[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 21 from proof refine-rename-file-dentry (previous step)

# links(m, cache_dirs) = m16, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m3].entries[str0]] = mkfile(m8, md4, m15, content0), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m4 = cache_dirs[m3].nlink, m5 = cache_dirs[m3].nsubdirs, m6 = cache_dirs[m3].size, m9 = cache_dirs[m3].entries[str0], new_child_inode = mkinode(entries[str], md1, false, m14, 0, m10), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m17, m11), old_child_inode = mkinode(cache_dirs[m3].entries[str0], md2, false, m15, 0, m13), old_dent = mkdentry(str0, cache_dirs[m3].entries[str0]), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), 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), cache_dirs[m3].entries[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ cache_dirs[m3].entries, str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, entries[str]); old_dent0 := mkdentry(str0, m9); new_parent_inode0 := mkinode(m, md, true, m16, m17, m11); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); new_child_inode0 := mkinode(entries[str], md1, false, m14, 0, m10); old_child_inode0 := mkinode(m9, md2, false, m15, 0, m13); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# links(m, cache_dirs) = m16, cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), cache_dirs[m3] = mkdir(m0, md6, m1, m2, entries0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m4 = m1, m5 = m2, m6 = m0, m9 = entries0[str0], new_child_inode = mkinode(entries[str], md1, false, m14, 0, m10), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, cache_dirs), m17, m11), old_child_inode = mkinode(entries0[str0], md2, false, m15, 0, m13), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m3, md0, true, m1, m2, m0), 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), str ∈ entries, str0 ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨new_dent0 := mkdentry(str, entries[str]); old_dent0 := mkdentry(str0, m9); new_parent_inode0 := mkinode(m, md, true, m16, m17, m11); old_parent_inode0 := mkinode(m3, md0, true, m4, m5, m6); new_child_inode0 := mkinode(entries[str], md1, false, m14, 0, m10); old_child_inode0 := mkinode(m9, md2, false, m15, 0, m13); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced))

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [cache_dirs[m3], m0, md6, m1, m2, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: cache_dirs[m3], m0, md6, m1, m2, entries0