[Imprint][Data Privacy Statement][E-Mail]

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Proof step 505 from proof refine-rename-file-dentry (previous step)

asynced ↔ false, ((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[m] = mkdir(m0, md3, # links(m, cache_dirs), m3, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], entries0 = entries, err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10), new_child_inode = (entries[str0] ∈ dirs ⊃ mkinode(entries[str0], dirs[entries[str0]].meta, true, dirs[entries[str0]].nlink, dirs[entries[str0]].nsubdirs, dirs[entries[str0]].size) ;mkinode (entries[str0], files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][entries[str0]].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][entries[str0]].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][entries[str0]].size) ), new_dent = mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino), new_parent_inode = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), old_dent1 = negdentry(mkdentry(str0, entries[str0]).name), old_parent_inode = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), str = str0, mkdentry(str0, entries[str0]).dentry?, 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), entries[str0] ∈ cache_files, m ∈ cache_dirs, ino ∈ files, str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), (entries[str0] ∈ dirs ⊃ str0 ∈ entries ∧ str0 ∈ entries ∧ str0 ∈ entries ∧ str0 ∈ entries ∧ str0 ∈ entries ;str0 ∈ entries ∧ str0 ∈ entries ∧ str0 ∈ entries ∧ str0 ∈ entries ), 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, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ dcache-cons (cache_dcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ pcache-cons (cache_pcache, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ afs-cons(dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) ∧ synced(dirs, cache_icache, cache_pcache) ∧ ( cache_sync → synced (files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta], cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); new_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13); cache_dirs0 := 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(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = dirs ∧ afs_files = (files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0))), entries[str0] ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 506:
cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m3, 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, err = ESUCCESS, 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), m ∈ cache_dirs, str0 ∈ entries, entries[str0] ∈ cache_files, ¬ entries[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set#(mkinode(m, md0, true, # links(m, cache_dirs), m3, m0), false; err, cache_icache); icache_set# ((m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m3, m0) ;mkinode (m, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .size) ), false ; err, cache_icache); str := str0; new_child_inode := (entries[str0] ∈ cache_dirs ⊃ mkinode (entries[str0], cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].meta, true, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].nlink, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].nsubdirs, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].size) ;mkinode (entries[str0], cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .size) ); entries0 := entries; if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete# ((m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m3, m0) ;mkinode (m, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .size) ) .ino, mkdentry(str0, entries[str0]).name ; err, cache_dcache); dcache_set# ((m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m3, m0) ;mkinode (m, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ dcache-cons (cache_dcache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ pcache-cons (cache_pcache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ afs-cons (cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ synced(cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1], cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); new_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); 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_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_dirs3 ⊃ mkinode(m, md0, true, # links(m, cache_dirs3), m3, m0) ;mkinode (m, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).meta, false, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).nlink, 0, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).size) ) = old_parent_inode0 ∧ (m ∈ cache_dirs3 ⊃ mkinode(m, md0, true, # links(m, cache_dirs3), m3, m0) ;mkinode (m, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).meta, false, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).nlink, 0, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).size) ) = new_parent_inode0 ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str0, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3[m, mkdir(m0, md0, # links(m, cache_dirs3), m3, entries)] ∧ afs_files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1] ⊕ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)