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Proof step 545 from proof refine-rename-file-dentry (previous step)

cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, cache_dirs1 = cache_dirs, cache_dirs2 = cache_dirs, cache_dirs3 = cache_dirs, cache_dirs4 = cache_dirs, dcache = cache_dcache -- dentrykey(m2, str0), dent = mkdentry(str0, mkdentry(str0, entries[str0]).ino), err = ESUCCESS, key = dentrykey(p_ino, name), name = mkdentry(str0, mkdentry(str0, entries[str0]).ino).name, new_child_inode0 = mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m), new_dent0 = mkdentry(str0, entries[str0]), new_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), old_child_inode0 = mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13), old_dent0 = mkdentry(str0, entries[str0]), old_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), p_ino = m2, mkdentry(str0, entries[str0]).dentry?, 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]), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons (dcache[key, dent], 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(cache_dcache, cache_dirs, cache_files), 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]), icache-cons(cache_icache, cache_dirs, cache_files), 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]), pcache-cons(cache_pcache, cache_dirs, cache_files), 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), synced(cache_dirs, cache_icache, cache_pcache), m2 ∈ cache_dirs, entries[str0] ∈ cache_files, str0 ∈ entries, 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨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)), entries[str0] ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 546:
cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode0 = mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m), new_dent0 = mkdentry(str0, entries[str0]), new_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), old_child_inode0 = mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13), old_dent0 = mkdentry(str0, entries[str0]), old_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons (cache_dcache[dentrykey(m2, str0), mkdentry(str0, entries[str0])], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), 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], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), 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), synced(cache_dirs, cache_icache, cache_pcache), m2 ∈ cache_dirs, entries[str0] ∈ cache_files, str0 ∈ entries, ¬ entries[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)], 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), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨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_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), 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_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), 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_dirs0 ⊃ mkinode (entries[str0], (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).meta, true, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nlink, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nsubdirs, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[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 ∧ ESUCCESS = err0 ∧ cache_dirs = cache_dirs0[m2, mkdir(m6, md5, # links(m2, cache_dirs0), 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_dirs0), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs0), 0, m)) ] ∧ (afs_asynced ↔ asynced0))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ (dcache -- key)[key, dent] = dcache[key, dent]; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)