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Proof step 528 from proof refine-rename-file-dentry (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), dcache = cache_dcache -- dentrykey(m2, str0), err = ESUCCESS, 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 ∈ entries, entries[str0] ∈ cache_files, m2 ∈ cache_dirs, ¬ entries[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ [dcache_set#(m2, mkdentry(str0, mkdentry(str0, entries[str0]).ino).name, mkdentry(str0, mkdentry(str0, entries[str0]).ino); err, dcache)] ( icache-cons (cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0]) ∧ dcache-cons (dcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0]) ∧ pcache-cons (cache_pcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0]) ∧ afs-cons (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0]) ∧ synced (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache) ∧ ( cache_sync → synced (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache)) → ⟨new_dent0 := mkdentry(str0, entries[str0]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6); old_parent_inode0 := mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6); new_child_inode0 := mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m); old_child_inode0 := mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs4 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m2 ∈ cache_dirs3 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs3), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = old_parent_inode0 ∧ (m2 ∈ cache_dirs3 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs3), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = new_parent_inode0 ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ (entries[str0] ∈ cache_dirs1 ⊃ mkinode (entries[str0], (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs1), m5, entries);cache_dirs1[entries[str0]]).meta, true, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs1), m5, entries);cache_dirs1[entries[str0]]).nlink, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs1), m5, entries);cache_dirs1[entries[str0]]).nsubdirs, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs1), m5, entries);cache_dirs1[entries[str0]]).size) ;mkinode(entries[str0], md0, false, cache_files[entries[str0]].nlink, 0, m) ) = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str0, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3[m2, mkdir(m6, md5, # links(m2, cache_dirs3), m5, entries)] ∧ afs_files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0] ⊕ cache_pcache) ⊕ cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs4), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs2), 0, m)) ] ∧ (afs_asynced ↔ asynced0)))

Heuristic unfold applied rule call right

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: dcache_set#(P_INO, NAME, DENT; ERR, DCACHE) {let KEY = dentrykey(P_INO, NAME) in DCACHE[KEY] := DENT};