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

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 749 from proof refine-rename-file-dentry (previous step)

# links(m3, cache_dirs) = m6, cache_files[entries1[str0]] = mkfile(m0, md6, # links(entries1[str0], cache_dirs), content3), cache_dirs[m] = mkdir(m2, md7, # links(m, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str0]] = mkfile(m8, md4, # links(entries1[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, # links(entries[str], cache_dirs), content), cache_dirs[m3] = mkdir(m4, md9, m6, m7, entries1), cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), entries1[str0] = entries0[str0], cache_dirs[m3] = mkdir(m4, md8, m6, m7, entries0), 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), str ∈ entries, str0 ∈ entries1, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries1[str0] ∈ cache_files, str0 ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; old_parent_inode := mkinode(m3, md0, true, m6, m7, m4); old_dent := mkdentry(str0, entries1[str0]); new_parent_inode := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); new_dent := mkdentry(str, entries[str]); new_child_inode := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries[str]); old_dent0 := mkdentry(str0, entries1[str0]); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m7, m4); new_child_inode0 := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries1[str0], md2, false, # links(entries1[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(entries1[str0], md2, false, # links(entries1[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))), entries[str] ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 750:
cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), cache_dirs[m3] = mkdir(m4, md8, # links(m3, cache_dirs), m7, 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(m2, md7, # links(m, cache_dirs), m5, entries), cache_files[entries0[str0]] = mkfile(m0, md6, # links(entries0[str0], cache_dirs), content3), 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), entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries0, str ∈ entries, ¬ entries[str] ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; old_parent_inode := mkinode(m3, md0, true, # links(m3, cache_dirs), m7, m4); old_dent := mkdentry(str0, entries0[str0]); new_parent_inode := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); new_dent := mkdentry(str, entries[str]); new_child_inode := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m7, m4); new_child_inode0 := mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries0[str0], md2, false, # links(entries0[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(entries0[str0], md2, false, # links(entries0[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)