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

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Proof step 102 from proof inv-rename-dir-negdentry (previous step)

(m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries0), err = ESUCCESS, afs-cons(dirs0, files), afs-cons (dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])).meta:= md1 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str] ∈ dirs0, m0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, ¬ str0 ∈ entries3, m0 = m → md1 = md0, asynced2 → synced(files, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); icache_set# (( m0 ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- 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# (( m ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache); dcache_set# (( m0 ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- 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, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ dcache-cons (dcache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ pcache-cons (pcache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ synced (dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[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 103:
(m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), ( m ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) = mkinode(m9, md4, boolvar, m11, m12, m13), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries0), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), err = ESUCCESS, afs-cons (dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[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), m ∈ dirs0, str ∈ entries0, m0 ∈ dirs0, entries0[str] ∈ dirs0, asynced2 → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); icache_set# (( m0 ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- 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#(m9, mkdentry(str, entries0[str]).name; err, dcache); dcache_set# (( m0 ∈ dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m0, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m0 ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)).meta:= md0 ] [m0, dirs0[m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])] [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- 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, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ dcache-cons (dcache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ pcache-cons (pcache, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], files) ∧ synced (dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ) .meta:= md1 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), str0 ∈ entries3

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] → [( m ∈ dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode (m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), m9, md4, boolvar, m11, m12, m13]

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: ( m ∈ dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] ⊃ mkinode (m, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .meta, true, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nlink, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .nsubdirs, dirs0 [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0, dirs0 [m0, mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ] [m, (m = m0 ⊃ mkdir (m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]) ;mkdir (m1, md, # links(m, dirs0), m2, entries0 -- str) ) .meta:= md0 ] [m0 ] .meta:= md1 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), m9, md4, boolvar, m11, m12, m13