[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 107 from proof inv-rename-file-negdentry (previous step)

# links (entries[str], dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ]) = # links(entries[str], dirs0), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), err = ESUCCESS, afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, ¬ entries[str] ∈ dirs0, ¬ str0 ∈ entries2, asynced2 → synced(files, icache, pcache), m = m8 → md5 = md0, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m8, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ] .meta, true, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ] .nlink, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ] .nsubdirs, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ] .size), false ; err, icache); icache_set# (( m ∈ dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] ⊃ mkinode (m, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .meta, true, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .nlink, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .nsubdirs, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); skip; dcache_delete#(m8, mkdentry(str, entries[str]).name; err, dcache); dcache_set#(m, mkdentry(str0, mkdentry(str, entries[str]).ino).name, mkdentry(str0, mkdentry(str, entries[str]).ino); err, dcache)⟫ ( icache-cons (icache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ dcache-cons (dcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ pcache-cons (pcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ synced (dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 108:
# links (entries[str], dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ]) = # links(entries[str], dirs0), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m ] .meta:= md5 ] [m8 ] = mkdir(m0, md1, m10, m11, entries0), err = ESUCCESS, afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m8 ∈ dirs0, m ∈ dirs0, entries[str] ∈ files, str ∈ entries, m = m8 → md5 = md0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ ⟪icache_set#(mkinode(m8, md1, true, m10, m11, m0), false; err, icache); icache_set# (( m ∈ dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] ⊃ mkinode (m, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .meta, true, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .nlink, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .nsubdirs, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, dirs0[m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); skip; dcache_delete#(m8, mkdentry(str, entries[str]).name; err, dcache); dcache_set#(m, mkdentry(str0, mkdentry(str, entries[str]).ino).name, mkdentry(str0, mkdentry(str, entries[str]).ino); err, dcache)⟫ ( icache-cons (icache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ dcache-cons (dcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ pcache-cons (pcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], files) ∧ synced (dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md5 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), entries[str] ∈ dirs0, str0 ∈ entries2

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] → [dirs0 [m8, (m8 = m ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m, dirs0 [m, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ], m0, md1, m10, m11, 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: dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m, dirs0 [m, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m ] .meta:= md5 ] [m8 ], m0, md1, m10, m11, entries0