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Proof step 459 from proof refine-rename-dir-dentry (previous step)

asynced ↔ false, cache_dirs[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], cache_dirs), m6, ∅), cache_dirs[m] = mkdir(m1, md3, # links(m, cache_dirs), m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)], err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3), new_child_inode = (entries0[str0] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (entries0[str0], dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].size) ;mkinode(entries0[str0], files[entries0[str0]].meta, false, files[entries0[str0]].nlink, 0, files[entries0[str0]].size) ), new_dent = mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino), new_parent_inode = (m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), old_dent1 = negdentry(mkdentry(str0, entries0[str0]).name), old_parent_inode = (m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), str = str0, mkdentry(str0, entries0[str0]).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, m ∈ cache_dirs, entries0[str0] ∈ cache_dirs, ino ∈ dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), (entries0[str0] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ str0 ∈ entries0 ∧ str0 ∈ entries0 ∧ str0 ∈ entries0 ∧ str0 ∈ entries0 ∧ str0 ∈ entries0 ;str0 ∈ entries0 ∧ str0 ∈ entries0 ∧ str0 ∈ entries0 ∧ str0 ∈ entries0 ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent1.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)] ( icache-cons(cache_icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(cache_dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(cache_pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m4, m1); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m4, m1); new_child_inode0 := mkinode (entries0[str], md1, true, # links(entries0[str], cache_dirs), cache_dirs[entries0[str]].nsubdirs, cache_dirs[entries0[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m6, m3); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := 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)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = dirs[ino, dirs[ino].meta:= inode.meta] ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0))), entries0[str0] = ROOT_INO, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 460:
cache_dirs[m] = mkdir(m1, md3, # links(m, cache_dirs), m4, entries0), cache_dirs[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], cache_dirs), m6, ∅), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, entries0[str0] ≠ ROOT_INO, 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), m ∈ cache_dirs, str0 ∈ entries0, entries0[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set# (mkinode (m, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]].meta:= md1 ] [m ] .meta, true, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]].meta:= md1 ] [m ] .nlink, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]].meta:= md1 ] [m ] .nsubdirs, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]].meta:= md1 ] [m ] .size), false ; err, cache_icache); icache_set# (( m ∈ cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] ⊃ mkinode (m, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .meta, true, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nlink, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nsubdirs, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), false ; err, cache_icache); str := str0; new_child_inode := (entries0[str0] ∈ cache_dirs ⊃ mkinode (entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [entries0[str0] ] .meta, true, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [entries0[str0] ] .nlink, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [entries0[str0] ] .nsubdirs, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [entries0[str0] ] .size) ;mkinode(entries0[str0], cache_files[entries0[str0]].meta, false, cache_files[entries0[str0]].nlink, 0, cache_files[entries0[str0]].size) ); if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete# (( m ∈ cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] ⊃ mkinode (m, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .meta, true, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nlink, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nsubdirs, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) .ino, mkdentry(str0, entries0[str0]).name ; err, cache_dcache); dcache_set# (( m ∈ cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] ⊃ mkinode (m, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .meta, true, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nlink, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .nsubdirs, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md1, true, # links(entries0[str0], cache_dirs), m6, m3).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) .ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0);cache_dirs[entries0[str0]]).meta:= md1 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0);cache_dirs[entries0[str0]]).meta:= md1 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0);cache_dirs[entries0[str0]]).meta:= md1 ], cache_files) ∧ afs-cons (cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0);cache_dirs[entries0[str0]]).meta:= md1 ], cache_files) ∧ synced (cache_dirs[m, mkdir(m1, md0, # links(m, cache_dirs), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0);cache_dirs[entries0[str0]]).meta:= md1 ], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m4, m1); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m4, m1); new_child_inode0 := mkinode (entries0[str], md1, true, # links(entries0[str], cache_dirs), cache_dirs[entries0[str]].nsubdirs, cache_dirs[entries0[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m6, m3); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; cache_dirs5 := 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)⟩ ( (m ∈ cache_dirs5 ⊃ mkinode (m, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .meta, true, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .nlink, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .nsubdirs, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = old_parent_inode0 ∧ (m ∈ cache_dirs5 ⊃ mkinode (m, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .meta, true, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .nlink, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .nsubdirs, (m = entries0[str0] ⊃ mkdir(m1, md1, # links(entries0[str0], cache_dirs5), m4, entries0) ;mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0) ) .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str0, entries0[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs5[m, mkdir(m1, md0, # links(m, cache_dirs5), m4, entries0)] [entries0[str0], (entries0[str0] = m ∧ entries0[str0] ∈ cache_dirs5 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs5), m4, entries0) ;cache_dirs5[entries0[str0]] ) .meta:= md1 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ negdentry(str).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)