[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 140 from proof refine-rename-file-negdentry (previous step)

# links (entries[str], cache_dirs [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m3, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ]) = # links(entries[str], cache_dirs), (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs), m5, entries -- str)) = mkdir(m, md, m12, m13, entries0), (m3 = m8 ⊃ mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str);mkdir(m7, md7, # links(m3, cache_dirs), m11, entries2)) = mkdir(m0, md6, m4, m6, entries1), cache_files[entries[str]] = mkfile(m2, md3, # links(entries[str], cache_dirs), content0), cache_dirs[m3] = mkdir(m7, md7, # links(m3, cache_dirs), m11, entries2), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m9, md2, # links(entries[str], cache_dirs), content), cache_dirs[m8] = mkdir(m1 + 1, md4, # links(m8, cache_dirs), m5, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode1 = new_child_inode0, new_dent0 = negdentry(str0), new_parent_inode0 = mkinode(m3, md5, true, # links(m3, cache_dirs), m11, m7), old_child_inode0 = mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10), old_dent0 = mkdentry(str, entries[str]), old_parent_inode0 = mkinode(m8, md0, true, # links(m8, cache_dirs), m5, m1 + 1), afs-cons (cache_dirs [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m3, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], cache_files), 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), m8 ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, str ∈ entries, ¬ entries[str] ∈ cache_dirs, ¬ str0 ∈ entries2, m3 = m8 → md5 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m8, cache_dirs) ≠ ∅ ∨ m8 = 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)⟩ ( (m8 ∈ cache_dirs0 ⊃ mkinode (m8, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .meta, true, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .nlink, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .nsubdirs, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .size) ;mkinode(m8, cache_files[m8].meta, false, cache_files[m8].nlink, 0, cache_files[m8].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode(entries[str], md1, false, # links(entries[str], cache_dirs0), 0, m10) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, entries[str]) = new_dent0 ∧ ESUCCESS = err0 ∧ cache_dirs = cache_dirs0 [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ;mkdir(m1, md4, # links(m8, cache_dirs0), m5, entries -- str) ) .meta:= md0 ] [m3, (m3 = m8 ∧ m8 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;(m3 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);cache_dirs0[m3]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m8, mkientry(false, mkinode(m8, md, true, m12, m13, m))] [(m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) .ino, mkientry (false, (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])) .nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) )) ] ∧ (afs_asynced ↔ asynced0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 141:
# links (entries[str], cache_dirs [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m3, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ]) = # links(entries[str], cache_dirs), (m3 = m8 ⊃ mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str);mkdir(m7, md7, # links(m3, cache_dirs), m11, entries2)) = mkdir(m0, md6, m4, m6, entries1), (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs), m5, entries -- str)) = mkdir(m, md, m12, m13, entries0), (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = mkinode(m14, md8, boolvar, m15, m16, m17), cache_dirs[m8] = mkdir(m1 + 1, md4, # links(m8, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m9, md2, # links(entries[str], cache_dirs), content), cache_dirs[m3] = mkdir(m7, md7, # links(m3, cache_dirs), m11, entries2), cache_files[entries[str]] = mkfile(m2, md3, # links(entries[str], cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode1 = new_child_inode0, new_dent0 = negdentry(str0), new_parent_inode0 = mkinode(m3, md5, true, # links(m3, cache_dirs), m11, m7), old_child_inode0 = mkinode(entries[str], md1, false, # links(entries[str], cache_dirs), 0, m10), old_dent0 = mkdentry(str, entries[str]), old_parent_inode0 = mkinode(m8, md0, true, # links(m8, cache_dirs), m5, m1 + 1), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons (cache_dirs [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md4, # links(m8, cache_dirs), m5, entries -- str)).meta:= md0 ] [m3, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], 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, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m8 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m8 → md5 = md0, links(m8, cache_dirs) ≠ ∅ ∨ m8 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = 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)⟩ ( (m8 ∈ cache_dirs0 ⊃ mkinode (m8, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .meta, true, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .nlink, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .nsubdirs, (m8 = m3 ⊃ mkdir(m0 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m1, md0, # links(m8, cache_dirs0), m5, entries -- str)) .size) ;mkinode(m8, cache_files[m8].meta, false, cache_files[m8].nlink, 0, cache_files[m8].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode(entries[str], md1, false, # links(entries[str], cache_dirs0), 0, m10) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, entries[str]) = new_dent0 ∧ ESUCCESS = err0 ∧ cache_dirs = cache_dirs0 [m8, (m8 = m3 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ;mkdir(m1, md4, # links(m8, cache_dirs0), m5, entries -- str) ) .meta:= md0 ] [m3, (m3 = m8 ∧ m8 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;(m3 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]);cache_dirs0[m3]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m8, mkientry(false, mkinode(m8, md, true, m12, m13, m))] [m14, mkientry (false, (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])) .nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]])).size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) )) ] ∧ (afs_asynced ↔ asynced0)), entries[str] ∈ cache_dirs, str0 ∈ entries2

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir (m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .nlink, (m3 = m8 ⊃ mkdir (m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .nsubdirs, (m3 = m8 ⊃ mkdir (m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .size) ;mkinode (m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ), m14, md8, boolvar, m15, m16, m17]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (m3 ∈ cache_dirs0 ⊃ mkinode (m3, md5, true, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .nlink, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .nsubdirs, (m3 = m8 ⊃ mkdir(m0 + 1, md0, m4, m6, entries1[str0, entries[str]]) ;mkdir(m0 + 1, md6, m4, m6, entries1[str0, entries[str]]) ) .size) ;mkinode (m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ), m14, md8, boolvar, m15, m16, m17