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

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Proof step 105 from proof inv-rename-file-negdentry (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 106:
# links (entries[str], dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ]) = # links(entries[str], dirs0), (m0 = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m0, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), ( m0 ∈ dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ) = mkinode(m, md5, boolvar, m10, m11, m12), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m0] = mkdir(m7, md4, # links(m0, dirs0), m9, entries2), err = ESUCCESS, afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ], 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, m0 ∈ dirs0, m8 ∈ dirs0, asynced2 → synced(files, icache, pcache), m0 = m8 → md1 = md0, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m8, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m8 ] .meta, true, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m8 ] .nlink, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m8 ] .nsubdirs, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)) .meta:= md0 ] [m0 ] .meta:= md1 ] [m8 ] .size), false ; err, icache); icache_set# (( m0 ∈ dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])] [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ], files) ∧ dcache-cons (dcache, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ], files) ∧ pcache-cons (pcache, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ], files) ∧ synced (dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m0, (m0 = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])).meta:= md1 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), entries[str] ∈ dirs0, 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] → [( m0 ∈ dirs0 [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .size) ;mkinode (m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), m, md5, boolvar, m10, m11, m12]

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: ( m0 ∈ dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m8, (m8 = m0 ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ] [m8, (m8 = m0 ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .size) ;mkinode (m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), m, md5, boolvar, m10, m11, m12