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

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Proof step 112 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), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (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), err = ESUCCESS, icache = icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))], 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(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m8 ∈ dirs0, m ∈ dirs0, entries[str] ∈ files, str ∈ entries, ¬ str0 ∈ entries2, ¬ entries[str] ∈ dirs0, m = m8 → md5 = md0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ ⟪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 ] ⊃ 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 unfold applied rule call right

And obtained the following new goals

Proof step 113:
# 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), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), asynced ↔ false, 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, icache = icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))], inode = ( 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 ] ⊃ 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) ), 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(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m8 → md5 = md0, (m8 = m ⊃ str ∈ entries;true), ( 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 ] ⊃ ((m8 = m ⊃ str ∈ entries;true) ∧ str ∈ entries ∧ (m8 = m ⊃ str ∈ entries;true)) ∧ ((m8 = m ⊃ str ∈ entries;true) ∧ str ∈ entries ∧ (m8 = m ⊃ str ∈ entries;true)) ∧ ((m8 = m ⊃ str ∈ entries;true) ∧ str ∈ entries ∧ (m8 = m ⊃ str ∈ entries;true)) ∧ (m8 = m ⊃ str ∈ entries;true) ∧ str ∈ entries ∧ (m8 = m ⊃ str ∈ entries;true) ;true ), links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); 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))), str0 ∈ entries2, entries[str] ∈ dirs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: icache_set#(INODE, DIRTY; ERR, ICACHE) {ICACHE[INODE.ino] := mkientry(DIRTY, INODE)};% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)