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Proof step 828 from proof refine-rename-file-dentry (previous step)

# 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], afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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_dent = mkdentry(str, entries[str]), 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), str ∈ entries, 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, ⌊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 ⊦ ⟨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]) = negdentry(old_dent.name) ∧ mkdentry(str, entries[str]) = mkdentry(new_dent.name, old_dent.ino) ∧ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 829:
# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md8, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m12, md3, # links(entries0[str0], cache_dirs), content), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_files[entries0[str0]] = mkfile(m1, md5, # links(entries0[str0], cache_dirs), content2), entries[str0] = entries0[str0], entries0[str0] = cache_dirs[m].entries[str0], 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 ∈ entries, str0 ∈ entries0, entries0[str0] ∈ cache_files, m ∈ cache_dirs, str0 ∈ cache_dirs[m].entries, ⌊err0⌋ , ¬ entries0[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m) = mkdentry(str0, m0) ↔ str = str0 ∧ m = m0; (ws)% ⊦ (ad.entries:= entries).entries = entries; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)