs[m3].entries[str0], asynced0, dirs = dirs0[new_ino, dirs0[new_ino].entries:= dirs0[new_ino].entries[mkdentry(str, entries[str]).name, old_dent.ino]], dirs0 = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str0, entries0[str0]).name)], new_ino = m, old_dent = mkdentry(str0, entries0[str0]), 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), str0 ∈ entries0, entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ cache_dirs[m].entries, str0 ∈ cache_dirs[m3].entries, str ∈ entries, ⌊err0⌋ , m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), old_ino = new_ino → str ∈ entries ∧ str0 ∈ entries0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨new_dent := mkdentry(str, entries[str]); 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 := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); 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 ∧ mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10) = new_child_inode ∧ mkdentry(str0, entries0[str0]) = old_dent ∧ mkdentry(str, entries[str]) = new_dent ∧ err0 = err ∧ dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced2)), ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), entries[str] ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m) = mkdentry(str0, m0) ↔ str = str0 ∧ m = m0; (ws)% ⊦ mkdentry(str, m).dentry?; (s)